%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP330-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:52 PM UTC 2026
% Result : Unsatisfiable 42.79s 7.87s
% Output : CNFRefutation 49.97s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c11 = inverse(sk_c3)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c6)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c11 = inverse(sk_c3)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c10 = inverse(sk_c4)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c8 = inverse(sk_c5)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( inverse(sk_c7) = sk_c6
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = inverse(sk_c6)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c11 = inverse(sk_c3)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f56]) ).
fof(f60,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c11 = inverse(sk_c3)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c8 = inverse(sk_c5)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f76]) ).
fof(f80,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f81,plain,
( sk_c8 = inverse(sk_c6)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f80]) ).
fof(f84,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c11 = inverse(sk_c3)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c10 = inverse(sk_c4)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f94]) ).
fof(f96,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f97,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f96]) ).
fof(f98,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
fof(f99,plain,
( inverse(sk_c7) = sk_c6
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f98]) ).
fof(f100,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
fof(f101,plain,
( sk_c8 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f100]) ).
fof(f102,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
fof(f103,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f102]) ).
fof(f104,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| sk_c11 != multiply(X5,sk_c10)
| inverse(X4) != X5
| sk_c11 != multiply(X4,X5)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11)
| sk_c9 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c11 != multiply(X0,sk_c10)
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(reorient_equations,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( multiply(X6,inverse(X4)) != X7
| inverse(X4) != inverse(X7)
| inverse(X6) != X7
| sk_c11 != multiply(inverse(X4),sk_c10)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11)
| sk_c9 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c11 != multiply(X0,sk_c10)
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(equality_resolution,[],[f105]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11)
| sk_c9 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c11 != multiply(X0,sk_c10)
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(equality_resolution,[],[f106]) ).
tcf(c_103,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_104,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c3,sk_c11) = sk_c10 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c9 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c11 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c8,sk_c10) = sk_c11 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c10,sk_c11) = sk_c9 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c11 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c1,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c11 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c11 )
| ( multiply(sk_c5,sk_c8) = sk_c11 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_122,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c11 )
| ( multiply(sk_c8,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_125,negated_conjecture,
( ( multiply(sk_c1,sk_c10) = sk_c11 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_128,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_130,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = sk_c11 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_132,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c8,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_136,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_138,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_140,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = sk_c11 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_141,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_142,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( multiply(sk_c8,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_144,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_146,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_147,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_148,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_149,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_150,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c11 ) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_151,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_152,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c8,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_153,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_154,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_155,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_156,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c10 )
| ( inverse(X4) != sk_c11 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c10 )
| ( multiply(sk_c10,sk_c11) != sk_c9 )
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(X5,sk_c10) != sk_c9 )
| ( multiply(X4,sk_c11) != sk_c10 )
| ( multiply(X3,sk_c9) != sk_c10 )
| ( multiply(X2,sk_c10) != sk_c11 )
| ( multiply(inverse(X1),sk_c10) != sk_c11 )
| ( multiply(X1,inverse(X1)) != sk_c11 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_158,plain,
multiply(inverse(sk_c10),sk_c10) = identity,
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_621,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_156]) ).
tcf(c_622,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_156]) ).
tcf(c_623,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_156]) ).
tcf(c_624,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c11 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_156]) ).
tcf(c_625,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_14
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(inverse(X1),sk_c10) != sk_c11 )
| ( multiply(X1,inverse(X1)) != sk_c11 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_156]) ).
tcf(c_626,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c10,sk_c11) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_156]) ).
tcf(c_627,definition,
iPr_def_15 = multiply(sk_c10,sk_c11),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_628,definition,
iPr_def_16 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_629,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_630,definition,
iPr_def_18 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_631,definition,
iPr_def_19 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_632,definition,
iPr_def_20 = multiply(sk_c8,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_633,definition,
iPr_def_21 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_634,definition,
iPr_def_22 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_635,definition,
iPr_def_23 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_636,definition,
iPr_def_24 = multiply(sk_c4,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_637,definition,
iPr_def_25 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_638,definition,
iPr_def_26 = multiply(sk_c3,sk_c11),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_639,definition,
iPr_def_27 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_640,definition,
iPr_def_28 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).
tcf(c_641,definition,
iPr_def_29 = multiply(sk_c1,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_29])],[]) ).
tcf(c_642,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_626,c_627]) ).
tcf(c_643,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_14
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(inverse(X1),sk_c10) != sk_c11 )
| ( multiply(X1,inverse(X1)) != sk_c11 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(demodulation,[status(thm)],[c_625]) ).
tcf(c_644,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c11 ) ),
inference(demodulation,[status(thm)],[c_624]) ).
tcf(c_645,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_623]) ).
tcf(c_646,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_622]) ).
tcf(c_647,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_621]) ).
tcf(c_648,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_155,c_629,c_628]) ).
tcf(c_649,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_154,c_630]) ).
tcf(c_650,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_153,c_631]) ).
tcf(c_651,negated_conjecture,
( ( iPr_def_20 = sk_c11 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_152,c_632]) ).
tcf(c_652,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_151,c_633]) ).
tcf(c_653,negated_conjecture,
( ( iPr_def_22 = sk_c11 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_150,c_634]) ).
tcf(c_654,negated_conjecture,
( ( iPr_def_23 = sk_c10 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_149,c_635]) ).
tcf(c_655,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_148,c_636]) ).
tcf(c_656,negated_conjecture,
( ( iPr_def_25 = sk_c11 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_147,c_637]) ).
tcf(c_657,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_146,c_638]) ).
tcf(c_659,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_144]) ).
tcf(c_661,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_20 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_142]) ).
tcf(c_662,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_141]) ).
tcf(c_663,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_22 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_140]) ).
tcf(c_664,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_23 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_139]) ).
tcf(c_665,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_24 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_138]) ).
tcf(c_666,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_25 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_137]) ).
tcf(c_667,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_26 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_136]) ).
tcf(c_668,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_135,c_640]) ).
tcf(c_669,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_134]) ).
tcf(c_671,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_20 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_672,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_673,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_22 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_674,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_23 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_675,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_24 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_676,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_25 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_677,negated_conjecture,
( ( iPr_def_28 = sk_c10 )
| ( iPr_def_26 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_678,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_125,c_641]) ).
tcf(c_679,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_680,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_681,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_20 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_682,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_683,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_22 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_684,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_23 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_685,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_24 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_686,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_25 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_687,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_26 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_688,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_689,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_690,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_691,negated_conjecture,
( ( iPr_def_20 = sk_c11 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_692,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_693,negated_conjecture,
( ( iPr_def_22 = sk_c11 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_694,negated_conjecture,
( ( iPr_def_23 = sk_c10 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_695,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_696,negated_conjecture,
( ( iPr_def_25 = sk_c11 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_697,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_698,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_701,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_704,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_709,plain,
( ~ iPr_def_14
| ( inverse(inverse(sk_c10)) != inverse(sk_c10) )
| ( multiply(sk_c10,inverse(sk_c10)) != sk_c11 )
| ( multiply(sk_c10,inverse(sk_c10)) != inverse(sk_c10) )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_643]) ).
tcf(c_1032,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_649,c_652]) ).
tcf(c_1119,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c10,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_661,c_627]) ).
tcf(c_1128,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_662,c_659]) ).
tcf(c_1136,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_661,c_663]) ).
tcf(c_1155,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_21,sk_c10) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_662,c_632]) ).
tcf(c_1157,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_21,sk_c10) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_652,c_632]) ).
tcf(c_1167,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_662,c_634]) ).
tcf(c_1169,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_652,c_634]) ).
tcf(c_1179,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_663,c_638]) ).
tcf(c_1185,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_657,c_639]) ).
tcf(c_1186,plain,
( ( sk_c11 = iPr_def_25 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_656,c_639]) ).
tcf(c_1187,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_655,c_639]) ).
tcf(c_1188,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_654,c_639]) ).
tcf(c_1189,plain,
( ( sk_c11 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_653,c_639]) ).
tcf(c_1190,plain,
( ( sk_c11 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_651,c_639]) ).
tcf(c_1203,plain,
multiply(iPr_def_25,sk_c3) = identity,
inference(superposition,[status(thm)],[c_637,c_104]) ).
tcf(c_1204,plain,
multiply(iPr_def_23,sk_c4) = identity,
inference(superposition,[status(thm)],[c_635,c_104]) ).
tcf(c_1205,plain,
multiply(iPr_def_21,sk_c5) = identity,
inference(superposition,[status(thm)],[c_633,c_104]) ).
tcf(c_1206,plain,
multiply(iPr_def_19,sk_c7) = identity,
inference(superposition,[status(thm)],[c_631,c_104]) ).
tcf(c_1207,plain,
multiply(iPr_def_18,sk_c6) = identity,
inference(superposition,[status(thm)],[c_630,c_104]) ).
tcf(c_1208,plain,
multiply(iPr_def_28,sk_c1) = identity,
inference(superposition,[status(thm)],[c_640,c_104]) ).
tcf(c_1209,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_629,c_104]) ).
tcf(c_1214,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_27) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_664,c_641]) ).
tcf(c_1217,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_664,c_627]) ).
tcf(c_1235,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_665,c_639]) ).
tcf(c_1264,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_666,c_638]) ).
tcf(c_1265,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_666,c_663]) ).
tcf(c_1280,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_27) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_667,c_641]) ).
tcf(c_1306,plain,
! [X0: $i] :
( ( iPr_def_15 = sk_c9 )
| ( iPr_def_15 != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1329,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1330,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_1331,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_1332,plain,
( ( sk_c9 = sk_c10 )
| ( sk_c9 != sk_c9 )
| ( sk_c10 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1330]) ).
tcf(c_1351,plain,
( ( sk_c9 = multiply(identity,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1330]) ).
tcf(c_1352,plain,
multiply(identity,sk_c9) = sk_c9,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_1354,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1365,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_671,c_638]) ).
tcf(c_1385,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_672,c_669]) ).
tcf(c_1386,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_672,c_634]) ).
tcf(c_1400,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_1401,plain,
( ( sk_c9 = sk_c10 )
| ( sk_c9 != iPr_def_24 )
| ( sk_c10 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1400]) ).
tcf(c_1403,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_1404,plain,
( ( sk_c9 = sk_c10 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1403]) ).
tcf(c_1412,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_673,c_671]) ).
tcf(c_1414,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_673,c_638]) ).
tcf(c_1430,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1354]) ).
tcf(c_1431,plain,
( ( sk_c10 = sk_c9 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1430]) ).
tcf(c_1432,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1354]) ).
tcf(c_1441,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_674,c_664]) ).
tcf(c_1442,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_674,c_641]) ).
tcf(c_1445,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_28,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_674,c_627]) ).
tcf(c_1459,plain,
( ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1330]) ).
tcf(c_1460,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c11 )
| ( sk_c11 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1461,plain,
( ( inverse(sk_c10) = sk_c11 )
| ( sk_c11 != sk_c10 )
| ( inverse(sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1460]) ).
tcf(c_1475,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_675,c_639]) ).
tcf(c_1501,plain,
multiply(identity,multiply(identity,sk_c9)) = multiply(identity,sk_c9),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_1503,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,sk_c9) )
| ( X1 != X0 )
| ( multiply(identity,sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1518,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_676,c_673]) ).
tcf(c_1519,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_676,c_671]) ).
tcf(c_1520,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_676,c_638]) ).
tcf(c_1539,plain,
( ( iPr_def_15 = sk_c9 )
| ( iPr_def_15 != iPr_def_17 )
| ( sk_c9 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1306]) ).
tcf(c_1540,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1354]) ).
tcf(c_1563,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_1566,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c11 )
| ( sk_c11 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1460]) ).
tcf(c_1574,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c10 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_677,c_667]) ).
tcf(c_1576,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_677,c_641]) ).
tcf(c_1579,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_28,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_677,c_627]) ).
tcf(c_1590,plain,
( ( iPr_def_15 = sk_c9 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c9 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1306]) ).
tcf(c_1591,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1354]) ).
tcf(c_1592,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_1593,plain,
( ( sk_c9 = sk_c10 )
| ( sk_c9 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1592]) ).
tcf(c_1594,plain,
( ( sk_c10 = sk_c9 )
| ( sk_c9 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1591]) ).
tcf(c_1647,plain,
( ( multiply(identity,multiply(identity,sk_c9)) = sk_c9 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( multiply(identity,multiply(identity,sk_c9)) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1430]) ).
tcf(c_1652,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c9) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1657,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c9) )
| ( X0 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1503]) ).
tcf(c_1693,plain,
( ( sk_c11 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_29) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_681,c_638]) ).
tcf(c_1696,plain,
( ( sk_c11 = iPr_def_20 )
| ( multiply(sk_c10,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_681,c_627]) ).
tcf(c_1720,plain,
multiply(identity,identity) = identity,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1737,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c11 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_682,c_679]) ).
tcf(c_1739,plain,
( ( sk_c11 = iPr_def_29 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_682,c_634]) ).
tcf(c_1757,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_17 != X0 )
| ( iPr_def_15 != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1773,plain,
( ( sk_c11 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_29) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_683,c_638]) ).
tcf(c_1776,plain,
( ( sk_c11 = iPr_def_22 )
| ( multiply(sk_c10,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_683,c_627]) ).
tcf(c_1804,plain,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_17 != iPr_def_17 )
| ( sk_c9 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1540]) ).
tcf(c_1805,plain,
iPr_def_17 = iPr_def_17,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_1806,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_17 )
| ( iPr_def_17 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1823,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_29) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_684,c_638]) ).
tcf(c_1861,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_1869,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_24 != X0 )
| ( iPr_def_15 != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1875,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1912,plain,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_24 != iPr_def_24 )
| ( sk_c9 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1432]) ).
tcf(c_1913,plain,
iPr_def_24 = iPr_def_24,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_1922,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,multiply(identity,sk_c9)) )
| ( X1 != X0 )
| ( multiply(identity,multiply(identity,sk_c9)) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_1943,plain,
( ( sk_c11 = iPr_def_25 )
| ( multiply(sk_c3,iPr_def_29) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_686,c_638]) ).
tcf(c_1946,plain,
( ( sk_c11 = iPr_def_25 )
| ( multiply(sk_c10,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_686,c_627]) ).
tcf(c_1983,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c3,iPr_def_29) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_687,c_638]) ).
tcf(c_2095,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2105,plain,
! [X0: $i] :
( ( multiply(identity,sk_c9) = X0 )
| ( X0 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1652]) ).
tcf(c_2158,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_691,c_651]) ).
tcf(c_2182,plain,
( ( iPr_def_15 = multiply(identity,sk_c9) )
| ( iPr_def_15 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1657]) ).
tcf(c_2190,plain,
( ( sk_c9 = multiply(identity,iPr_def_15) )
| ( sk_c9 != iPr_def_15 )
| ( multiply(identity,iPr_def_15) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1592]) ).
tcf(c_2191,plain,
multiply(identity,iPr_def_15) = iPr_def_15,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_2193,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2205,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_692,c_689]) ).
tcf(c_2208,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_692,c_634]) ).
tcf(c_2209,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_21,sk_c10) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_692,c_632]) ).
tcf(c_2260,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_693,c_653]) ).
tcf(c_2320,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_694,c_654]) ).
tcf(c_2366,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_695,c_639]) ).
tcf(c_2434,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_696,c_656]) ).
tcf(c_2471,plain,
sk_c11 = sk_c11,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_2473,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2510,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_697,c_639]) ).
tcf(c_2511,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c10 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_697,c_657]) ).
tcf(c_2549,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2551,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = inverse(X2) )
| ( inverse(X2) != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_2552,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c2) )
| ( inverse(X0) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_2553,plain,
( ( inverse(sk_c10) = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c2) )
| ( inverse(sk_c10) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_2552]) ).
tcf(c_2560,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c4) )
| ( inverse(X0) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_2562,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c3) )
| ( inverse(X0) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_2563,plain,
( ( inverse(sk_c10) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c3) )
| ( inverse(sk_c10) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_2562]) ).
tcf(c_2564,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_28 )
| ( iPr_def_28 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_2579,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_697,c_642]) ).
tcf(c_2581,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_695,c_642]) ).
tcf(c_2582,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_694,c_642]) ).
tcf(c_2590,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_17 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_655,c_642]) ).
tcf(c_2692,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_24 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_636,c_644]) ).
tcf(c_2693,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_20 )
| ( inverse(sk_c8) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_632,c_644]) ).
tcf(c_2694,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_29 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_641,c_644]) ).
tcf(c_2695,plain,
( ~ iPr_def_13
| ( sk_c10 != sk_c11 )
| ( inverse(identity) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_103,c_644]) ).
tcf(c_2696,plain,
( ~ iPr_def_13
| ( sk_c11 != identity )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_104,c_644]) ).
tcf(c_2704,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_29 )
| ( sk_c10 != iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_2694,c_640]) ).
tcf(c_2711,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_24 )
| ( sk_c10 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2692,c_635]) ).
tcf(c_2808,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_634,c_105]) ).
tcf(c_2811,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(iPr_def_29,X0),
inference(superposition,[status(thm)],[c_641,c_105]) ).
tcf(c_2814,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_104,c_105]) ).
tcf(c_2816,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1203,c_105]) ).
tcf(c_2817,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1204,c_105]) ).
tcf(c_2818,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1205,c_105]) ).
tcf(c_2819,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1206,c_105]) ).
tcf(c_2820,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1207,c_105]) ).
tcf(c_2821,plain,
! [X0: $i] : multiply(iPr_def_28,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1208,c_105]) ).
tcf(c_2822,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1209,c_105]) ).
tcf(c_2825,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2822,c_103]) ).
tcf(c_2826,plain,
! [X0: $i] : multiply(iPr_def_28,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2821,c_103]) ).
tcf(c_2827,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2820,c_103]) ).
tcf(c_2828,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2819,c_103]) ).
tcf(c_2829,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2818,c_103]) ).
tcf(c_2830,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2817,c_103]) ).
tcf(c_2831,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2816,c_103]) ).
tcf(c_2871,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_2872,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2918,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2919,plain,
! [X0: $i] :
( ( X0 = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c2) )
| ( X0 != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1806]) ).
tcf(c_2946,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1032,c_639]) ).
tcf(c_2974,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_24 = X0 )
| ( iPr_def_24 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_2977,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1875]) ).
tcf(c_2978,plain,
( ( sk_c10 = iPr_def_24 )
| ( iPr_def_24 != sk_c9 )
| ( sk_c10 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2977]) ).
tcf(c_3066,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1128,c_627]) ).
tcf(c_3107,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1136,c_627]) ).
tcf(c_3145,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,multiply(identity,sk_c9)) = X1 )
| ( X1 != X0 )
| ( multiply(identity,multiply(identity,sk_c9)) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_3165,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1265,c_627]) ).
tcf(c_3349,plain,
( ( multiply(identity,sk_c9) = iPr_def_24 )
| ( iPr_def_24 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2105]) ).
tcf(c_3360,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_24 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_636,c_645]) ).
tcf(c_3362,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_29 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_641,c_645]) ).
tcf(c_3363,plain,
( ~ iPr_def_12
| ( sk_c10 != sk_c9 )
| ( inverse(identity) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_103,c_645]) ).
tcf(c_3379,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_29 )
| ( sk_c10 != iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_3362,c_640]) ).
tcf(c_3386,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_24 )
| ( sk_c10 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3360,c_635]) ).
tcf(c_3499,plain,
( ~ iPr_def_11
| ( sk_c10 != iPr_def_27 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_639,c_646]) ).
tcf(c_3500,plain,
( ~ iPr_def_11
| ( sk_c10 != sk_c9 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_103,c_646]) ).
tcf(c_3523,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_17 )
| ( sk_c10 != iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_3499,c_629]) ).
tcf(c_3667,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_15 )
| ( inverse(sk_c10) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_627,c_647]) ).
tcf(c_3668,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_26 )
| ( inverse(sk_c3) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_638,c_647]) ).
tcf(c_3669,plain,
( ~ iPr_def_10
| ( sk_c10 != sk_c11 )
| ( inverse(identity) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_103,c_647]) ).
tcf(c_3673,plain,
! [X0: $i] :
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,iPr_def_29) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_686,c_647]) ).
tcf(c_3686,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_25 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_3668,c_637]) ).
tcf(c_3752,plain,
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_10
| ( inverse(sk_c10) != sk_c11 )
| ( multiply(sk_c10,iPr_def_29) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_3673]) ).
tcf(c_3757,plain,
! [X0: $i] :
( ( multiply(identity,sk_c9) = X0 )
| ( X0 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1652]) ).
tcf(c_3758,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c9) )
| ( X0 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1503]) ).
tcf(c_3816,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_17 != sk_c9 )
| ( iPr_def_15 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1757]) ).
tcf(c_3818,plain,
( ( multiply(identity,sk_c9) = iPr_def_15 )
| ( iPr_def_15 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2105]) ).
tcf(c_3824,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2193]) ).
tcf(c_3923,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2193]) ).
tcf(c_3924,plain,
( ( sk_c10 = iPr_def_15 )
| ( iPr_def_15 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_3923]) ).
tcf(c_3940,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_18 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1385,c_1128]) ).
tcf(c_3945,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1385,c_641]) ).
tcf(c_3948,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_28,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1385,c_627]) ).
tcf(c_4015,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1412,c_1136]) ).
tcf(c_4021,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1412,c_641]) ).
tcf(c_4024,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_28,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1412,c_627]) ).
tcf(c_4101,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1441,c_636]) ).
tcf(c_4103,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( multiply(iPr_def_23,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1441,c_627]) ).
tcf(c_4161,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != multiply(identity,iPr_def_15) )
| ( X0 != multiply(identity,iPr_def_15) ) ),
inference(instantiation,[status(thm)],[c_1354]) ).
tcf(c_4221,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_24 != sk_c9 )
| ( iPr_def_17 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2977]) ).
tcf(c_4267,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1518,c_1265]) ).
tcf(c_4274,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1518,c_641]) ).
tcf(c_4366,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_2473]) ).
tcf(c_4497,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1574,c_1441]) ).
tcf(c_4515,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( multiply(iPr_def_26,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1574,c_627]) ).
tcf(c_4648,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_2549]) ).
tcf(c_4653,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c2) )
| ( X0 != sk_c2 ) ),
inference(instantiation,[status(thm)],[c_701]) ).
tcf(c_4654,plain,
( ( inverse(sk_c10) = inverse(sk_c2) )
| ( sk_c10 != sk_c2 ) ),
inference(instantiation,[status(thm)],[c_4653]) ).
tcf(c_4655,plain,
( ( inverse(sk_c2) = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c2) )
| ( inverse(sk_c2) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_2552]) ).
tcf(c_4656,plain,
inverse(sk_c2) = inverse(sk_c2),
inference(instantiation,[status(thm)],[c_1563]) ).
tcf(c_4912,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_2205,c_1032]) ).
tcf(c_5093,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_23,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_2320,c_627]) ).
tcf(c_5168,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_2434,c_2260]) ).
tcf(c_5169,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_2434,c_2158]) ).
tcf(c_5180,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_2434,c_638]) ).
tcf(c_5217,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_2511,c_2320]) ).
tcf(c_5236,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2511,c_636]) ).
tcf(c_5238,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_26,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_2511,c_627]) ).
tcf(c_5398,plain,
multiply(iPr_def_17,iPr_def_27) = sk_c9,
inference(superposition,[status(thm)],[c_639,c_2825]) ).
tcf(c_5410,plain,
multiply(iPr_def_28,iPr_def_29) = sk_c10,
inference(superposition,[status(thm)],[c_641,c_2826]) ).
tcf(c_5497,plain,
( ( inverse(sk_c4) = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c4) )
| ( inverse(sk_c4) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_2560]) ).
tcf(c_5498,plain,
inverse(sk_c4) = inverse(sk_c4),
inference(instantiation,[status(thm)],[c_1563]) ).
tcf(c_5499,plain,
multiply(iPr_def_19,iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_628,c_2828]) ).
tcf(c_5507,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c3) )
| ( X0 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_701]) ).
tcf(c_5508,plain,
( ( inverse(sk_c10) = inverse(sk_c3) )
| ( sk_c10 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_5507]) ).
tcf(c_5509,plain,
( ( inverse(sk_c3) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c3) )
| ( inverse(sk_c3) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_2562]) ).
tcf(c_5510,plain,
inverse(sk_c3) = inverse(sk_c3),
inference(instantiation,[status(thm)],[c_1563]) ).
tcf(c_5511,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_634,c_2829]) ).
tcf(c_5594,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c1) )
| ( X0 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_701]) ).
tcf(c_5595,plain,
( ( inverse(sk_c10) = inverse(sk_c1) )
| ( sk_c10 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_5594]) ).
tcf(c_5596,plain,
( ( inverse(sk_c1) = iPr_def_28 )
| ( iPr_def_28 != inverse(sk_c1) )
| ( inverse(sk_c1) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_2564]) ).
tcf(c_5597,plain,
inverse(sk_c1) = inverse(sk_c1),
inference(instantiation,[status(thm)],[c_1563]) ).
tcf(c_5690,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c10,
inference(superposition,[status(thm)],[c_636,c_2830]) ).
tcf(c_5707,plain,
multiply(iPr_def_25,iPr_def_26) = sk_c11,
inference(superposition,[status(thm)],[c_638,c_2831]) ).
tcf(c_5750,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_27,iPr_def_29) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_3940,c_5410]) ).
tcf(c_5752,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_27,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_3940,c_1208]) ).
tcf(c_5764,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,iPr_def_29) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4015,c_5410]) ).
tcf(c_5766,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_4015,c_1208]) ).
tcf(c_6088,plain,
! [X0: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_2872]) ).
tcf(c_6089,plain,
( ( iPr_def_15 = sk_c10 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_6088]) ).
tcf(c_6106,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_21,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2511,c_1155]) ).
tcf(c_6167,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_2918]) ).
tcf(c_6176,plain,
! [X0: $i] :
( ( iPr_def_24 = X0 )
| ( iPr_def_24 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2974]) ).
tcf(c_6270,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,iPr_def_29) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4267,c_5410]) ).
tcf(c_6272,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_4267,c_1208]) ).
tcf(c_6306,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_27,iPr_def_29) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4497,c_5410]) ).
tcf(c_6308,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_27,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_4497,c_1208]) ).
tcf(c_6339,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2511,c_1157]) ).
tcf(c_6628,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c5,multiply(iPr_def_21,X0)) = multiply(iPr_def_22,X0) ) ),
inference(superposition,[status(thm)],[c_1167,c_105]) ).
tcf(c_6668,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c3,multiply(iPr_def_22,X0)) = multiply(iPr_def_26,X0) ) ),
inference(superposition,[status(thm)],[c_1179,c_105]) ).
tcf(c_6669,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1179,c_2831]) ).
tcf(c_6670,plain,
( ( sk_c11 = iPr_def_22 )
| ( sk_c10 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_6669,c_5707]) ).
tcf(c_6733,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c2,multiply(iPr_def_17,X0)) = multiply(iPr_def_27,X0) ) ),
inference(superposition,[status(thm)],[c_1185,c_105]) ).
tcf(c_6734,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1185,c_2825]) ).
tcf(c_6735,plain,
( ( sk_c9 = iPr_def_17 )
| ( sk_c10 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_6734,c_5398]) ).
tcf(c_6746,plain,
( ( sk_c11 = iPr_def_25 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1186,c_2825]) ).
tcf(c_6747,plain,
( ( sk_c9 = iPr_def_17 )
| ( sk_c11 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_6746,c_5398]) ).
tcf(c_6758,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1187,c_2825]) ).
tcf(c_6759,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6758,c_5398]) ).
tcf(c_6770,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1188,c_2825]) ).
tcf(c_6771,plain,
( ( sk_c9 = iPr_def_17 )
| ( sk_c10 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_6770,c_5398]) ).
tcf(c_6866,plain,
( ( sk_c11 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1189,c_2825]) ).
tcf(c_6867,plain,
( ( sk_c9 = iPr_def_17 )
| ( sk_c11 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_6866,c_5398]) ).
tcf(c_6890,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1214,c_2826]) ).
tcf(c_6891,plain,
( ( sk_c10 = iPr_def_27 )
| ( sk_c10 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_6890,c_5410]) ).
tcf(c_6954,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_27,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_684,c_1217]) ).
tcf(c_7015,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1235,c_2825]) ).
tcf(c_7016,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c10 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_7015,c_5398]) ).
tcf(c_7029,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1264,c_2831]) ).
tcf(c_7030,plain,
( ( sk_c11 = iPr_def_25 )
| ( sk_c10 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_7029,c_5707]) ).
tcf(c_7163,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1280,c_2826]) ).
tcf(c_7164,plain,
( ( sk_c10 = iPr_def_27 )
| ( sk_c10 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_7163,c_5410]) ).
tcf(c_7474,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1365,c_2831]) ).
tcf(c_7475,plain,
( ( sk_c11 = iPr_def_20 )
| ( sk_c10 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_7474,c_5707]) ).
tcf(c_7657,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1414,c_2831]) ).
tcf(c_7658,plain,
( ( sk_c11 = iPr_def_22 )
| ( sk_c10 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_7657,c_5707]) ).
tcf(c_7720,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1442,c_2826]) ).
tcf(c_7721,plain,
( ( sk_c10 = iPr_def_28 )
| ( sk_c10 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_7720,c_5410]) ).
tcf(c_7936,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_684,c_1445]) ).
tcf(c_7947,plain,
( ( sk_c10 = iPr_def_23 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_7936,c_5410]) ).
tcf(c_7968,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1475,c_2825]) ).
tcf(c_7969,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c10 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_7968,c_5398]) ).
tcf(c_7987,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1520,c_2831]) ).
tcf(c_7988,plain,
( ( sk_c11 = iPr_def_25 )
| ( sk_c10 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_7987,c_5707]) ).
tcf(c_8130,plain,
( ( sk_c10 = iPr_def_27 )
| ( sk_c10 = iPr_def_15 )
| ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_7947,c_1119]) ).
tcf(c_8150,plain,
( ( sk_c10 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_7947,c_636]) ).
tcf(c_8483,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1576,c_2826]) ).
tcf(c_8484,plain,
( ( sk_c10 = iPr_def_28 )
| ( sk_c10 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_8483,c_5410]) ).
tcf(c_8563,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_687,c_1579]) ).
tcf(c_8576,plain,
( ( sk_c10 = iPr_def_26 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8563,c_5410]) ).
tcf(c_8760,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c10 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_8576,c_7947]) ).
tcf(c_8993,plain,
( ( sk_c11 = iPr_def_20 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1693,c_2831]) ).
tcf(c_8994,plain,
( ( sk_c11 = iPr_def_29 )
| ( sk_c11 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_8993,c_5707]) ).
tcf(c_9181,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_20 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1412,c_1696]) ).
tcf(c_9219,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_20 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9181,c_5410]) ).
tcf(c_9453,plain,
( ( sk_c11 = iPr_def_22 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1773,c_2831]) ).
tcf(c_9454,plain,
( ( sk_c11 = iPr_def_29 )
| ( sk_c11 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_9453,c_5707]) ).
tcf(c_9473,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_22 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1412,c_1776]) ).
tcf(c_9511,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_22 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9473,c_5410]) ).
tcf(c_9588,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1823,c_2831]) ).
tcf(c_9589,plain,
( ( sk_c11 = iPr_def_29 )
| ( sk_c10 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_9588,c_5707]) ).
tcf(c_9672,plain,
( ( sk_c11 = iPr_def_25 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1943,c_2831]) ).
tcf(c_9673,plain,
( ( sk_c11 = iPr_def_29 )
| ( sk_c11 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_9672,c_5707]) ).
tcf(c_9689,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c11 = iPr_def_25 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1519,c_1946]) ).
tcf(c_9741,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c11 = iPr_def_25 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9689,c_5410]) ).
tcf(c_9799,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1983,c_2831]) ).
tcf(c_9800,plain,
( ( sk_c11 = iPr_def_29 )
| ( sk_c10 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_9799,c_5707]) ).
tcf(c_10214,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2918]) ).
tcf(c_10228,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2511,c_2209]) ).
tcf(c_10619,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2366,c_2825]) ).
tcf(c_10620,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_10619,c_5398]) ).
tcf(c_10643,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_2510,c_2825]) ).
tcf(c_10644,plain,
( ( sk_c9 = iPr_def_15 )
| ( sk_c10 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_10643,c_5398]) ).
tcf(c_10883,plain,
! [X0: $i] :
( ( multiply(identity,sk_c9) = X0 )
| ( X0 != iPr_def_15 )
| ( multiply(identity,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1652]) ).
tcf(c_10884,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c9) )
| ( X0 != iPr_def_15 )
| ( multiply(identity,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1503]) ).
tcf(c_11336,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_28 )
| ( sk_c10 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_8760,c_677]) ).
tcf(c_11337,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_28 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_8760,c_674]) ).
tcf(c_11340,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_15) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_8760,c_641]) ).
tcf(c_11343,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_15,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_8760,c_627]) ).
tcf(c_11513,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_2473]) ).
tcf(c_11516,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c11 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11513]) ).
tcf(c_11528,plain,
! [X0: $i] :
( ( multiply(identity,multiply(identity,sk_c9)) = X0 )
| ( X0 != iPr_def_15 )
| ( multiply(identity,multiply(identity,sk_c9)) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_3145]) ).
tcf(c_11529,plain,
! [X0: $i] :
( ( X0 = multiply(identity,multiply(identity,sk_c9)) )
| ( X0 != iPr_def_15 )
| ( multiply(identity,multiply(identity,sk_c9)) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1922]) ).
tcf(c_11533,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_2918]) ).
tcf(c_11534,plain,
! [X0: $i] :
( ( X0 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1806]) ).
tcf(c_11535,plain,
( ( sk_c10 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11534]) ).
tcf(c_11538,plain,
! [X0: $i] :
( ( iPr_def_24 = X0 )
| ( iPr_def_24 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_2974]) ).
tcf(c_11539,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1875]) ).
tcf(c_11684,plain,
multiply(sk_c5,iPr_def_20) = multiply(iPr_def_22,sk_c10),
inference(superposition,[status(thm)],[c_632,c_2808]) ).
tcf(c_12215,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c2 )
| ( sk_c2 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_12269,plain,
multiply(sk_c1,iPr_def_15) = multiply(iPr_def_29,sk_c11),
inference(superposition,[status(thm)],[c_627,c_2811]) ).
tcf(c_13523,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c11 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_696,c_642]) ).
tcf(c_13526,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c11 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_693,c_642]) ).
tcf(c_14063,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1737,c_3948]) ).
tcf(c_14078,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_14063,c_5410]) ).
tcf(c_14151,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_14078,c_1385]) ).
tcf(c_14167,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_15,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14078,c_627]) ).
tcf(c_14654,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_10
| ( sk_c10 != iPr_def_15 )
| ( inverse(iPr_def_23) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_4103,c_647]) ).
tcf(c_14692,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2814,c_103]) ).
tcf(c_14718,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_103,c_14692]) ).
tcf(c_14719,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_104,c_14692]) ).
tcf(c_14865,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2831,c_14692]) ).
tcf(c_14866,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2830,c_14692]) ).
tcf(c_14867,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2829,c_14692]) ).
tcf(c_14869,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2827,c_14692]) ).
tcf(c_14870,plain,
! [X0: $i] : multiply(inverse(iPr_def_28),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2826,c_14692]) ).
tcf(c_14871,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2825,c_14692]) ).
tcf(c_14889,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_14692,c_14692]) ).
tcf(c_15156,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c2) )
| ( X0 != iPr_def_17 )
| ( inverse(sk_c2) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_2549]) ).
tcf(c_15157,plain,
! [X0: $i] :
( ( inverse(sk_c2) = X0 )
| ( X0 != iPr_def_17 )
| ( inverse(sk_c2) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_15160,plain,
( ( sk_c10 = inverse(sk_c2) )
| ( sk_c10 != iPr_def_17 )
| ( inverse(sk_c2) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_15156]) ).
tcf(c_15162,plain,
( ( inverse(sk_c2) = sk_c9 )
| ( sk_c9 != iPr_def_17 )
| ( inverse(sk_c2) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1540]) ).
tcf(c_15255,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c4) )
| ( X0 != iPr_def_23 )
| ( inverse(sk_c4) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_2549]) ).
tcf(c_15256,plain,
! [X0: $i] :
( ( inverse(sk_c4) = X0 )
| ( X0 != iPr_def_23 )
| ( inverse(sk_c4) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_15259,plain,
( ( sk_c10 = inverse(sk_c4) )
| ( sk_c10 != iPr_def_23 )
| ( inverse(sk_c4) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_15255]) ).
tcf(c_15260,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c3) )
| ( X0 != iPr_def_25 )
| ( inverse(sk_c3) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_2549]) ).
tcf(c_15262,plain,
( ( inverse(sk_c3) = sk_c11 )
| ( sk_c11 != iPr_def_25 )
| ( inverse(sk_c3) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_1460]) ).
tcf(c_15265,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c1) )
| ( X0 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_2549]) ).
tcf(c_15266,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_15268,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( sk_c10 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_15266]) ).
tcf(c_15269,plain,
( ( sk_c10 = inverse(sk_c1) )
| ( sk_c10 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_15265]) ).
tcf(c_15485,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1727]) ).
tcf(c_15486,plain,
( ( sk_c10 = identity )
| ( identity != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_15485]) ).
tcf(c_15498,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_14719,c_14889]) ).
tcf(c_15521,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15498,c_14718]) ).
tcf(c_16202,plain,
multiply(sk_c3,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_14865,c_104]) ).
tcf(c_16206,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_14865,c_14692]) ).
tcf(c_16207,plain,
multiply(sk_c3,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_14865,c_15498]) ).
tcf(c_16230,plain,
( ( identity = iPr_def_26 )
| ( sk_c10 = iPr_def_28 ) ),
inference(demodulation,[status(thm)],[c_1520,c_16202]) ).
tcf(c_16231,plain,
( ( identity = iPr_def_26 )
| ( sk_c10 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_1264,c_16202]) ).
tcf(c_16280,plain,
inverse(iPr_def_25) = sk_c3,
inference(demodulation,[status(thm)],[c_16207,c_15498]) ).
tcf(c_16282,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_20) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_5169,c_16280]) ).
tcf(c_16283,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_22) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_5168,c_16280]) ).
tcf(c_16726,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_16231,c_16230]) ).
tcf(c_17089,plain,
! [X0: $i] :
( ( iPr_def_27 = iPr_def_28 )
| ( multiply(iPr_def_26,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_16726,c_103]) ).
tcf(c_17105,plain,
multiply(sk_c4,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_14866,c_104]) ).
tcf(c_17110,plain,
multiply(sk_c4,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_14866,c_15498]) ).
tcf(c_17130,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_4101,c_17105]) ).
tcf(c_17191,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_17418,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_24 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_16726,c_17130]) ).
tcf(c_17517,plain,
inverse(iPr_def_23) = sk_c4,
inference(demodulation,[status(thm)],[c_17110,c_15498]) ).
tcf(c_17550,plain,
( ( multiply(identity,multiply(identity,sk_c9)) = iPr_def_15 )
| ( iPr_def_15 != sk_c9 )
| ( multiply(identity,multiply(identity,sk_c9)) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_3824]) ).
tcf(c_17654,plain,
( ( iPr_def_17 = iPr_def_15 )
| ( iPr_def_17 != iPr_def_17 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_6167]) ).
tcf(c_17919,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_2193]) ).
tcf(c_17920,plain,
( ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != sk_c10 )
| ( sk_c9 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_17919]) ).
tcf(c_17929,plain,
! [X0: $i] :
( ( identity = iPr_def_15 )
| ( iPr_def_15 != X0 )
| ( identity != X0 ) ),
inference(instantiation,[status(thm)],[c_2193]) ).
tcf(c_17939,plain,
( ( identity = iPr_def_15 )
| ( iPr_def_15 != sk_c10 )
| ( identity != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_17929]) ).
tcf(c_18072,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_11337,c_11336]) ).
tcf(c_18636,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( identity = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_5180,c_16202]) ).
tcf(c_18649,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_26,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_18636,c_103]) ).
tcf(c_19474,plain,
( ( sk_c11 = multiply(identity,sk_c11) )
| ( sk_c11 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_4366]) ).
tcf(c_19475,plain,
multiply(identity,sk_c11) = sk_c11,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_19477,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_19808,plain,
multiply(sk_c5,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_14867,c_104]) ).
tcf(c_19812,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_14867,c_14692]) ).
tcf(c_19813,plain,
multiply(sk_c5,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_14867,c_15498]) ).
tcf(c_19834,plain,
( ( identity = iPr_def_22 )
| ( sk_c9 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_2208,c_19808]) ).
tcf(c_19835,plain,
( ( identity = iPr_def_22 )
| ( sk_c11 = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_1739,c_19808]) ).
tcf(c_19836,plain,
( ( identity = iPr_def_22 )
| ( sk_c10 = iPr_def_28 ) ),
inference(demodulation,[status(thm)],[c_1386,c_19808]) ).
tcf(c_19837,plain,
( ( identity = iPr_def_22 )
| ( sk_c9 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_1169,c_19808]) ).
tcf(c_19838,plain,
( ( identity = iPr_def_22 )
| ( sk_c10 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_1167,c_19808]) ).
tcf(c_19904,plain,
inverse(iPr_def_21) = sk_c5,
inference(demodulation,[status(thm)],[c_19813,c_15498]) ).
tcf(c_19906,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_18) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_4912,c_19904]) ).
tcf(c_19925,plain,
multiply(sk_c5,sk_c8) = iPr_def_22,
inference(superposition,[status(thm)],[c_5511,c_19812]) ).
tcf(c_20077,plain,
( ~ iPr_def_13
| ( inverse(sk_c8) != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_2693,c_2704,c_2693,c_7475,c_8994]) ).
tcf(c_20094,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_13
| ( inverse(iPr_def_18) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_689,c_20077]) ).
tcf(c_20096,plain,
( ( sk_c11 = iPr_def_29 )
| ~ iPr_def_13
| ( inverse(iPr_def_18) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_679,c_20077]) ).
tcf(c_20098,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_13
| ( inverse(iPr_def_18) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_669,c_20077]) ).
tcf(c_20270,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_19834,c_642]) ).
tcf(c_20366,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_22 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_19835,c_4024]) ).
tcf(c_20397,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c10,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_19835,c_627]) ).
tcf(c_20440,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_22 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_20366,c_5410]) ).
tcf(c_20566,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_19836,c_641]) ).
tcf(c_20782,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_19837,c_19834]) ).
tcf(c_20807,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_19837,c_639]) ).
tcf(c_20868,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_19838,c_19836]) ).
tcf(c_20925,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_19838,c_627]) ).
tcf(c_21011,plain,
( ( iPr_def_22 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_20782,c_18636]) ).
tcf(c_21015,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_20782,c_15521]) ).
tcf(c_21017,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_20782,c_103]) ).
tcf(c_21121,plain,
( iPr_def_14
| iPr_def_10
| ( identity = iPr_def_22 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_20270,c_2704,c_3523,c_19838,c_19837,c_19836,c_19835,c_20270]) ).
tcf(c_21122,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( identity = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_21121]) ).
tcf(c_21206,plain,
( ( inverse(iPr_def_18) != sk_c10 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_20094,c_2704,c_20098,c_20096]) ).
tcf(c_21207,plain,
( ~ iPr_def_13
| ( inverse(iPr_def_18) != sk_c10 ) ),
inference(renaming,[status(thm)],[c_21206]) ).
tcf(c_21265,plain,
( ( identity = iPr_def_24 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8150,c_17105]) ).
tcf(c_21359,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( identity = iPr_def_24 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_21265,c_674]) ).
tcf(c_21361,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( identity = iPr_def_24 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_21265,c_664]) ).
tcf(c_21543,plain,
( ( iPr_def_15 = inverse(sk_c2) )
| ( iPr_def_15 != iPr_def_15 )
| ( inverse(sk_c2) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_6088]) ).
tcf(c_21544,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c2) )
| ( iPr_def_15 != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_2919]) ).
tcf(c_21755,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_21011,c_5217]) ).
tcf(c_22349,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( identity = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_21359,c_636]) ).
tcf(c_22361,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_22349,c_17105]) ).
tcf(c_22829,plain,
! [X0: $i,X1: $i] :
( ( inverse(sk_c3) = inverse(X0) )
| ( inverse(sk_c3) != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_2551]) ).
tcf(c_22858,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_22) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_21755,c_17517]) ).
tcf(c_23206,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( identity = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_21361,c_636]) ).
tcf(c_23218,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_23206,c_17105]) ).
tcf(c_23223,plain,
( ~ iPr_def_13
| ( sk_c10 != identity )
| ( sk_c10 != sk_c11 ) ),
inference(light_normalisation,[status(thm)],[c_2695,c_15521]) ).
tcf(c_23259,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_13
| ( identity != iPr_def_27 )
| ( sk_c10 != sk_c11 ) ),
inference(superposition,[status(thm)],[c_1136,c_23223]) ).
tcf(c_23432,plain,
( ~ iPr_def_12
| ( sk_c10 != identity )
| ( sk_c10 != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3363,c_15521]) ).
tcf(c_23463,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_15 )
| ( sk_c10 != identity ) ),
inference(superposition,[status(thm)],[c_697,c_23432]) ).
tcf(c_23464,plain,
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_15 )
| ( sk_c10 != identity ) ),
inference(superposition,[status(thm)],[c_696,c_23432]) ).
tcf(c_23466,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_15 )
| ( sk_c10 != identity ) ),
inference(superposition,[status(thm)],[c_694,c_23432]) ).
tcf(c_23476,plain,
( ( sk_c11 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_17 )
| ( sk_c10 != identity ) ),
inference(superposition,[status(thm)],[c_653,c_23432]) ).
tcf(c_23590,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( sk_c10 != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3500,c_15521]) ).
tcf(c_23623,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( sk_c10 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_695,c_23590]) ).
tcf(c_23629,plain,
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( sk_c10 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_665,c_23590]) ).
tcf(c_23632,plain,
( ( sk_c9 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( sk_c10 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_655,c_23590]) ).
tcf(c_23893,plain,
( ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != sk_c11 ) ),
inference(light_normalisation,[status(thm)],[c_3669,c_15521]) ).
tcf(c_23921,plain,
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_686,c_23893]) ).
tcf(c_24046,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_2581,c_642,c_1590,c_2581,c_2871]) ).
tcf(c_24103,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_27 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_23218,c_103]) ).
tcf(c_24495,plain,
( ( sk_c10 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c11 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_7947,c_2696]) ).
tcf(c_24578,plain,
( ( sk_c10 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c11 != identity ) ),
inference(ground_joinability,[status(thm)],[c_24495,c_635,c_17517]) ).
tcf(c_24998,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_29,sk_c11) = iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_11340,c_12269]) ).
tcf(c_25457,plain,
multiply(sk_c6,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_14869,c_104]) ).
tcf(c_25461,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_14869,c_14692]) ).
tcf(c_25462,plain,
multiply(sk_c6,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_14869,c_15498]) ).
tcf(c_26075,plain,
inverse(iPr_def_18) = sk_c6,
inference(demodulation,[status(thm)],[c_25462,c_15498]) ).
tcf(c_26082,plain,
( ~ iPr_def_13
| ( sk_c10 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_21207,c_26075]) ).
tcf(c_26110,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_688,c_26082]) ).
tcf(c_26112,plain,
( ( sk_c11 = iPr_def_29 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_678,c_26082]) ).
tcf(c_26114,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_668,c_26082]) ).
tcf(c_26349,plain,
( ( sk_c10 != iPr_def_16 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_26110,c_2704,c_26114,c_26112]) ).
tcf(c_26350,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_16 ) ),
inference(renaming,[status(thm)],[c_26349]) ).
tcf(c_26383,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_13
| ( iPr_def_16 != iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_677,c_26350]) ).
tcf(c_26384,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_13
| ( iPr_def_16 != iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_674,c_26350]) ).
tcf(c_26995,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_26383,c_2704,c_8484,c_9800]) ).
tcf(c_27001,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_26 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2579,c_26995]) ).
tcf(c_27007,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_26384,c_2704,c_7721,c_9589]) ).
tcf(c_27013,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_23 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2582,c_27007]) ).
tcf(c_27185,plain,
( iPr_def_14
| iPr_def_12
| ( sk_c10 = iPr_def_26 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_27001,c_642,c_1539,c_2511,c_3523,c_6735,c_7164,c_26995]) ).
tcf(c_27186,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c10 = iPr_def_26 ) ),
inference(renaming,[status(thm)],[c_27185]) ).
tcf(c_27195,plain,
( iPr_def_14
| iPr_def_12
| ( sk_c10 = iPr_def_23 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_27013,c_642,c_1539,c_2320,c_3523,c_6771,c_6891,c_27007]) ).
tcf(c_27196,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c10 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_27195]) ).
tcf(c_27403,plain,
multiply(sk_c1,iPr_def_28) = identity,
inference(superposition,[status(thm)],[c_14870,c_104]) ).
tcf(c_27407,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_28,X0)) = X0,
inference(superposition,[status(thm)],[c_14870,c_14692]) ).
tcf(c_27408,plain,
multiply(sk_c1,identity) = inverse(iPr_def_28),
inference(superposition,[status(thm)],[c_14870,c_15498]) ).
tcf(c_27453,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( identity = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_4274,c_27403]) ).
tcf(c_27454,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_4021,c_27403]) ).
tcf(c_27455,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( identity = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_3945,c_27403]) ).
tcf(c_27457,plain,
( ( identity = iPr_def_29 )
| ( sk_c10 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1576,c_27403]) ).
tcf(c_27458,plain,
( ( identity = iPr_def_29 )
| ( sk_c10 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1442,c_27403]) ).
tcf(c_27596,plain,
( iPr_def_14
| iPr_def_10
| ( sk_c11 = iPr_def_25 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_13523,c_642,c_1539,c_2434,c_2704,c_3523,c_6747,c_7030,c_7988,c_9673]) ).
tcf(c_27597,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c11 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_27596]) ).
tcf(c_27653,plain,
inverse(iPr_def_28) = sk_c1,
inference(demodulation,[status(thm)],[c_27408,c_15498]) ).
tcf(c_27748,plain,
multiply(sk_c1,sk_c10) = iPr_def_29,
inference(superposition,[status(thm)],[c_5410,c_27407]) ).
tcf(c_27827,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_25 )
| ( X0 != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_2473]) ).
tcf(c_27831,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_2473]) ).
tcf(c_27834,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c11 != iPr_def_29 )
| ( sk_c10 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_27831]) ).
tcf(c_27852,plain,
! [X0: $i] :
( ( iPr_def_17 = inverse(X0) )
| ( iPr_def_17 != sk_c9 )
| ( inverse(X0) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_10214]) ).
tcf(c_27854,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = iPr_def_17 )
| ( iPr_def_17 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_28203,plain,
! [X0: $i] :
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(X0,iPr_def_29) = X0 ) ),
inference(superposition,[status(thm)],[c_27453,c_15498]) ).
tcf(c_28227,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c10,iPr_def_29) = sk_c10 ) ),
inference(instantiation,[status(thm)],[c_28203]) ).
tcf(c_28340,plain,
( iPr_def_14
| iPr_def_10
| ( sk_c11 = iPr_def_22 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_13526,c_642,c_1539,c_2260,c_2704,c_3523,c_6670,c_6867,c_7658,c_9454]) ).
tcf(c_28341,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c11 = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_28340]) ).
tcf(c_28812,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,identity) )
| ( X1 != X0 )
| ( multiply(identity,identity) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_28860,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_27458,c_27457]) ).
tcf(c_28864,plain,
( ( identity = iPr_def_29 )
| ~ iPr_def_13
| ( sk_c11 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_27458,c_2696]) ).
tcf(c_28931,plain,
( ( identity = iPr_def_29 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_27458,c_636]) ).
tcf(c_28940,plain,
( ( identity = iPr_def_29 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_28931,c_17105]) ).
tcf(c_29056,plain,
( ( identity = iPr_def_29 )
| ~ iPr_def_13
| ( sk_c11 != identity ) ),
inference(ground_joinability,[status(thm)],[c_28864,c_635,c_17517]) ).
tcf(c_29656,plain,
! [X0: $i] :
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_29,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_28860,c_103]) ).
tcf(c_29742,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_17)) != sk_c10 )
| ( multiply(sk_c2,sk_c10) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_14871,c_644]) ).
tcf(c_29745,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_14871,c_104]) ).
tcf(c_29747,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c11 )
| ( multiply(sk_c2,sk_c11) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_14871,c_647]) ).
tcf(c_29749,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_14871,c_14692]) ).
tcf(c_29750,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_14871,c_15498]) ).
tcf(c_29769,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( identity = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_2946,c_29745]) ).
tcf(c_29771,plain,
( ( identity = iPr_def_27 )
| ( sk_c11 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1190,c_29745]) ).
tcf(c_29772,plain,
( ( identity = iPr_def_27 )
| ( sk_c11 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1189,c_29745]) ).
tcf(c_29773,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1188,c_29745]) ).
tcf(c_29774,plain,
( ( identity = iPr_def_27 )
| ( sk_c11 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1186,c_29745]) ).
tcf(c_29775,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1185,c_29745]) ).
tcf(c_29816,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_29750,c_15498]) ).
tcf(c_29898,plain,
! [X0: $i] :
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_29769,c_103]) ).
tcf(c_30304,plain,
( ( iPr_def_24 = iPr_def_15 )
| ( iPr_def_24 != iPr_def_24 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_6176]) ).
tcf(c_30308,plain,
( ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_24 )
| ( sk_c9 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1400]) ).
tcf(c_30425,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_29772,c_29771]) ).
tcf(c_30668,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1875]) ).
tcf(c_30900,plain,
( ( identity = iPr_def_27 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_29773,c_636]) ).
tcf(c_30907,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_30900,c_17105]) ).
tcf(c_31223,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_29774,c_29772]) ).
tcf(c_31553,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_29775,c_29773]) ).
tcf(c_31793,plain,
( ( iPr_def_27 = iPr_def_29 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_30907,c_28940]) ).
tcf(c_31809,plain,
! [X0: $i] :
( ( identity = iPr_def_24 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_30907,c_103]) ).
tcf(c_32493,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_30425,c_103]) ).
tcf(c_32603,plain,
! [X0: $i] :
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_31223,c_103]) ).
tcf(c_32952,plain,
! [X0: $i] :
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_31553,c_103]) ).
tcf(c_34479,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_11
| ( sk_c10 != sk_c9 )
| ( inverse(iPr_def_26) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_17089,c_646]) ).
tcf(c_34483,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_17089,c_4515]) ).
tcf(c_34863,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_15 = iPr_def_20 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_34483,c_671]) ).
tcf(c_34867,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_15 = iPr_def_20 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_34483,c_661]) ).
tcf(c_37689,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_18649,c_5238]) ).
tcf(c_37865,plain,
! [X0: $i] :
( ( X0 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1806]) ).
tcf(c_38119,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_37689,c_2260]) ).
tcf(c_38193,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c2) )
| ( X0 != sk_c9 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_2549]) ).
tcf(c_38197,plain,
( ( sk_c10 = inverse(sk_c2) )
| ( sk_c10 != sk_c9 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_38193]) ).
tcf(c_38661,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_34867,c_34863]) ).
tcf(c_38762,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_19836,c_20397]) ).
tcf(c_38804,plain,
( ( identity = iPr_def_22 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_38762,c_5410]) ).
tcf(c_38855,plain,
( ( identity = iPr_def_29 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_20566,c_27403]) ).
tcf(c_39774,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_38804,c_19838]) ).
tcf(c_39775,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_38804,c_19836]) ).
tcf(c_39839,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_15,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_38804,c_627]) ).
tcf(c_40046,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_20807,c_29745]) ).
tcf(c_40072,plain,
( ( iPr_def_27 = iPr_def_29 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_40046,c_38855]) ).
tcf(c_40093,plain,
! [X0: $i] :
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_40046,c_103]) ).
tcf(c_40205,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_39774,c_23218]) ).
tcf(c_40338,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_39775,c_22361]) ).
tcf(c_40423,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_649,c_652]) ).
tcf(c_40542,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c10,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_661,c_627]) ).
tcf(c_40835,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_672,c_669]) ).
tcf(c_40857,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_673,c_671]) ).
tcf(c_40879,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_674,c_664]) ).
tcf(c_41046,plain,
multiply(iPr_def_28,sk_c1) = identity,
inference(superposition,[status(thm)],[c_640,c_104]) ).
tcf(c_41199,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(sk_c10,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_684,c_627]) ).
tcf(c_41501,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_692,c_689]) ).
tcf(c_41762,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_696,c_656]) ).
tcf(c_41945,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_24 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_636,c_644]) ).
tcf(c_41947,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_29 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_641,c_644]) ).
tcf(c_41959,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_29 )
| ( sk_c10 != iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_41947,c_640]) ).
tcf(c_41966,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_24 )
| ( sk_c10 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_41945,c_635]) ).
tcf(c_41999,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_24 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_636,c_645]) ).
tcf(c_42001,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_29 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_641,c_645]) ).
tcf(c_42013,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_29 )
| ( sk_c10 != iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_42001,c_640]) ).
tcf(c_42020,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_24 )
| ( sk_c10 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_41999,c_635]) ).
tcf(c_42053,plain,
( ~ iPr_def_11
| ( sk_c10 != iPr_def_27 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_639,c_646]) ).
tcf(c_42080,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_17 )
| ( sk_c10 != iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_42053,c_629]) ).
tcf(c_42158,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_26 )
| ( inverse(sk_c3) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_638,c_647]) ).
tcf(c_42175,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_25 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_42158,c_637]) ).
tcf(c_42248,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_104,c_105]) ).
tcf(c_42805,plain,
! [X0: $i] : multiply(iPr_def_28,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_41046,c_105]) ).
tcf(c_42806,plain,
! [X0: $i] : multiply(iPr_def_28,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_42805,c_103]) ).
tcf(c_43984,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_28,iPr_def_29) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_674,c_41199]) ).
tcf(c_44127,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_40879,c_40542]) ).
tcf(c_44709,plain,
multiply(iPr_def_28,iPr_def_29) = sk_c10,
inference(superposition,[status(thm)],[c_641,c_42806]) ).
tcf(c_46060,plain,
( ( iPr_def_27 = iPr_def_29 )
| ( iPr_def_22 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_40072,c_31793]) ).
tcf(c_46523,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_46525,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_47070,plain,
( ( sk_c9 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_15 )
| ( sk_c9 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1592]) ).
tcf(c_47233,plain,
( ( inverse(sk_c2) = iPr_def_15 )
| ( iPr_def_15 != sk_c9 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_3824]) ).
tcf(c_48565,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_15 )
| ( iPr_def_17 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11533]) ).
tcf(c_48734,plain,
( ( iPr_def_24 = iPr_def_17 )
| ( iPr_def_24 != iPr_def_15 )
| ( iPr_def_17 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11534]) ).
tcf(c_48736,plain,
( ( multiply(identity,iPr_def_15) = iPr_def_17 )
| ( iPr_def_17 != iPr_def_15 )
| ( multiply(identity,iPr_def_15) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11534]) ).
tcf(c_48748,plain,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_24 != iPr_def_15 )
| ( sk_c9 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11538]) ).
tcf(c_48941,plain,
( ( inverse(sk_c2) = sk_c9 )
| ( sk_c9 != iPr_def_24 )
| ( inverse(sk_c2) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1432]) ).
tcf(c_48957,plain,
( ( inverse(sk_c2) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_17 )
| ( inverse(sk_c2) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_15157]) ).
tcf(c_48958,plain,
( ( inverse(sk_c2) = iPr_def_24 )
| ( iPr_def_24 != iPr_def_15 )
| ( inverse(sk_c2) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11539]) ).
tcf(c_49005,plain,
( ( inverse(sk_c2) = multiply(identity,iPr_def_15) )
| ( inverse(sk_c2) != iPr_def_17 )
| ( multiply(identity,iPr_def_15) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_15157]) ).
tcf(c_49009,plain,
( ( inverse(sk_c2) = sk_c9 )
| ( sk_c9 != multiply(identity,iPr_def_15) )
| ( inverse(sk_c2) != multiply(identity,iPr_def_15) ) ),
inference(instantiation,[status(thm)],[c_4161]) ).
tcf(c_49765,plain,
( ( iPr_def_15 = iPr_def_27 )
| ~ iPr_def_11
| ( sk_c10 != sk_c9 )
| ( inverse(iPr_def_24) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_24103,c_646]) ).
tcf(c_50000,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c5 = sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_19906,c_26075]) ).
tcf(c_50019,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(sk_c6,sk_c8) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_50000,c_634]) ).
tcf(c_50082,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c3 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_21015,c_16283]) ).
tcf(c_50126,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_22) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_50082,c_637]) ).
tcf(c_50240,plain,
( ( sk_c10 = iPr_def_23 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_43984,c_44709]) ).
tcf(c_50295,plain,
( ( iPr_def_23 = iPr_def_28 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_50240,c_40857]) ).
tcf(c_50726,plain,
( ( multiply(identity,sk_c9) = inverse(sk_c4) )
| ( inverse(sk_c4) != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_3757]) ).
tcf(c_50760,plain,
( ( inverse(sk_c4) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_23 )
| ( inverse(sk_c4) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_15256]) ).
tcf(c_50761,plain,
( ( inverse(sk_c4) = iPr_def_24 )
| ( iPr_def_24 != iPr_def_15 )
| ( inverse(sk_c4) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11539]) ).
tcf(c_51018,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c3 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_50126,c_16283]) ).
tcf(c_51385,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c4 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_22858,c_50126]) ).
tcf(c_51386,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c4 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22858,c_21015]) ).
tcf(c_51809,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_51385,c_5236]) ).
tcf(c_51833,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_51385,c_635]) ).
tcf(c_51836,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c3 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_51833,c_16280]) ).
tcf(c_51845,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_51809,c_5707]) ).
tcf(c_51902,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_22,sk_c10) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_51386,c_636]) ).
tcf(c_52397,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_51845,c_37689]) ).
tcf(c_52430,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_51845,c_5093]) ).
tcf(c_52490,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c10 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_52430,c_5690]) ).
tcf(c_53371,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_29656,c_24998]) ).
tcf(c_53462,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_17 )
| ( inverse(X0) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_53463,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c11 )
| ( sk_c11 != iPr_def_17 )
| ( inverse(X0) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1460]) ).
tcf(c_53465,plain,
( ( inverse(sk_c10) = sk_c11 )
| ( sk_c11 != iPr_def_17 )
| ( inverse(sk_c10) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_53463]) ).
tcf(c_53466,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != iPr_def_17 )
| ( inverse(sk_c10) != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_53462]) ).
tcf(c_53473,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_53479,plain,
( ( sk_c10 = sk_c11 )
| ( sk_c11 != iPr_def_17 )
| ( sk_c10 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_53473]) ).
tcf(c_53598,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_29898,c_3066]) ).
tcf(c_53604,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c10 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_29898,c_5750]) ).
tcf(c_53612,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_29898,c_5752]) ).
tcf(c_54723,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != inverse(sk_c2) )
| ( inverse(X0) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_4648]) ).
tcf(c_54724,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != inverse(sk_c2) )
| ( inverse(X0) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_54725,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != inverse(sk_c2) )
| ( inverse(sk_c10) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_54724]) ).
tcf(c_54726,plain,
( ( sk_c10 = inverse(sk_c10) )
| ( sk_c10 != inverse(sk_c2) )
| ( inverse(sk_c10) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_54723]) ).
tcf(c_55223,plain,
( ( iPr_def_23 = iPr_def_26 )
| ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_53371,c_23893]) ).
tcf(c_55449,plain,
( ( iPr_def_18 = iPr_def_21 )
| ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_53598,c_23893]) ).
tcf(c_55492,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_53598,c_1737]) ).
tcf(c_55775,plain,
( ( sk_c11 = inverse(sk_c4) )
| ( sk_c11 != iPr_def_23 )
| ( inverse(sk_c4) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_15255]) ).
tcf(c_55776,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != inverse(sk_c4) )
| ( X0 != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_55781,plain,
( ( sk_c10 = sk_c11 )
| ( sk_c11 != inverse(sk_c4) )
| ( sk_c10 != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_55776]) ).
tcf(c_55784,plain,
( ( multiply(identity,sk_c9) = inverse(sk_c4) )
| ( inverse(sk_c4) != iPr_def_23 )
| ( multiply(identity,sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_15255]) ).
tcf(c_55787,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c9) )
| ( X0 != inverse(sk_c4) )
| ( multiply(identity,sk_c9) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_1503]) ).
tcf(c_55788,plain,
( ( sk_c10 = multiply(identity,sk_c9) )
| ( sk_c10 != inverse(sk_c4) )
| ( multiply(identity,sk_c9) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_55787]) ).
tcf(c_56796,plain,
multiply(identity,iPr_def_25) = iPr_def_25,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_56800,plain,
( ( sk_c11 = inverse(sk_c3) )
| ( sk_c11 != iPr_def_25 )
| ( inverse(sk_c3) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_15260]) ).
tcf(c_58255,plain,
( ( iPr_def_24 = inverse(sk_c1) )
| ( iPr_def_24 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_15265]) ).
tcf(c_58256,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_24 != inverse(sk_c1) )
| ( iPr_def_15 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1869]) ).
tcf(c_58260,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c9) )
| ( X0 != inverse(sk_c1) )
| ( multiply(identity,sk_c9) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1503]) ).
tcf(c_58261,plain,
( ( sk_c10 = multiply(identity,sk_c9) )
| ( sk_c10 != inverse(sk_c1) )
| ( multiply(identity,sk_c9) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_58260]) ).
tcf(c_58281,plain,
! [X0: $i] :
( ( X0 = multiply(identity,multiply(identity,sk_c9)) )
| ( X0 != inverse(sk_c1) )
| ( multiply(identity,multiply(identity,sk_c9)) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1922]) ).
tcf(c_58282,plain,
( ( sk_c10 = multiply(identity,multiply(identity,sk_c9)) )
| ( sk_c10 != inverse(sk_c1) )
| ( multiply(identity,multiply(identity,sk_c9)) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_58281]) ).
tcf(c_58284,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_4648]) ).
tcf(c_58285,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1861]) ).
tcf(c_58286,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != inverse(sk_c1) )
| ( inverse(sk_c10) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_58285]) ).
tcf(c_58287,plain,
( ( sk_c10 = inverse(sk_c10) )
| ( sk_c10 != inverse(sk_c1) )
| ( inverse(sk_c10) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_58284]) ).
tcf(c_60185,plain,
( ( sk_c11 = multiply(identity,iPr_def_29) )
| ( sk_c11 != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_27831]) ).
tcf(c_60186,plain,
multiply(identity,iPr_def_29) = iPr_def_29,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_60359,plain,
( ( iPr_def_15 = inverse(sk_c1) )
| ( iPr_def_15 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_15265]) ).
tcf(c_60743,plain,
( ( identity = iPr_def_17 )
| ( iPr_def_17 != iPr_def_24 )
| ( identity != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_37865]) ).
tcf(c_60746,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1727]) ).
tcf(c_60747,plain,
( ( sk_c10 = identity )
| ( identity != iPr_def_17 )
| ( sk_c10 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_60746]) ).
tcf(c_61120,plain,
( ( iPr_def_22 = sk_c11 )
| ( iPr_def_22 != iPr_def_22 )
| ( sk_c11 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_46523]) ).
tcf(c_61121,plain,
iPr_def_22 = iPr_def_22,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_61137,plain,
( ( iPr_def_20 = sk_c11 )
| ( iPr_def_20 != iPr_def_20 )
| ( sk_c11 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_46525]) ).
tcf(c_61138,plain,
iPr_def_20 = iPr_def_20,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_61207,plain,
iPr_def_25 = iPr_def_25,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_61218,plain,
iPr_def_29 = iPr_def_29,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_61503,plain,
( ( inverse(sk_c1) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_15266]) ).
tcf(c_61507,plain,
( ( iPr_def_17 = inverse(sk_c1) )
| ( iPr_def_17 != iPr_def_15 )
| ( inverse(sk_c1) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11533]) ).
tcf(c_61509,plain,
( ( multiply(identity,multiply(identity,sk_c9)) = inverse(sk_c1) )
| ( inverse(sk_c1) != iPr_def_15 )
| ( multiply(identity,multiply(identity,sk_c9)) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11528]) ).
tcf(c_61511,plain,
( ( multiply(identity,sk_c9) = inverse(sk_c1) )
| ( inverse(sk_c1) != iPr_def_15 )
| ( multiply(identity,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_10883]) ).
tcf(c_61764,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( identity = iPr_def_24 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_31809,c_6954]) ).
tcf(c_62066,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_32493,c_3107]) ).
tcf(c_62072,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_32493,c_5764]) ).
tcf(c_62080,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_32493,c_5766]) ).
tcf(c_62181,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_32603,c_3165]) ).
tcf(c_63380,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_42248,c_103]) ).
tcf(c_63407,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_104,c_63380]) ).
tcf(c_63408,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_105,c_63380]) ).
tcf(c_63628,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_63380,c_63380]) ).
tcf(c_64810,plain,
! [X0: $i] :
( ( X0 = multiply(identity,identity) )
| ( X0 != identity )
| ( multiply(identity,identity) != identity ) ),
inference(instantiation,[status(thm)],[c_28812]) ).
tcf(c_64811,plain,
( ( sk_c10 = multiply(identity,identity) )
| ( sk_c10 != identity )
| ( multiply(identity,identity) != identity ) ),
inference(instantiation,[status(thm)],[c_64810]) ).
tcf(c_65079,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_62066,c_23893]) ).
tcf(c_65128,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_29 )
| ( sk_c11 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_62066,c_683]) ).
tcf(c_65129,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_29 )
| ( sk_c11 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_62066,c_681]) ).
tcf(c_65722,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_62072,c_1412]) ).
tcf(c_66002,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(identity) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_62080,c_640]) ).
tcf(c_66003,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_66002,c_15521]) ).
tcf(c_66624,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c11 )
| ( sk_c11 != inverse(sk_c3) )
| ( inverse(X0) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_1567]) ).
tcf(c_66625,plain,
( ( inverse(sk_c10) = sk_c11 )
| ( sk_c11 != inverse(sk_c3) )
| ( inverse(sk_c10) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_66624]) ).
tcf(c_67071,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_65129,c_65128]) ).
tcf(c_67174,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_26) = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_6106,c_1590,c_1804,c_1805,c_2871,c_3816,c_6339,c_10228]) ).
tcf(c_67182,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_21011,c_67174]) ).
tcf(c_67197,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_67182,c_5511]) ).
tcf(c_67667,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_29 )
| ( sk_c11 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_62181,c_686]) ).
tcf(c_67669,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_29 )
| ( sk_c11 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_62181,c_683]) ).
tcf(c_68247,plain,
! [X0: $i] :
( ( inverse(sk_c3) = inverse(X0) )
| ( inverse(sk_c3) != inverse(sk_c3) )
| ( inverse(X0) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_22829]) ).
tcf(c_68248,plain,
( ( inverse(sk_c3) = inverse(sk_c10) )
| ( inverse(sk_c3) != inverse(sk_c3) )
| ( inverse(sk_c10) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_68247]) ).
tcf(c_69472,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_67669,c_67667]) ).
tcf(c_69923,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_28) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_66003,c_15521]) ).
tcf(c_69926,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_69923,c_27653]) ).
tcf(c_70028,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_67071,c_65722]) ).
tcf(c_70304,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_67197,c_692]) ).
tcf(c_70310,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_67197,c_634]) ).
tcf(c_70315,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_67197,c_652]) ).
tcf(c_70322,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_22,sk_c10) = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_70310,c_11684]) ).
tcf(c_70411,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_63407,c_63628]) ).
tcf(c_70683,plain,
( ( iPr_def_18 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c11 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_40835,c_41959]) ).
tcf(c_71575,plain,
( ( identity = iPr_def_22 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_40093,c_20925]) ).
tcf(c_71776,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_28,sk_c10) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_69926,c_641]) ).
tcf(c_71815,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_41966,c_2711,c_2704,c_7721,c_9589]) ).
tcf(c_71836,plain,
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_13
| ( iPr_def_24 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_686,c_71815]) ).
tcf(c_71838,plain,
( ( sk_c11 = iPr_def_22 )
| ~ iPr_def_13
| ( iPr_def_24 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_683,c_71815]) ).
tcf(c_71839,plain,
( ( sk_c11 = iPr_def_20 )
| ~ iPr_def_13
| ( iPr_def_24 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_681,c_71815]) ).
tcf(c_71842,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_13
| ( iPr_def_20 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_671,c_71815]) ).
tcf(c_72552,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_29 ) ),
inference(global_subsumption_just,[status(thm)],[c_42013,c_3386,c_3379,c_7721,c_7969]) ).
tcf(c_72559,plain,
( ( iPr_def_18 = iPr_def_21 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_41501,c_72552]) ).
tcf(c_72562,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_697,c_72552]) ).
tcf(c_72565,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_694,c_72552]) ).
tcf(c_73165,plain,
( ( identity = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_71575,c_23893]) ).
tcf(c_73167,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_71575,c_19835]) ).
tcf(c_73683,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_70304,c_1590,c_1804,c_1805,c_2871,c_3816,c_70315,c_70304]) ).
tcf(c_73710,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_73683,c_4912]) ).
tcf(c_74019,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_42020,c_1804,c_1805,c_1912,c_1913,c_2320,c_3386,c_4221,c_6771,c_7947,c_11535,c_17654,c_23466,c_60743,c_60747,c_61764,c_72565]) ).
tcf(c_74029,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_697,c_74019]) ).
tcf(c_74031,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_695,c_74019]) ).
tcf(c_74037,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_675,c_74019]) ).
tcf(c_74039,plain,
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_665,c_74019]) ).
tcf(c_74226,plain,
( ( sk_c11 = multiply(identity,iPr_def_25) )
| ( sk_c11 != iPr_def_25 )
| ( multiply(identity,iPr_def_25) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_27827]) ).
tcf(c_74748,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_18) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_73710,c_16282]) ).
tcf(c_74774,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c3 = sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_74748,c_26075]) ).
tcf(c_74899,plain,
! [X0: $i] :
( ( sk_c9 = identity )
| ( identity != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_74907,plain,
( ( sk_c9 = identity )
| ( identity != sk_c10 )
| ( sk_c9 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_74899]) ).
tcf(c_75618,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_690,c_50019]) ).
tcf(c_75620,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_29 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_680,c_50019]) ).
tcf(c_75626,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_650,c_50019]) ).
tcf(c_76068,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_74774,c_51836]) ).
tcf(c_76069,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_74774,c_51018]) ).
tcf(c_76092,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(sk_c6) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_74774,c_637]) ).
tcf(c_76099,plain,
( ( iPr_def_18 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_76092,c_630]) ).
tcf(c_76391,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_76068,c_26082]) ).
tcf(c_76656,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_76069,c_688]) ).
tcf(c_76666,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_76069,c_648]) ).
tcf(c_76942,plain,
( ( iPr_def_18 = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c10 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_40423,c_42080]) ).
tcf(c_76943,plain,
( ( sk_c9 = iPr_def_17 )
| ~ iPr_def_11
| ( iPr_def_17 != iPr_def_24 )
| ( sk_c10 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_655,c_42080]) ).
tcf(c_76944,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_11
| ( sk_c10 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_654,c_42080]) ).
tcf(c_77713,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_10
| ( sk_c10 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_41762,c_42175]) ).
tcf(c_77724,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_10
| ( sk_c10 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_676,c_42175]) ).
tcf(c_77727,plain,
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_10
| ( sk_c10 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_666,c_42175]) ).
tcf(c_77931,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_76656,c_1590,c_1804,c_1805,c_2871,c_3816,c_76666,c_76656]) ).
tcf(c_77946,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_77931,c_76099]) ).
tcf(c_78027,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_78032,plain,
( ( sk_c10 = sk_c11 )
| ( sk_c11 != iPr_def_24 )
| ( sk_c10 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_78027]) ).
tcf(c_78048,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2095]) ).
tcf(c_78049,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1727]) ).
tcf(c_78050,plain,
( ( sk_c10 = identity )
| ( identity != iPr_def_24 )
| ( sk_c10 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_78049]) ).
tcf(c_78051,plain,
( ( identity = sk_c10 )
| ( identity != iPr_def_24 )
| ( sk_c10 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_78048]) ).
tcf(c_78183,plain,
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_71836,c_2704,c_7988,c_9673]) ).
tcf(c_78191,plain,
( ( sk_c11 = iPr_def_22 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_71838,c_2704,c_7658,c_9454]) ).
tcf(c_78197,plain,
( ( sk_c11 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_71839,c_2704,c_7475,c_8994]) ).
tcf(c_78308,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c10 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_51902,c_21017]) ).
tcf(c_78500,plain,
( ( iPr_def_15 != iPr_def_24 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_74029,c_1913,c_30304,c_47070,c_74019,c_74031]) ).
tcf(c_78501,plain,
( ~ iPr_def_12
| ( iPr_def_15 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_78500]) ).
tcf(c_78556,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_76944,c_6891,c_76944]) ).
tcf(c_78574,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_77724,c_8484,c_77724]) ).
tcf(c_78580,plain,
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_77727,c_7164,c_77727]) ).
tcf(c_78864,plain,
( ( multiply(identity,sk_c9) = iPr_def_23 )
| ( iPr_def_23 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_3757]) ).
tcf(c_79739,plain,
( ( sk_c11 = multiply(identity,sk_c9) )
| ( sk_c11 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_3758]) ).
tcf(c_79747,plain,
( ( identity = multiply(identity,sk_c9) )
| ( identity != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_3758]) ).
tcf(c_79780,plain,
( ( sk_c2 = multiply(identity,sk_c9) )
| ( sk_c2 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_3758]) ).
tcf(c_79799,plain,
( ( sk_c1 = multiply(identity,sk_c9) )
| ( sk_c1 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_3758]) ).
tcf(c_80747,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_80753,plain,
( ( sk_c10 = sk_c11 )
| ( sk_c11 != sk_c9 )
| ( sk_c10 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_80747]) ).
tcf(c_80862,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c9 )
| ( sk_c9 != X0 )
| ( inverse(sk_c1) != X0 ) ),
inference(instantiation,[status(thm)],[c_1354]) ).
tcf(c_80863,plain,
( ( inverse(sk_c1) = sk_c9 )
| ( sk_c9 != sk_c10 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_80862]) ).
tcf(c_83540,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_19477]) ).
tcf(c_83541,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2473]) ).
tcf(c_83545,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c11 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_83541]) ).
tcf(c_83546,plain,
( ( sk_c10 = sk_c11 )
| ( sk_c11 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_83540]) ).
tcf(c_83565,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2095]) ).
tcf(c_83566,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1727]) ).
tcf(c_83568,plain,
( ( sk_c10 = identity )
| ( identity != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_83566]) ).
tcf(c_83569,plain,
( ( identity = sk_c10 )
| ( identity != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_83565]) ).
tcf(c_83583,plain,
! [X0: $i] :
( ( X0 = sk_c2 )
| ( sk_c2 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_12215]) ).
tcf(c_83585,plain,
( ( sk_c10 = sk_c2 )
| ( sk_c2 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_83583]) ).
tcf(c_83620,plain,
! [X0: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_17191]) ).
tcf(c_83622,plain,
( ( sk_c10 = sk_c1 )
| ( sk_c1 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_83620]) ).
tcf(c_84039,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_6270,c_32603]) ).
tcf(c_84505,plain,
( ( sk_c11 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_29 )
| ( sk_c11 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_27831]) ).
tcf(c_87509,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_6272,c_32603]) ).
tcf(c_87572,plain,
( ( sk_c2 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_17 )
| ( sk_c2 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_30668]) ).
tcf(c_87949,plain,
( ( sk_c11 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_17 )
| ( sk_c11 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_30668]) ).
tcf(c_88034,plain,
( ( sk_c1 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_17 )
| ( sk_c1 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_30668]) ).
tcf(c_88162,plain,
( ( iPr_def_17 = inverse(sk_c1) )
| ( iPr_def_17 != sk_c9 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_27852]) ).
tcf(c_88176,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_27854]) ).
tcf(c_88178,plain,
( ( inverse(sk_c10) = iPr_def_17 )
| ( iPr_def_17 != inverse(sk_c1) )
| ( inverse(sk_c10) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_88176]) ).
tcf(c_88353,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_75618,c_10620,c_30308,c_52397]) ).
tcf(c_88384,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( sk_c10 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_88353,c_23590]) ).
tcf(c_88755,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_75620,c_629,c_1590,c_2871,c_4655,c_4656,c_15162,c_21543,c_21544,c_47233,c_75626,c_88353]) ).
tcf(c_88778,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_29 )
| ( multiply(iPr_def_19,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_679,c_88755]) ).
tcf(c_88784,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_19,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_649,c_88755]) ).
tcf(c_89207,plain,
( ( sk_c11 = sk_c9 )
| ( sk_c9 != iPr_def_15 )
| ( sk_c11 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1591]) ).
tcf(c_89489,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_84039,c_1518]) ).
tcf(c_89508,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_29,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_84039,c_627]) ).
tcf(c_90025,plain,
! [X0: $i] :
( ( X0 = sk_c2 )
| ( sk_c2 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_12215]) ).
tcf(c_90026,plain,
( ( sk_c10 = sk_c2 )
| ( sk_c2 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_90025]) ).
tcf(c_91402,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_89489,c_69472]) ).
tcf(c_92030,plain,
( ( sk_c11 = multiply(identity,sk_c9) )
| ( sk_c11 != iPr_def_15 )
| ( multiply(identity,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_10884]) ).
tcf(c_92031,plain,
( ( identity = multiply(identity,sk_c9) )
| ( identity != iPr_def_15 )
| ( multiply(identity,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_10884]) ).
tcf(c_92293,plain,
( ( sk_c1 = multiply(identity,multiply(identity,sk_c9)) )
| ( sk_c1 != iPr_def_15 )
| ( multiply(identity,multiply(identity,sk_c9)) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11529]) ).
tcf(c_92294,plain,
! [X0: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != multiply(identity,multiply(identity,sk_c9)) )
| ( X0 != multiply(identity,multiply(identity,sk_c9)) ) ),
inference(instantiation,[status(thm)],[c_17191]) ).
tcf(c_92295,plain,
( ( sk_c10 = sk_c1 )
| ( sk_c1 != multiply(identity,multiply(identity,sk_c9)) )
| ( sk_c10 != multiply(identity,multiply(identity,sk_c9)) ) ),
inference(instantiation,[status(thm)],[c_92294]) ).
tcf(c_93249,plain,
( ( sk_c11 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_15 )
| ( sk_c11 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11534]) ).
tcf(c_93270,plain,
( ( sk_c2 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_15 )
| ( sk_c2 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11534]) ).
tcf(c_93277,plain,
( ( sk_c1 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_15 )
| ( sk_c1 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_11534]) ).
tcf(c_93538,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_19,iPr_def_18) = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_88778,c_629,c_1590,c_2871,c_4655,c_4656,c_15162,c_21543,c_21544,c_47233,c_88353,c_88784]) ).
tcf(c_93547,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_19,iPr_def_16) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_77946,c_93538]) ).
tcf(c_93561,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c8 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_93547,c_5499]) ).
tcf(c_93819,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c10 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_6306,c_32952]) ).
tcf(c_94778,plain,
( ( sk_c2 = multiply(identity,sk_c9) )
| ( sk_c2 != iPr_def_15 )
| ( multiply(identity,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_10884]) ).
tcf(c_94883,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c11 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_93561,c_682]) ).
tcf(c_94892,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_93561,c_652]) ).
tcf(c_95414,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_16)) = sk_c8,
inference(superposition,[status(thm)],[c_628,c_63408]) ).
tcf(c_97390,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_29,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_93819,c_627]) ).
tcf(c_97561,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_94883,c_629,c_1590,c_2871,c_4655,c_4656,c_15162,c_21543,c_21544,c_47233,c_88353,c_94892]) ).
tcf(c_97608,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_97561,c_38119]) ).
tcf(c_99083,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c10 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_70322,c_21017]) ).
tcf(c_99923,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_6308,c_32952]) ).
tcf(c_100022,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_677,c_71776]) ).
tcf(c_100023,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_28,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_674,c_71776]) ).
tcf(c_100208,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c11 )
| ( sk_c11 != X1 )
| ( multiply(inverse(X0),sk_c10) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100209,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c11 )
| ( sk_c11 != sk_c10 )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_100208]) ).
tcf(c_100211,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100212,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100220,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100226,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100229,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100235,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100236,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c11 )
| ( sk_c11 != iPr_def_29 )
| ( multiply(inverse(X0),sk_c10) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100208]) ).
tcf(c_100237,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c11 )
| ( sk_c11 != iPr_def_29 )
| ( multiply(inverse(sk_c10),sk_c10) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100236]) ).
tcf(c_100238,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(identity,sk_c11) )
| ( X0 != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100244,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100220]) ).
tcf(c_100247,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100220]) ).
tcf(c_100253,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( iPr_def_20 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100259,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_22 )
| ( iPr_def_22 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100265,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_25 )
| ( iPr_def_25 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100271,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_29 )
| ( iPr_def_29 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100302,plain,
( ( sk_c11 = multiply(identity,multiply(identity,sk_c11)) )
| ( sk_c11 != multiply(identity,sk_c11) )
| ( multiply(identity,multiply(identity,sk_c11)) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_100238]) ).
tcf(c_100303,plain,
multiply(identity,multiply(identity,sk_c11)) = multiply(identity,sk_c11),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_100307,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != multiply(identity,sk_c11) )
| ( multiply(X0,X1) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_100238]) ).
tcf(c_100308,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,sk_c11) )
| ( X1 != sk_c11 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_100309,plain,
( ( sk_c11 = multiply(sk_c10,sk_c10) )
| ( sk_c11 != multiply(identity,sk_c11) )
| ( multiply(sk_c10,sk_c10) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_100307]) ).
tcf(c_100310,plain,
( ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c11) )
| ( sk_c10 != identity )
| ( sk_c10 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100308]) ).
tcf(c_100335,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(identity,iPr_def_25) )
| ( X0 != multiply(identity,iPr_def_25) ) ),
inference(instantiation,[status(thm)],[c_100220]) ).
tcf(c_100336,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(identity,iPr_def_25) )
| ( X0 != multiply(identity,iPr_def_25) ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100344,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(identity,iPr_def_29) )
| ( X0 != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100359,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_20 = X0 )
| ( iPr_def_20 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100366,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_22 = X0 )
| ( iPr_def_22 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100369,plain,
! [X0: $i] :
( ( X0 = iPr_def_22 )
| ( iPr_def_22 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100259]) ).
tcf(c_100373,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_25 = X0 )
| ( iPr_def_25 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100374,plain,
! [X0: $i] :
( ( X0 = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c3) )
| ( X0 != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_100265]) ).
tcf(c_100380,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_29 = X0 )
| ( iPr_def_29 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100389,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c11) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c11) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100397,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(identity,multiply(identity,sk_c11)) )
| ( X0 != multiply(identity,multiply(identity,sk_c11)) ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_100425,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100534,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,iPr_def_25) )
| ( X1 != iPr_def_25 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_100541,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,iPr_def_29) )
| ( X1 != X0 )
| ( multiply(identity,iPr_def_29) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100543,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != multiply(identity,iPr_def_29) )
| ( multiply(X0,X1) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_100344]) ).
tcf(c_100544,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,iPr_def_29) )
| ( X1 != iPr_def_29 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_100545,plain,
( ( sk_c11 = multiply(sk_c10,sk_c10) )
| ( sk_c11 != multiply(identity,iPr_def_29) )
| ( multiply(sk_c10,sk_c10) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_100543]) ).
tcf(c_100546,plain,
( ( multiply(sk_c10,sk_c10) = multiply(identity,iPr_def_29) )
| ( sk_c10 != iPr_def_29 )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_100544]) ).
tcf(c_100550,plain,
( ( sk_c11 = multiply(multiply(identity,identity),sk_c11) )
| ( sk_c11 != multiply(identity,multiply(identity,sk_c11)) )
| ( multiply(multiply(identity,identity),sk_c11) != multiply(identity,multiply(identity,sk_c11)) ) ),
inference(instantiation,[status(thm)],[c_100397]) ).
tcf(c_100551,plain,
multiply(multiply(identity,identity),sk_c11) = multiply(identity,multiply(identity,sk_c11)),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_100607,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c5,sk_c8) )
| ( X1 != X0 )
| ( multiply(sk_c5,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100630,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c1,sk_c10) )
| ( X1 != sk_c10 )
| ( X0 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_100632,plain,
( ( multiply(sk_c10,sk_c10) = multiply(sk_c1,sk_c10) )
| ( sk_c10 != sk_c1 )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_100630]) ).
tcf(c_100641,plain,
! [X0: $i] :
( ( iPr_def_20 = X0 )
| ( iPr_def_20 != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100359]) ).
tcf(c_100646,plain,
! [X0: $i] :
( ( iPr_def_22 = X0 )
| ( iPr_def_22 != multiply(sk_c5,sk_c8) )
| ( X0 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_100366]) ).
tcf(c_100650,plain,
! [X0: $i] :
( ( iPr_def_22 = X0 )
| ( iPr_def_22 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100366]) ).
tcf(c_100660,plain,
! [X0: $i] :
( ( iPr_def_25 = X0 )
| ( iPr_def_25 != iPr_def_25 )
| ( X0 != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100373]) ).
tcf(c_100667,plain,
! [X0: $i] :
( ( iPr_def_29 = X0 )
| ( iPr_def_29 != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100380]) ).
tcf(c_100668,plain,
( ( iPr_def_29 = sk_c10 )
| ( iPr_def_29 != iPr_def_29 )
| ( sk_c10 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100667]) ).
tcf(c_100679,plain,
! [X0: $i] :
( ( multiply(identity,sk_c11) = X0 )
| ( X0 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100389]) ).
tcf(c_100680,plain,
( ( multiply(identity,sk_c11) = sk_c10 )
| ( sk_c10 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100679]) ).
tcf(c_100815,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_100834,plain,
! [X0: $i] :
( ( iPr_def_22 = X0 )
| ( iPr_def_22 != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100366]) ).
tcf(c_100847,plain,
! [X0: $i] :
( ( iPr_def_20 = X0 )
| ( iPr_def_20 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100359]) ).
tcf(c_100848,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ( iPr_def_20 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100253]) ).
tcf(c_100861,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ( iPr_def_20 != iPr_def_25 )
| ( X0 != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100253]) ).
tcf(c_100867,plain,
! [X0: $i] :
( ( X0 = iPr_def_22 )
| ( iPr_def_22 != iPr_def_25 )
| ( X0 != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100259]) ).
tcf(c_101033,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,iPr_def_29) = X1 )
| ( X1 != X0 )
| ( multiply(identity,iPr_def_29) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_101035,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,iPr_def_29) = multiply(X0,X1) )
| ( iPr_def_29 != X1 )
| ( identity != X0 ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_101037,plain,
( ( multiply(identity,iPr_def_29) = multiply(sk_c10,sk_c10) )
| ( iPr_def_29 != sk_c10 )
| ( identity != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_101035]) ).
tcf(c_101102,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(multiply(identity,identity),sk_c11) )
| ( X0 != multiply(multiply(identity,identity),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_100220]) ).
tcf(c_101103,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(multiply(identity,identity),sk_c11) )
| ( X0 != multiply(multiply(identity,identity),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_101139,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_22 != iPr_def_20 )
| ( iPr_def_20 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100641]) ).
tcf(c_101150,plain,
( ( iPr_def_22 = iPr_def_20 )
| ( iPr_def_22 != iPr_def_22 )
| ( iPr_def_20 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100650]) ).
tcf(c_101159,plain,
( ( iPr_def_25 = iPr_def_22 )
| ( iPr_def_25 != iPr_def_25 )
| ( iPr_def_22 != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100660]) ).
tcf(c_101160,plain,
( ( iPr_def_25 = iPr_def_20 )
| ( iPr_def_25 != iPr_def_25 )
| ( iPr_def_20 != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100660]) ).
tcf(c_101171,plain,
( ( iPr_def_29 = iPr_def_20 )
| ( iPr_def_29 != iPr_def_29 )
| ( iPr_def_20 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100667]) ).
tcf(c_101172,plain,
( ( iPr_def_29 = multiply(identity,iPr_def_29) )
| ( iPr_def_29 != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100667]) ).
tcf(c_101255,plain,
! [X0: $i] :
( ( X0 = multiply(identity,iPr_def_29) )
| ( X0 != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100541]) ).
tcf(c_101256,plain,
( ( sk_c10 = multiply(identity,iPr_def_29) )
| ( sk_c10 != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_101255]) ).
tcf(c_101364,plain,
( ( sk_c11 = multiply(sk_c1,sk_c10) )
| ( sk_c11 != iPr_def_29 )
| ( multiply(sk_c1,sk_c10) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100235]) ).
tcf(c_101382,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c3 )
| ( sk_c3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_101493,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c5,sk_c8) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c5,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_101541,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_101670,plain,
! [X0: $i] :
( ( X0 = iPr_def_29 )
| ( iPr_def_29 != multiply(identity,iPr_def_29) )
| ( X0 != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_100271]) ).
tcf(c_101738,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_25 != iPr_def_20 )
| ( iPr_def_22 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100834]) ).
tcf(c_101779,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( iPr_def_25 != iPr_def_22 )
| ( iPr_def_20 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100847]) ).
tcf(c_101791,plain,
( ( multiply(sk_c5,sk_c8) = iPr_def_20 )
| ( iPr_def_20 != iPr_def_22 )
| ( multiply(sk_c5,sk_c8) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100848]) ).
tcf(c_101832,plain,
( ( inverse(sk_c3) = iPr_def_20 )
| ( iPr_def_20 != iPr_def_25 )
| ( inverse(sk_c3) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100861]) ).
tcf(c_101859,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c3) )
| ( iPr_def_22 != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_100374]) ).
tcf(c_101867,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c11 )
| ( sk_c11 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_100208]) ).
tcf(c_101873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c10) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_101874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c11 )
| ( sk_c11 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c10) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_100208]) ).
tcf(c_101880,plain,
! [X0: $i] :
( ( sk_c11 = iPr_def_25 )
| ( iPr_def_25 != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_101882,plain,
! [X0: $i] :
( ( sk_c11 = identity )
| ( identity != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_101889,plain,
( ( sk_c11 = identity )
| ( identity != sk_c10 )
| ( sk_c11 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_101882]) ).
tcf(c_101900,plain,
! [X0: $i] :
( ( sk_c11 = sk_c3 )
| ( sk_c3 != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_101951,plain,
( ( identity = iPr_def_22 )
| ( iPr_def_22 != sk_c11 )
| ( identity != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100369]) ).
tcf(c_102060,plain,
( ( sk_c11 = iPr_def_29 )
| ( iPr_def_29 != multiply(identity,iPr_def_25) )
| ( sk_c11 != multiply(identity,iPr_def_25) ) ),
inference(instantiation,[status(thm)],[c_100336]) ).
tcf(c_102192,plain,
( ( sk_c11 = multiply(identity,iPr_def_25) )
| ( sk_c11 != iPr_def_20 )
| ( multiply(identity,iPr_def_25) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100226]) ).
tcf(c_102216,plain,
( ( sk_c11 = multiply(identity,iPr_def_25) )
| ( sk_c11 != iPr_def_22 )
| ( multiply(identity,iPr_def_25) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100229]) ).
tcf(c_102252,plain,
( ( identity = sk_c11 )
| ( identity != iPr_def_22 )
| ( sk_c11 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100244]) ).
tcf(c_102253,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100815]) ).
tcf(c_102254,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100425]) ).
tcf(c_102255,plain,
( ( sk_c10 = identity )
| ( identity != sk_c11 )
| ( sk_c10 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_102254]) ).
tcf(c_102256,plain,
( ( identity = sk_c10 )
| ( identity != sk_c11 )
| ( sk_c10 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_102253]) ).
tcf(c_102355,plain,
( ( identity = sk_c11 )
| ( identity != iPr_def_29 )
| ( sk_c11 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100247]) ).
tcf(c_102476,plain,
( ( identity = iPr_def_20 )
| ( iPr_def_20 != iPr_def_22 )
| ( identity != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100848]) ).
tcf(c_102496,plain,
( ( multiply(identity,iPr_def_25) = iPr_def_20 )
| ( iPr_def_20 != iPr_def_22 )
| ( multiply(identity,iPr_def_25) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100848]) ).
tcf(c_102584,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100815]) ).
tcf(c_102585,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100425]) ).
tcf(c_102586,plain,
( ( sk_c10 = identity )
| ( identity != iPr_def_22 )
| ( sk_c10 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_102585]) ).
tcf(c_102587,plain,
( ( identity = sk_c10 )
| ( identity != iPr_def_22 )
| ( sk_c10 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_102584]) ).
tcf(c_102604,plain,
( ( multiply(identity,iPr_def_25) = iPr_def_22 )
| ( iPr_def_22 != iPr_def_25 )
| ( multiply(identity,iPr_def_25) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100867]) ).
tcf(c_102653,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100425]) ).
tcf(c_102896,plain,
! [X0: $i] :
( ( iPr_def_22 = iPr_def_20 )
| ( iPr_def_22 != X0 )
| ( iPr_def_20 != X0 ) ),
inference(instantiation,[status(thm)],[c_100253]) ).
tcf(c_103064,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100815]) ).
tcf(c_103065,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100425]) ).
tcf(c_103067,plain,
( ( sk_c10 = identity )
| ( identity != iPr_def_29 )
| ( sk_c10 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_103065]) ).
tcf(c_103068,plain,
( ( identity = sk_c10 )
| ( identity != iPr_def_29 )
| ( sk_c10 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_103064]) ).
tcf(c_103069,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_29 )
| ( iPr_def_29 != X0 )
| ( iPr_def_20 != X0 ) ),
inference(instantiation,[status(thm)],[c_100271]) ).
tcf(c_103092,plain,
! [X0: $i] :
( ( multiply(identity,iPr_def_25) = iPr_def_29 )
| ( iPr_def_29 != X0 )
| ( multiply(identity,iPr_def_25) != X0 ) ),
inference(instantiation,[status(thm)],[c_100271]) ).
tcf(c_104339,plain,
( ( identity = multiply(identity,iPr_def_29) )
| ( identity != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_101255]) ).
tcf(c_104859,plain,
! [X0: $i] :
( ( multiply(identity,iPr_def_29) = X0 )
| ( X0 != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_101033]) ).
tcf(c_106165,plain,
! [X0: $i] :
( ( X0 = iPr_def_25 )
| ( iPr_def_25 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_100265]) ).
tcf(c_106167,plain,
( ( sk_c10 = iPr_def_25 )
| ( iPr_def_25 != identity )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_106165]) ).
tcf(c_106207,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = sk_c11 )
| ( sk_c11 != multiply(multiply(identity,identity),sk_c11) )
| ( multiply(X0,inverse(X0)) != multiply(multiply(identity,identity),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_101102]) ).
tcf(c_106218,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = sk_c11 )
| ( sk_c11 != X1 )
| ( multiply(X0,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_100220]) ).
tcf(c_106230,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = sk_c11 )
| ( sk_c11 != multiply(multiply(identity,identity),sk_c11) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(multiply(identity,identity),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_106207]) ).
tcf(c_107155,plain,
( ( iPr_def_20 = identity )
| ( iPr_def_20 != iPr_def_20 )
| ( identity != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100641]) ).
tcf(c_107243,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = multiply(multiply(identity,identity),sk_c11) )
| ( X0 != multiply(identity,identity) )
| ( inverse(X0) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_107244,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = multiply(multiply(identity,identity),sk_c11) )
| ( sk_c10 != multiply(identity,identity) )
| ( inverse(sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_107243]) ).
tcf(c_107275,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = multiply(identity,iPr_def_29) )
| ( multiply(identity,iPr_def_29) != X1 )
| ( multiply(X0,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_100541]) ).
tcf(c_107384,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = multiply(X0,inverse(X0)),
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_107386,plain,
multiply(sk_c10,inverse(sk_c10)) = multiply(sk_c10,inverse(sk_c10)),
inference(instantiation,[status(thm)],[c_107384]) ).
tcf(c_107387,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = X2 )
| ( X2 != X1 )
| ( multiply(X0,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_107388,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = sk_c11 )
| ( sk_c11 != multiply(X1,X2) )
| ( multiply(X0,inverse(X0)) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_106218]) ).
tcf(c_107389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = multiply(X2,X1) )
| ( X0 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_107390,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = sk_c11 )
| ( sk_c11 != multiply(sk_c10,sk_c10) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(sk_c10,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_107388]) ).
tcf(c_107391,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = multiply(sk_c10,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_107389]) ).
tcf(c_107393,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = identity )
| ( identity != X1 )
| ( multiply(X0,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_100425]) ).
tcf(c_107531,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c10),sk_c10) = X0 )
| ( X0 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_101873]) ).
tcf(c_107532,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c10 )
| ( sk_c10 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_107531]) ).
tcf(c_107574,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c10) = X1 )
| ( X1 != multiply(identity,iPr_def_29) )
| ( multiply(inverse(X0),sk_c10) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_101873]) ).
tcf(c_107575,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c10 )
| ( sk_c10 != multiply(identity,iPr_def_29) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_107574]) ).
tcf(c_107598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_107633,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = iPr_def_22 )
| ( iPr_def_22 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_100259]) ).
tcf(c_107647,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = iPr_def_29 )
| ( iPr_def_29 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_100271]) ).
tcf(c_107653,plain,
( ( inverse(sk_c10) = iPr_def_29 )
| ( iPr_def_29 != sk_c10 )
| ( inverse(sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_107647]) ).
tcf(c_107791,plain,
! [X0: $i] :
( ( sk_c3 = sk_c11 )
| ( sk_c3 != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_100220]) ).
tcf(c_108929,plain,
( ( iPr_def_22 = inverse(sk_c3) )
| ( iPr_def_22 != multiply(sk_c5,sk_c8) )
| ( inverse(sk_c3) != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_100646]) ).
tcf(c_108978,plain,
( ( sk_c11 = inverse(sk_c3) )
| ( sk_c11 != iPr_def_22 )
| ( inverse(sk_c3) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100229]) ).
tcf(c_108979,plain,
( ( sk_c11 = inverse(sk_c3) )
| ( sk_c11 != iPr_def_20 )
| ( inverse(sk_c3) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100226]) ).
tcf(c_109550,plain,
( ( sk_c11 = iPr_def_25 )
| ( iPr_def_25 != identity )
| ( sk_c11 != identity ) ),
inference(instantiation,[status(thm)],[c_101880]) ).
tcf(c_109553,plain,
( ( iPr_def_20 = identity )
| ( iPr_def_20 != sk_c11 )
| ( identity != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_102254]) ).
tcf(c_110358,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = iPr_def_29 )
| ( iPr_def_29 != multiply(identity,iPr_def_29) )
| ( multiply(X0,inverse(X0)) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_101670]) ).
tcf(c_110359,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = iPr_def_29 )
| ( iPr_def_29 != multiply(identity,iPr_def_29) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_110358]) ).
tcf(c_110446,plain,
( ( iPr_def_22 = identity )
| ( iPr_def_22 != iPr_def_22 )
| ( identity != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100650]) ).
tcf(c_110778,plain,
( ( sk_c11 = sk_c3 )
| ( sk_c3 != identity )
| ( sk_c11 != identity ) ),
inference(instantiation,[status(thm)],[c_101900]) ).
tcf(c_111614,plain,
( ( multiply(identity,iPr_def_25) = identity )
| ( identity != iPr_def_22 )
| ( multiply(identity,iPr_def_25) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_102585]) ).
tcf(c_111628,plain,
( ( iPr_def_25 = identity )
| ( iPr_def_25 != iPr_def_22 )
| ( identity != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_102585]) ).
tcf(c_113062,plain,
( ( sk_c3 = identity )
| ( identity != iPr_def_22 )
| ( sk_c3 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_102585]) ).
tcf(c_113404,plain,
( ( multiply(identity,iPr_def_25) = iPr_def_29 )
| ( iPr_def_29 != identity )
| ( multiply(identity,iPr_def_25) != identity ) ),
inference(instantiation,[status(thm)],[c_103092]) ).
tcf(c_113719,plain,
! [X0: $i] :
( ( X0 = sk_c3 )
| ( sk_c3 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_101382]) ).
tcf(c_113720,plain,
( ( sk_c10 = sk_c3 )
| ( sk_c3 != identity )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_113719]) ).
tcf(c_113744,plain,
( ( iPr_def_20 = iPr_def_29 )
| ( iPr_def_29 != identity )
| ( iPr_def_20 != identity ) ),
inference(instantiation,[status(thm)],[c_103069]) ).
tcf(c_113747,plain,
( ( iPr_def_22 = iPr_def_20 )
| ( iPr_def_22 != identity )
| ( iPr_def_20 != identity ) ),
inference(instantiation,[status(thm)],[c_102896]) ).
tcf(c_114007,plain,
( ( iPr_def_29 = multiply(identity,iPr_def_25) )
| ( iPr_def_29 != iPr_def_29 )
| ( multiply(identity,iPr_def_25) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100667]) ).
tcf(c_114495,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_107598]) ).
tcf(c_114504,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != sk_c11 )
| ( inverse(X0) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_107598]) ).
tcf(c_114518,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != sk_c11 )
| ( inverse(sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_114504]) ).
tcf(c_114530,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_29 )
| ( inverse(X0) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_107598]) ).
tcf(c_116731,plain,
! [X0: $i] :
( ( sk_c11 = multiply(X0,inverse(X0)) )
| ( sk_c11 != multiply(multiply(identity,identity),sk_c11) )
| ( multiply(X0,inverse(X0)) != multiply(multiply(identity,identity),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_101103]) ).
tcf(c_116751,plain,
( ( sk_c11 = multiply(sk_c10,inverse(sk_c10)) )
| ( sk_c11 != multiply(multiply(identity,identity),sk_c11) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(multiply(identity,identity),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_116731]) ).
tcf(c_116915,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = X1 )
| ( X1 != multiply(X0,inverse(X0)) )
| ( multiply(X0,inverse(X0)) != multiply(X0,inverse(X0)) ) ),
inference(instantiation,[status(thm)],[c_107387]) ).
tcf(c_117799,plain,
( ( inverse(sk_c3) = iPr_def_22 )
| ( iPr_def_22 != iPr_def_25 )
| ( inverse(sk_c3) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_107633]) ).
tcf(c_119318,plain,
! [X0: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_101541]) ).
tcf(c_119325,plain,
( ( sk_c10 = sk_c1 )
| ( sk_c1 != identity )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_119318]) ).
tcf(c_119568,plain,
( ( sk_c3 = sk_c11 )
| ( sk_c3 != sk_c3 )
| ( sk_c11 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_107791]) ).
tcf(c_119569,plain,
sk_c3 = sk_c3,
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_121027,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c10) = iPr_def_29 )
| ( iPr_def_29 != multiply(identity,iPr_def_29) )
| ( multiply(inverse(X0),sk_c10) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_107574]) ).
tcf(c_121035,plain,
( ( multiply(inverse(sk_c10),sk_c10) = iPr_def_29 )
| ( iPr_def_29 != multiply(identity,iPr_def_29) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_121027]) ).
tcf(c_123310,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c8) = X0 )
| ( X0 != identity )
| ( multiply(sk_c5,sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_101493]) ).
tcf(c_123312,plain,
( ( multiply(sk_c5,sk_c8) = identity )
| ( identity != iPr_def_20 )
| ( multiply(sk_c5,sk_c8) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_102653]) ).
tcf(c_123317,plain,
( ( multiply(sk_c5,sk_c8) = sk_c10 )
| ( sk_c10 != identity )
| ( multiply(sk_c5,sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_123310]) ).
tcf(c_126202,plain,
! [X0: $i,X1: $i] :
( ( inverse(sk_c3) = X1 )
| ( X1 != inverse(X0) )
| ( inverse(sk_c3) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_114495]) ).
tcf(c_126203,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( sk_c10 != inverse(sk_c10) )
| ( inverse(sk_c3) != inverse(sk_c10) ) ),
inference(instantiation,[status(thm)],[c_126202]) ).
tcf(c_126219,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_20 )
| ( iPr_def_20 != iPr_def_25 )
| ( inverse(X0) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100861]) ).
tcf(c_126228,plain,
( ( inverse(sk_c10) = iPr_def_20 )
| ( iPr_def_20 != iPr_def_25 )
| ( inverse(sk_c10) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_126219]) ).
tcf(c_126531,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = X1 )
| ( X1 != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_107387]) ).
tcf(c_126544,plain,
! [X0: $i,X1: $i] :
( ( inverse(inverse(X0)) = inverse(X1) )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_701]) ).
tcf(c_126545,plain,
( ( inverse(inverse(sk_c10)) = inverse(sk_c10) )
| ( inverse(sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_126544]) ).
tcf(c_126702,plain,
( ( sk_c10 = iPr_def_15 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_50295,c_9219,c_9511,c_20440,c_61121,c_61137,c_61138,c_101139,c_102252,c_109553,c_110446,c_113747]) ).
tcf(c_126703,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_126702]) ).
tcf(c_126980,plain,
! [X0: $i,X1: $i] :
( ( multiply(X1,inverse(X0)) = multiply(identity,iPr_def_25) )
| ( X1 != identity )
| ( inverse(X0) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_100534]) ).
tcf(c_126982,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = multiply(identity,iPr_def_25) )
| ( sk_c10 != identity )
| ( inverse(sk_c10) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_126980]) ).
tcf(c_127065,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = identity )
| ( identity != multiply(identity,iPr_def_29) )
| ( multiply(X0,inverse(X0)) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_107393]) ).
tcf(c_127072,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = identity )
| ( identity != multiply(identity,iPr_def_29) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(identity,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_127065]) ).
tcf(c_127351,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c3) )
| ( inverse(sk_c3) != sk_c11 )
| ( inverse(X0) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_114504]) ).
tcf(c_127352,plain,
( ( inverse(sk_c10) = inverse(sk_c3) )
| ( inverse(sk_c3) != sk_c11 )
| ( inverse(sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_127351]) ).
tcf(c_127636,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = sk_c11 )
| ( sk_c11 != multiply(identity,iPr_def_25) )
| ( multiply(X0,inverse(X0)) != multiply(identity,iPr_def_25) ) ),
inference(instantiation,[status(thm)],[c_100335]) ).
tcf(c_127638,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = sk_c11 )
| ( sk_c11 != multiply(identity,iPr_def_25) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(identity,iPr_def_25) ) ),
inference(instantiation,[status(thm)],[c_127636]) ).
tcf(c_127657,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = multiply(identity,iPr_def_29) )
| ( multiply(identity,iPr_def_29) != multiply(X1,X2) )
| ( multiply(X0,inverse(X0)) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_107275]) ).
tcf(c_127659,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = multiply(identity,iPr_def_29) )
| ( multiply(identity,iPr_def_29) != multiply(sk_c10,sk_c10) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(sk_c10,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_127657]) ).
tcf(c_129799,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = inverse(X1) )
| ( inverse(X1) != multiply(X0,inverse(X0)) )
| ( multiply(X0,inverse(X0)) != multiply(X0,inverse(X0)) ) ),
inference(instantiation,[status(thm)],[c_116915]) ).
tcf(c_129800,plain,
! [X0: $i,X1: $i] :
( ( inverse(X1) = multiply(X0,inverse(X0)) )
| ( inverse(X1) != iPr_def_29 )
| ( multiply(X0,inverse(X0)) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_114530]) ).
tcf(c_129801,plain,
! [X0: $i,X1: $i] :
( ( inverse(X1) = multiply(X0,inverse(X0)) )
| ( inverse(X1) != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_114504]) ).
tcf(c_129802,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = inverse(sk_c10) )
| ( inverse(sk_c10) != multiply(sk_c10,inverse(sk_c10)) )
| ( multiply(sk_c10,inverse(sk_c10)) != multiply(sk_c10,inverse(sk_c10)) ) ),
inference(instantiation,[status(thm)],[c_129799]) ).
tcf(c_129803,plain,
( ( inverse(sk_c10) = multiply(sk_c10,inverse(sk_c10)) )
| ( inverse(sk_c10) != sk_c11 )
| ( multiply(sk_c10,inverse(sk_c10)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_129801]) ).
tcf(c_129804,plain,
( ( inverse(sk_c10) = multiply(sk_c10,inverse(sk_c10)) )
| ( inverse(sk_c10) != iPr_def_29 )
| ( multiply(sk_c10,inverse(sk_c10)) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_129800]) ).
tcf(c_131586,plain,
! [X0: $i] :
( ( inverse(sk_c3) = multiply(sk_c5,sk_c8) )
| ( inverse(sk_c3) != X0 )
| ( multiply(sk_c5,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_100607]) ).
tcf(c_131594,plain,
( ( inverse(sk_c3) = multiply(sk_c5,sk_c8) )
| ( inverse(sk_c3) != sk_c10 )
| ( multiply(sk_c5,sk_c8) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_131586]) ).
tcf(c_132039,plain,
( ( sk_c11 = identity )
| ( identity != iPr_def_29 )
| ( sk_c11 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100235]) ).
tcf(c_132040,plain,
( ( sk_c11 = identity )
| ( identity != iPr_def_22 )
| ( sk_c11 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_100229]) ).
tcf(c_132041,plain,
( ( sk_c11 = identity )
| ( identity != iPr_def_20 )
| ( sk_c11 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100226]) ).
tcf(c_132107,plain,
( ( iPr_def_29 = identity )
| ( iPr_def_29 != iPr_def_29 )
| ( identity != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_100667]) ).
tcf(c_132170,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != sk_c11 )
| ( multiply(X0,X1) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_100212]) ).
tcf(c_132171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_132229,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c11 )
| ( sk_c11 != multiply(X1,inverse(X1)) )
| ( multiply(inverse(X0),sk_c10) != multiply(X1,inverse(X1)) ) ),
inference(instantiation,[status(thm)],[c_101874]) ).
tcf(c_132230,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c11 )
| ( sk_c11 != multiply(sk_c10,inverse(sk_c10)) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(sk_c10,inverse(sk_c10)) ) ),
inference(instantiation,[status(thm)],[c_132229]) ).
tcf(c_132409,plain,
( ( multiply(inverse(sk_c10),sk_c10) = multiply(identity,iPr_def_29) )
| ( multiply(identity,iPr_def_29) != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_107531]) ).
tcf(c_132410,plain,
( ( multiply(identity,iPr_def_29) = identity )
| ( identity != iPr_def_29 )
| ( multiply(identity,iPr_def_29) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_104859]) ).
tcf(c_132425,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c10),sk_c10) = multiply(X0,inverse(X0)) )
| ( multiply(inverse(sk_c10),sk_c10) != identity )
| ( multiply(X0,inverse(X0)) != identity ) ),
inference(instantiation,[status(thm)],[c_107531]) ).
tcf(c_132426,plain,
( ( multiply(inverse(sk_c10),sk_c10) = multiply(sk_c10,inverse(sk_c10)) )
| ( multiply(sk_c10,inverse(sk_c10)) != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_132425]) ).
tcf(c_132761,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = multiply(inverse(X1),sk_c10) )
| ( X2 != sk_c10 )
| ( X0 != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_700]) ).
tcf(c_132763,plain,
( ( multiply(sk_c10,sk_c10) = multiply(inverse(sk_c10),sk_c10) )
| ( sk_c10 != sk_c10 )
| ( sk_c10 != inverse(sk_c10) ) ),
inference(instantiation,[status(thm)],[c_132761]) ).
tcf(c_133018,plain,
iPr_def_15 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_97608,c_158,c_709,c_629,c_637,c_1590,c_1593,c_2260,c_2320,c_2434,c_2511,c_2563,c_2590,c_2871,c_4655,c_4656,c_5508,c_5509,c_5510,c_15162,c_20782,c_21543,c_21544,c_47233,c_50082,c_51845,c_52490,c_52397,c_56796,c_56800,c_66625,c_74226,c_74907,c_76391,c_77713,c_78032,c_78308,c_78501,c_88353,c_88384,c_99083,c_101867,c_102586,c_102587,c_107386,c_113062,c_113720,c_114518,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040]) ).
tcf(c_133094,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_15,X0)) = X0,
inference(demodulation,[status(thm)],[c_29749,c_133018]) ).
tcf(c_133095,plain,
inverse(iPr_def_15) = sk_c2,
inference(demodulation,[status(thm)],[c_29816,c_133018]) ).
tcf(c_133096,plain,
multiply(sk_c2,iPr_def_15) = identity,
inference(demodulation,[status(thm)],[c_29745,c_133018]) ).
tcf(c_133138,plain,
multiply(iPr_def_15,iPr_def_27) = sk_c9,
inference(demodulation,[status(thm)],[c_5398,c_133018]) ).
tcf(c_133148,plain,
multiply(iPr_def_15,sk_c2) = identity,
inference(demodulation,[status(thm)],[c_1209,c_133018]) ).
tcf(c_133151,plain,
inverse(sk_c2) = iPr_def_15,
inference(demodulation,[status(thm)],[c_629,c_133018]) ).
tcf(c_133326,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_100022,c_158,c_704,c_709,c_640,c_1461,c_5595,c_5596,c_5597,c_8484,c_8576,c_9800,c_15269,c_27186,c_27457,c_27834,c_58286,c_60185,c_60186,c_62080,c_62072,c_65079,c_67071,c_72562,c_100545,c_100546,c_101867,c_103067,c_107386,c_107390,c_107391,c_119325,c_126545,c_129802,c_129803,c_132039]) ).
tcf(c_133387,plain,
( ( iPr_def_26 = iPr_def_29 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_133326,c_62072]) ).
tcf(c_133633,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c10 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_100023,c_158,c_704,c_709,c_640,c_1461,c_2582,c_5595,c_5596,c_5597,c_7721,c_7947,c_9589,c_15269,c_27007,c_27458,c_27834,c_58286,c_60185,c_60186,c_62080,c_62072,c_65079,c_67071,c_72565,c_78556,c_100545,c_100546,c_101867,c_103067,c_107386,c_107390,c_107391,c_119325,c_126545,c_129802,c_129803,c_132039]) ).
tcf(c_133775,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_133633,c_636]) ).
tcf(c_133790,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_133775,c_17105]) ).
tcf(c_134825,plain,
( ( iPr_def_24 = iPr_def_28 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_133790,c_66003]) ).
tcf(c_136328,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(identity) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_99923,c_640]) ).
tcf(c_136329,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_136328,c_15521]) ).
tcf(c_136362,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_15) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_39839,c_133094]) ).
tcf(c_136364,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_15) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_14167,c_133094]) ).
tcf(c_136365,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c2,iPr_def_15) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_11343,c_133094]) ).
tcf(c_136372,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = identity ) ),
inference(light_normalisation,[status(thm)],[c_136365,c_133096]) ).
tcf(c_136375,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c11 = identity ) ),
inference(light_normalisation,[status(thm)],[c_136364,c_133096]) ).
tcf(c_136381,plain,
( ( identity = iPr_def_22 )
| ( sk_c11 = identity ) ),
inference(light_normalisation,[status(thm)],[c_136362,c_133096]) ).
tcf(c_136859,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12
| ( sk_c10 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_23463,c_8576,c_23463]) ).
tcf(c_136908,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12
| ( identity != iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_677,c_136859]) ).
tcf(c_136910,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12
| ( identity != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_667,c_136859]) ).
tcf(c_137176,plain,
iPr_def_20 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_133387,c_158,c_704,c_709,c_640,c_1136,c_1412,c_1461,c_1805,c_1913,c_2471,c_3523,c_5595,c_5596,c_5597,c_11516,c_11535,c_15269,c_17654,c_19474,c_19475,c_23259,c_24046,c_27454,c_30304,c_30425,c_48565,c_53479,c_58255,c_58256,c_58286,c_60186,c_60359,c_62080,c_62072,c_62066,c_65079,c_70028,c_76943,c_78501,c_93249,c_100209,c_100309,c_100310,c_101256,c_101889,c_103067,c_103068,c_107386,c_107390,c_107391,c_107575,c_119325,c_126545,c_126703,c_129802,c_129803,c_132409,c_132410,c_133018,c_134825]) ).
tcf(c_137212,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_73167,c_137176]) ).
tcf(c_137213,plain,
( ( identity = iPr_def_20 )
| ( sk_c11 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_71575,c_137176]) ).
tcf(c_137256,plain,
( ( iPr_def_27 = iPr_def_29 )
| ( iPr_def_20 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_46060,c_137176]) ).
tcf(c_137258,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_28 ) ),
inference(demodulation,[status(thm)],[c_40338,c_137176]) ).
tcf(c_137262,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_40205,c_137176]) ).
tcf(c_137270,plain,
( ( identity = iPr_def_20 )
| ( sk_c10 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_38804,c_137176]) ).
tcf(c_137274,plain,
( ( identity = iPr_def_29 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_38855,c_137176]) ).
tcf(c_137289,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_21122,c_137176]) ).
tcf(c_137290,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_20868,c_137176]) ).
tcf(c_137293,plain,
( ( identity = iPr_def_20 )
| ( sk_c10 = iPr_def_28 ) ),
inference(demodulation,[status(thm)],[c_19836,c_137176]) ).
tcf(c_137294,plain,
( ( identity = iPr_def_20 )
| ( sk_c11 = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_19835,c_137176]) ).
tcf(c_137295,plain,
( ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_19834,c_137176]) ).
tcf(c_137331,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c8,
inference(demodulation,[status(thm)],[c_5511,c_137176]) ).
tcf(c_137484,plain,
( iPr_def_14
| ( identity = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_137289,c_1594,c_1805,c_11535,c_17654,c_23476,c_28341,c_61120,c_61121,c_73165,c_80753,c_89207,c_101951,c_102255,c_102355,c_102476,c_132039,c_133018,c_137176,c_137295,c_137294,c_137274,c_137270,c_137213]) ).
tcf(c_137490,plain,
( ( sk_c10 = iPr_def_26 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_136908,c_29775,c_136910]) ).
tcf(c_137496,plain,
( iPr_def_14
| iPr_def_10
| ( sk_c10 = iPr_def_26 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_27186,c_137490]) ).
tcf(c_137630,plain,
iPr_def_22 = iPr_def_25,
inference(global_subsumption_just,[status(thm)],[c_89508,c_158,c_704,c_709,c_629,c_634,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2871,c_3523,c_3752,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_9741,c_11516,c_11535,c_15162,c_15262,c_15269,c_17654,c_19474,c_19475,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_24046,c_27454,c_27453,c_27597,c_28227,c_30304,c_30425,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78308,c_78501,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101160,c_101172,c_101256,c_101738,c_101791,c_101859,c_101867,c_101889,c_102586,c_102587,c_103067,c_103068,c_104339,c_106230,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_110359,c_113062,c_113720,c_114518,c_116751,c_119325,c_123317,c_123312,c_126203,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132040,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484]) ).
tcf(c_137632,plain,
iPr_def_20 = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_137630,c_137176]) ).
tcf(c_137678,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(demodulation,[status(thm)],[c_16206,c_137632]) ).
tcf(c_137679,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_16280,c_137632]) ).
tcf(c_137680,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(demodulation,[status(thm)],[c_16202,c_137632]) ).
tcf(c_137696,plain,
multiply(iPr_def_20,iPr_def_26) = sk_c11,
inference(demodulation,[status(thm)],[c_5707,c_137632]) ).
tcf(c_137705,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(demodulation,[status(thm)],[c_1203,c_137632]) ).
tcf(c_137706,plain,
inverse(sk_c3) = iPr_def_20,
inference(demodulation,[status(thm)],[c_637,c_137632]) ).
tcf(c_137758,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c10 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_23466,c_7947,c_23466]) ).
tcf(c_137790,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_12
| ( identity != iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_674,c_137758]) ).
tcf(c_137792,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_12
| ( identity != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_664,c_137758]) ).
tcf(c_137819,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_137790,c_29773,c_137792]) ).
tcf(c_137825,plain,
( iPr_def_14
| iPr_def_10
| ( sk_c10 = iPr_def_23 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_27196,c_137819]) ).
tcf(c_137980,plain,
( ( sk_c10 != iPr_def_24 )
| ( sk_c9 != identity )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_23623,c_3523,c_23632,c_23629]) ).
tcf(c_137981,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( sk_c10 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_137980]) ).
tcf(c_138007,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_11
| ( iPr_def_24 != iPr_def_26 )
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_1574,c_137981]) ).
tcf(c_138219,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_97390,c_29656]) ).
tcf(c_138428,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_28) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_136329,c_15521]) ).
tcf(c_138431,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c1 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_138428,c_27653]) ).
tcf(c_138616,plain,
iPr_def_18 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_136375,c_158,c_704,c_709,c_629,c_637,c_640,c_642,c_1032,c_1128,c_1385,c_1539,c_1590,c_1593,c_1737,c_1805,c_2260,c_2320,c_2434,c_2511,c_2563,c_2590,c_2871,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_14078,c_14151,c_15162,c_15269,c_17654,c_20782,c_21543,c_21544,c_27455,c_47233,c_50082,c_51845,c_52490,c_52397,c_53465,c_53612,c_53604,c_53598,c_55492,c_55449,c_56796,c_56800,c_58286,c_60185,c_60186,c_61503,c_61507,c_66625,c_70683,c_72559,c_74226,c_74907,c_76391,c_76942,c_77713,c_78032,c_78308,c_78501,c_88178,c_88353,c_88384,c_93249,c_99083,c_100545,c_100546,c_101867,c_102586,c_102587,c_103067,c_107386,c_107390,c_107391,c_113062,c_113720,c_114518,c_119325,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040,c_136375]) ).
tcf(c_138618,plain,
multiply(iPr_def_18,iPr_def_20) = sk_c8,
inference(demodulation,[status(thm)],[c_137331,c_138616]) ).
tcf(c_138652,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_19904,c_138616]) ).
tcf(c_138693,plain,
sk_c5 = sk_c6,
inference(light_normalisation,[status(thm)],[c_138652,c_26075]) ).
tcf(c_138713,plain,
( ( sk_c11 = iPr_def_25 )
| ~ iPr_def_10
| ( sk_c11 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_23921,c_158,c_704,c_709,c_629,c_634,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2871,c_3523,c_3752,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_9741,c_11516,c_11535,c_15162,c_15262,c_15269,c_17654,c_19474,c_19475,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_24046,c_27454,c_27453,c_27597,c_28227,c_30304,c_30425,c_38804,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_73165,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78308,c_78501,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101159,c_101160,c_101172,c_101256,c_101738,c_101791,c_101859,c_101867,c_101889,c_102586,c_102587,c_103067,c_103068,c_104339,c_106230,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_109550,c_110359,c_111628,c_113062,c_113720,c_114518,c_116751,c_119325,c_123317,c_123312,c_126203,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132040,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484]) ).
tcf(c_138715,plain,
( ( sk_c11 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c11 != identity ) ),
inference(light_normalisation,[status(thm)],[c_138713,c_137632]) ).
tcf(c_138739,plain,
( ( sk_c11 = iPr_def_20 )
| ~ iPr_def_10
| ( identity != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_681,c_138715]) ).
tcf(c_138904,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_138618,c_105]) ).
tcf(c_139010,plain,
multiply(sk_c8,sk_c3) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_137705,c_138904]) ).
tcf(c_139279,plain,
( ( identity = iPr_def_20 )
| ( sk_c11 = identity ) ),
inference(light_normalisation,[status(thm)],[c_136381,c_137176]) ).
tcf(c_140548,plain,
( ( identity = iPr_def_20 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_137213,c_139279]) ).
tcf(c_140802,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_15 )
| ( multiply(sk_c2,sk_c10) != sk_c11 ) ),
inference(light_normalisation,[status(thm)],[c_29742,c_133018,c_133095,c_133151]) ).
tcf(c_140891,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_15 )
| ( multiply(sk_c2,sk_c11) != sk_c10 ) ),
inference(light_normalisation,[status(thm)],[c_29747,c_133018,c_133095,c_133151]) ).
tcf(c_141139,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_2704,c_158,c_704,c_709,c_629,c_634,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2704,c_2871,c_3523,c_3752,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_9741,c_11516,c_11535,c_15162,c_15262,c_15269,c_17654,c_19474,c_19475,c_19835,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_24046,c_27454,c_27453,c_27597,c_28227,c_29056,c_30304,c_30425,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78183,c_78191,c_78308,c_78501,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101160,c_101172,c_101256,c_101738,c_101791,c_101859,c_101867,c_101889,c_102060,c_102586,c_102587,c_102604,c_103067,c_103068,c_104339,c_106230,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_110359,c_111614,c_113062,c_113404,c_113720,c_114007,c_114518,c_116751,c_119325,c_123317,c_123312,c_126203,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132040,c_132107,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484]) ).
tcf(c_141154,plain,
( ( identity = iPr_def_26 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_16230,c_141139]) ).
tcf(c_141769,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( inverse(iPr_def_15) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_137258,c_27653]) ).
tcf(c_141783,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_141769,c_133095]) ).
tcf(c_141978,plain,
( ~ iPr_def_13
| ( sk_c11 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_2711,c_2711,c_2704,c_7721,c_9589]) ).
tcf(c_142002,plain,
( ( sk_c10 = iPr_def_28 )
| ~ iPr_def_13
| ( iPr_def_20 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_671,c_141978]) ).
tcf(c_142072,plain,
( ( iPr_def_20 != iPr_def_24 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_142002,c_158,c_704,c_709,c_629,c_634,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2704,c_2871,c_3523,c_3752,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_9741,c_11516,c_11535,c_15162,c_15262,c_15269,c_17654,c_19474,c_19475,c_19835,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_24046,c_27454,c_27453,c_27597,c_28227,c_29056,c_30304,c_30425,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_71842,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78183,c_78191,c_78308,c_78501,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101160,c_101172,c_101256,c_101738,c_101791,c_101859,c_101867,c_101889,c_102060,c_102586,c_102587,c_102604,c_103067,c_103068,c_104339,c_106230,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_110359,c_111614,c_113062,c_113404,c_113720,c_114007,c_114518,c_116751,c_119325,c_123317,c_123312,c_126203,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132040,c_132107,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484]) ).
tcf(c_142073,plain,
( ~ iPr_def_13
| ( iPr_def_20 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_142072]) ).
tcf(c_142155,plain,
( ( sk_c11 = iPr_def_29 )
| ( iPr_def_29 != iPr_def_20 )
| ( sk_c11 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_100226]) ).
tcf(c_142468,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_29 ) ),
inference(global_subsumption_just,[status(thm)],[c_3379,c_3386,c_3379,c_7721,c_7969]) ).
tcf(c_143149,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_15 )
| ( sk_c10 != iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_3523,c_133018]) ).
tcf(c_143274,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_20 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_3686,c_137632]) ).
tcf(c_143292,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_10
| ( iPr_def_15 != iPr_def_20 )
| ( sk_c10 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_34483,c_143274]) ).
tcf(c_143720,plain,
( ( identity = iPr_def_20 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_137293,c_141139]) ).
tcf(c_145920,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_28,sk_c10) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_138431,c_641]) ).
tcf(c_146262,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c10 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_28) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_677,c_145920]) ).
tcf(c_146675,plain,
multiply(sk_c8,sk_c3) = iPr_def_18,
inference(demodulation,[status(thm)],[c_139010,c_15498]) ).
tcf(c_146682,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(iPr_def_18,sk_c3) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_669,c_146675]) ).
tcf(c_146683,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_18,sk_c3) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_659,c_146675]) ).
tcf(c_146853,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(sk_c6,iPr_def_18) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_146682,c_25461]) ).
tcf(c_146854,plain,
( ( sk_c3 = identity )
| ( sk_c10 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_146853,c_25457]) ).
tcf(c_146886,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c6,iPr_def_18) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_146683,c_25461]) ).
tcf(c_146887,plain,
( ( sk_c3 = identity )
| ( sk_c10 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_146886,c_25457]) ).
tcf(c_150367,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = inverse(X1) )
| ( inverse(X1) != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_126531]) ).
tcf(c_150368,plain,
( ( multiply(sk_c10,inverse(sk_c10)) = inverse(sk_c10) )
| ( inverse(sk_c10) != sk_c11 )
| ( multiply(sk_c10,inverse(sk_c10)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_150367]) ).
tcf(c_150593,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != multiply(sk_c1,sk_c10) )
| ( multiply(X0,X1) != multiply(sk_c1,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_132171]) ).
tcf(c_150594,plain,
( ( sk_c11 = multiply(sk_c10,sk_c10) )
| ( sk_c11 != multiply(sk_c1,sk_c10) )
| ( multiply(sk_c10,sk_c10) != multiply(sk_c1,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_150593]) ).
tcf(c_150905,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( inverse(X0) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_114504]) ).
tcf(c_150906,plain,
( ( inverse(sk_c10) = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( inverse(sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_150905]) ).
tcf(c_150914,plain,
! [X0: $i] :
( ( X0 = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_101382]) ).
tcf(c_150915,plain,
( ( sk_c10 = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( sk_c10 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_150914]) ).
tcf(c_150991,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_100211]) ).
tcf(c_150992,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c11 != identity )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_150991]) ).
tcf(c_151365,plain,
( ( sk_c11 = multiply(inverse(sk_c10),sk_c10) )
| ( sk_c11 != sk_c11 )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_132170]) ).
tcf(c_151621,plain,
! [X0: $i] :
( ( identity = iPr_def_15 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_140548,c_103]) ).
tcf(c_151661,plain,
( ( iPr_def_20 = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_15 )
| ( multiply(sk_c1,sk_c10) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_141783,c_140802]) ).
tcf(c_151693,plain,
( ( iPr_def_20 = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c11 != iPr_def_29 )
| ( sk_c10 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_151661,c_27748]) ).
tcf(c_151703,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c10 = iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_146262,c_158,c_704,c_709,c_629,c_637,c_640,c_1590,c_1593,c_1804,c_1805,c_2260,c_2320,c_2434,c_2511,c_2563,c_2590,c_2871,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_6735,c_8484,c_8576,c_9800,c_10644,c_15162,c_15268,c_15269,c_17654,c_20782,c_21543,c_21544,c_27457,c_47233,c_50082,c_51845,c_52490,c_52397,c_53465,c_55223,c_56796,c_56800,c_58286,c_60185,c_60186,c_66625,c_74226,c_74907,c_76391,c_77713,c_78032,c_78308,c_78501,c_80863,c_88162,c_88178,c_88353,c_88384,c_93249,c_93819,c_99083,c_99923,c_100545,c_100546,c_101867,c_102586,c_102587,c_103067,c_107386,c_107390,c_107391,c_113062,c_113720,c_114518,c_119325,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040,c_132039,c_137496,c_138219,c_150368]) ).
tcf(c_151800,plain,
( ( iPr_def_26 = iPr_def_28 )
| ( iPr_def_23 = iPr_def_26 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_151703,c_674]) ).
tcf(c_151977,plain,
( ( sk_c10 = iPr_def_23 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_151800,c_158,c_704,c_709,c_629,c_637,c_640,c_1590,c_1593,c_1805,c_2260,c_2320,c_2434,c_2511,c_2563,c_2590,c_2871,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_8760,c_11535,c_15162,c_17654,c_18072,c_20782,c_21543,c_21544,c_28860,c_47233,c_50082,c_51845,c_52490,c_52397,c_53371,c_53465,c_53466,c_55223,c_56796,c_56800,c_60185,c_60186,c_61503,c_61507,c_66625,c_74226,c_74907,c_76391,c_77713,c_78032,c_78308,c_78501,c_88178,c_88353,c_88384,c_93249,c_93819,c_99083,c_99923,c_100545,c_100546,c_101867,c_102586,c_102587,c_103067,c_107386,c_107390,c_107391,c_113062,c_113720,c_114518,c_119325,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040,c_136372,c_137825,c_138219,c_150368]) ).
tcf(c_151978,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c10 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_151977]) ).
tcf(c_152008,plain,
iPr_def_23 = iPr_def_26,
inference(superposition,[status(thm)],[c_151978,c_151703]) ).
tcf(c_152092,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_20 )
| ( sk_c10 != iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_143274,c_152008]) ).
tcf(c_152097,plain,
( ( identity = iPr_def_23 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_141154,c_152008]) ).
tcf(c_152109,plain,
multiply(iPr_def_20,iPr_def_23) = sk_c11,
inference(demodulation,[status(thm)],[c_137696,c_152008]) ).
tcf(c_152150,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_23 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_17418,c_152008]) ).
tcf(c_152181,plain,
multiply(sk_c3,sk_c11) = iPr_def_23,
inference(demodulation,[status(thm)],[c_638,c_152008]) ).
tcf(c_152967,plain,
~ iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_152097,c_24578,c_29056,c_61138,c_61218,c_78197,c_101171,c_107155,c_113744,c_132041,c_132107,c_142073,c_142155,c_143720,c_151693]) ).
tcf(c_152969,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_642,c_152967]) ).
tcf(c_152978,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_23,X0)) = multiply(sk_c11,X0),
inference(superposition,[status(thm)],[c_152109,c_105]) ).
tcf(c_152980,plain,
( ( identity = iPr_def_15 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_152109,c_151621]) ).
tcf(c_153050,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_695,c_152969]) ).
tcf(c_153092,plain,
( iPr_def_14
| ( iPr_def_15 != iPr_def_24 )
| iPr_def_10
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_153050,c_642,c_1590,c_2581,c_2871,c_24578,c_29056,c_61138,c_61218,c_78197,c_78501,c_101171,c_107155,c_113744,c_132041,c_132107,c_142073,c_142155,c_143720,c_151693]) ).
tcf(c_153093,plain,
( iPr_def_14
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_153092]) ).
tcf(c_153928,plain,
multiply(sk_c11,sk_c4) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_1204,c_152978]) ).
tcf(c_154369,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_6628,c_25461,c_137176,c_138616,c_138693]) ).
tcf(c_154406,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_14
| ( inverse(X0) != inverse(iPr_def_20) )
| ( inverse(inverse(iPr_def_20)) != inverse(X0) )
| ( multiply(inverse(X0),sk_c10) != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_154369,c_643]) ).
tcf(c_154433,plain,
( ( sk_c11 = iPr_def_23 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_154369,c_152109]) ).
tcf(c_154474,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_14
| ( inverse(X0) != iPr_def_20 )
| ( inverse(X0) != sk_c3 )
| ( multiply(inverse(X0),sk_c10) != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(light_normalisation,[status(thm)],[c_154406,c_137679,c_137706]) ).
tcf(c_154488,plain,
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_14
| ( inverse(sk_c10) != iPr_def_20 )
| ( inverse(sk_c10) != sk_c3 )
| ( multiply(sk_c10,inverse(sk_c10)) != sk_c11 )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_154474]) ).
tcf(c_155803,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_14654,c_1574,c_38661,c_143292]) ).
tcf(c_155902,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_6668,c_137176,c_137678,c_152008]) ).
tcf(c_155937,plain,
( ( sk_c10 = iPr_def_27 )
| ( sk_c10 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_155902,c_5690]) ).
tcf(c_156201,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_34479,c_635,c_1331,c_1351,c_1352,c_1404,c_1912,c_1913,c_3349,c_3523,c_5497,c_5498,c_6759,c_6891,c_7016,c_15259,c_17130,c_17418,c_55784,c_55788,c_74907,c_76944,c_78864,c_79747,c_83569,c_138007,c_152150]) ).
tcf(c_156210,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_6733,c_133018,c_133094,c_152008]) ).
tcf(c_156232,plain,
( ( sk_c11 = iPr_def_15 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_156210,c_1217]) ).
tcf(c_156235,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_156210,c_6954]) ).
tcf(c_159196,plain,
( ( iPr_def_23 = iPr_def_29 )
| ( identity = iPr_def_15 )
| ( sk_c10 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_152980,c_684]) ).
tcf(c_159366,plain,
( ( sk_c10 = iPr_def_23 )
| ( identity = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_159196,c_158,c_709,c_629,c_637,c_1590,c_1593,c_1805,c_2260,c_2320,c_2434,c_2511,c_2563,c_2590,c_2871,c_4655,c_4656,c_5508,c_5509,c_5510,c_6089,c_7947,c_9589,c_11535,c_15162,c_17654,c_17939,c_20782,c_21543,c_21544,c_27458,c_47233,c_50082,c_51845,c_52490,c_52397,c_53479,c_56796,c_56800,c_66625,c_74226,c_74907,c_76391,c_77713,c_78032,c_78308,c_78501,c_88353,c_88384,c_93249,c_99083,c_101867,c_102256,c_102355,c_102586,c_102587,c_107386,c_113062,c_113720,c_114518,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040,c_156232]) ).
tcf(c_159367,plain,
( ( identity = iPr_def_15 )
| ( sk_c10 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_159366]) ).
tcf(c_159433,plain,
( ( identity = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_159367,c_636]) ).
tcf(c_159441,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_159433,c_17105]) ).
tcf(c_161452,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_159441,c_140548]) ).
tcf(c_161560,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_25 )
| ( inverse(X0) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_107598]) ).
tcf(c_161561,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != iPr_def_25 )
| ( inverse(sk_c10) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_161560]) ).
tcf(c_161593,plain,
( ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 )
| ( sk_c10 = iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_44127,c_158,c_704,c_709,c_629,c_634,c_635,c_637,c_640,c_1136,c_1401,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2871,c_3523,c_3752,c_4655,c_4656,c_5497,c_5498,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_6089,c_6670,c_6891,c_7016,c_8130,c_9741,c_11516,c_11535,c_15162,c_15259,c_15262,c_15269,c_17654,c_17920,c_19474,c_19475,c_19838,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_23632,c_23629,c_24046,c_27454,c_27453,c_27597,c_28227,c_30304,c_30425,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_55775,c_55781,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_74039,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78308,c_78501,c_78580,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101159,c_101160,c_101172,c_101256,c_101738,c_101779,c_101791,c_101859,c_101867,c_101889,c_102216,c_102252,c_102255,c_102256,c_102586,c_102587,c_102604,c_103067,c_103068,c_104339,c_106230,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_108978,c_110359,c_110778,c_113062,c_113720,c_114518,c_116751,c_117799,c_119325,c_119568,c_119569,c_123317,c_123312,c_126203,c_126228,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132040,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484,c_146887,c_150906,c_150915,c_152969,c_154433,c_154488,c_155937]) ).
tcf(c_161594,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_161593]) ).
tcf(c_161727,plain,
multiply(sk_c11,sk_c4) = iPr_def_20,
inference(demodulation,[status(thm)],[c_153928,c_15498]) ).
tcf(c_161746,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_20,sk_c4) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_661,c_161727]) ).
tcf(c_161749,plain,
multiply(inverse(sk_c11),iPr_def_20) = sk_c4,
inference(superposition,[status(thm)],[c_161727,c_14692]) ).
tcf(c_161960,plain,
( ( identity = iPr_def_27 )
| ( multiply(inverse(iPr_def_20),iPr_def_20) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_29771,c_161749]) ).
tcf(c_161967,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(inverse(iPr_def_20),iPr_def_20) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_671,c_161749]) ).
tcf(c_161975,plain,
( ( sk_c4 = identity )
| ( sk_c10 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_161967,c_137679,c_137680]) ).
tcf(c_161982,plain,
( ( identity = iPr_def_27 )
| ( sk_c4 = identity ) ),
inference(light_normalisation,[status(thm)],[c_161960,c_137679,c_137680]) ).
tcf(c_162608,plain,
( ( sk_c4 = iPr_def_20 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_161746,c_154369]) ).
tcf(c_163211,plain,
( ( sk_c10 = iPr_def_24 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_155937,c_143149]) ).
tcf(c_163538,plain,
( ( sk_c10 = iPr_def_23 )
| ~ iPr_def_10
| ( sk_c11 != identity )
| ( sk_c10 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_156232,c_23893]) ).
tcf(c_163950,plain,
( ( iPr_def_15 = iPr_def_27 )
| ~ iPr_def_11
| ( sk_c10 != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_49765,c_695,c_1332,c_1331,c_1459,c_2978,c_23218,c_74907,c_78051,c_137981,c_163211]) ).
tcf(c_163970,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( sk_c10 = iPr_def_27 )
| ~ iPr_def_11
| ( sk_c10 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_665,c_163950]) ).
tcf(c_164168,plain,
multiply(inverse(multiply(inverse(iPr_def_16),sk_c7)),identity) = sk_c8,
inference(superposition,[status(thm)],[c_104,c_95414]) ).
tcf(c_164395,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_156235,c_636]) ).
tcf(c_164397,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( multiply(iPr_def_23,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_156235,c_627]) ).
tcf(c_164403,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_164395,c_17105]) ).
tcf(c_165081,plain,
( ~ iPr_def_11
| ( sk_c10 = iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_163970,c_635,c_1401,c_5497,c_5498,c_6670,c_6891,c_7016,c_15259,c_19838,c_23629,c_55775,c_55781,c_74907,c_102252,c_102256,c_154433,c_155937]) ).
tcf(c_165082,plain,
( ( sk_c10 = iPr_def_27 )
| ~ iPr_def_11 ),
inference(renaming,[status(thm)],[c_165081]) ).
tcf(c_165087,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_143149,c_165082]) ).
tcf(c_165133,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_164403,c_137212]) ).
tcf(c_165550,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c9 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_152969,c_165087]) ).
tcf(c_165562,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_695,c_165087]) ).
tcf(c_165565,plain,
( ( sk_c11 = iPr_def_29 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_685,c_165087]) ).
tcf(c_165828,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( inverse(iPr_def_15) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_161452,c_15521]) ).
tcf(c_165830,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_24 )
| ( multiply(iPr_def_15,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_161452,c_103]) ).
tcf(c_165831,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c2 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_165828,c_133095]) ).
tcf(c_165871,plain,
( ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_165562,c_10620,c_30308]) ).
tcf(c_165877,plain,
( ( iPr_def_15 != iPr_def_24 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_165565,c_165087,c_165562]) ).
tcf(c_165878,plain,
( ~ iPr_def_11
| ( iPr_def_15 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_165877]) ).
tcf(c_165883,plain,
( iPr_def_14
| iPr_def_10
| ( iPr_def_15 != iPr_def_24 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_153093,c_165878]) ).
tcf(c_166179,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_661,c_164397]) ).
tcf(c_166582,plain,
( ( sk_c10 = iPr_def_28 )
| ( multiply(identity,sk_c10) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_161975,c_636]) ).
tcf(c_166759,plain,
( ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 )
| ( sk_c10 = iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_166179,c_161594]) ).
tcf(c_166760,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_23,iPr_def_20) = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_166759]) ).
tcf(c_166771,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_166760,c_155902]) ).
tcf(c_167181,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c9 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_165830,c_133138]) ).
tcf(c_167183,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c2 = identity ) ),
inference(superposition,[status(thm)],[c_165830,c_133148]) ).
tcf(c_167309,plain,
inverse(multiply(inverse(iPr_def_16),sk_c7)) = sk_c8,
inference(demodulation,[status(thm)],[c_164168,c_70411]) ).
tcf(c_167315,plain,
multiply(sk_c8,multiply(inverse(iPr_def_16),sk_c7)) = identity,
inference(superposition,[status(thm)],[c_167309,c_104]) ).
tcf(c_167439,plain,
( ( identity = iPr_def_27 )
| ( multiply(identity,sk_c10) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_161982,c_636]) ).
tcf(c_167504,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_20,iPr_def_23) = identity ) ),
inference(superposition,[status(thm)],[c_162608,c_17105]) ).
tcf(c_167520,plain,
( ( sk_c11 = identity )
| ( sk_c10 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_167504,c_152109]) ).
tcf(c_167667,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_18,multiply(inverse(iPr_def_16),sk_c7)) = identity ) ),
inference(superposition,[status(thm)],[c_659,c_167315]) ).
tcf(c_167723,plain,
( ( sk_c10 = iPr_def_28 )
| ( sk_c10 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_166582,c_103]) ).
tcf(c_167756,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c10 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_167723,c_155937]) ).
tcf(c_168475,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_167439,c_103]) ).
tcf(c_168571,plain,
( ( identity = iPr_def_27 )
| ( multiply(iPr_def_24,sk_c11) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_168475,c_627]) ).
tcf(c_168968,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c1 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_165831,c_141783]) ).
tcf(c_168982,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( multiply(iPr_def_15,sk_c9) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_165831,c_639]) ).
tcf(c_169315,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( iPr_def_20 = iPr_def_24 )
| ( iPr_def_15 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_167181,c_165550]) ).
tcf(c_169322,plain,
( ( iPr_def_20 = iPr_def_24 )
| ~ iPr_def_12
| ( iPr_def_27 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_167181,c_142468]) ).
tcf(c_169338,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_24 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_167181,c_695]) ).
tcf(c_169341,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_24 )
| ( sk_c11 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_167181,c_685]) ).
tcf(c_169342,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_24 )
| ( sk_c10 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_167181,c_675]) ).
tcf(c_169477,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_169338,c_158,c_704,c_709,c_629,c_637,c_640,c_1331,c_1351,c_1352,c_1431,c_1501,c_1590,c_1593,c_1647,c_1805,c_2182,c_2190,c_2191,c_2260,c_2320,c_2434,c_2511,c_2553,c_2563,c_2590,c_2871,c_3667,c_3818,c_3924,c_4654,c_4655,c_4656,c_5508,c_5509,c_5510,c_5596,c_5597,c_15162,c_15269,c_17550,c_17654,c_20782,c_21543,c_21544,c_27748,c_38197,c_47233,c_48736,c_49005,c_49009,c_50082,c_51845,c_52490,c_52397,c_53465,c_54725,c_56796,c_56800,c_58261,c_58282,c_61503,c_61511,c_61509,c_66625,c_74226,c_74907,c_76391,c_77713,c_78032,c_78308,c_78501,c_83545,c_83568,c_83585,c_84505,c_88353,c_88384,c_92030,c_92031,c_92293,c_92295,c_93249,c_94778,c_99083,c_100209,c_100632,c_101364,c_101867,c_102586,c_102587,c_107386,c_107390,c_107391,c_107532,c_113062,c_113720,c_114518,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040,c_137262,c_137258,c_137256,c_150368,c_150594,c_161452,c_165133,c_165831,c_168968,c_169322,c_169315,c_169342,c_169341,c_169338]) ).
tcf(c_169501,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_169477,c_137262]) ).
tcf(c_169930,plain,
( ( iPr_def_20 = iPr_def_24 )
| ~ iPr_def_10
| ( sk_c11 != iPr_def_15 )
| ( multiply(identity,sk_c11) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_167183,c_140891]) ).
tcf(c_171712,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_27 )
| ( multiply(iPr_def_24,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_661,c_168571]) ).
tcf(c_171822,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c10 = iPr_def_23 )
| ( multiply(iPr_def_15,iPr_def_15) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_694,c_168982]) ).
tcf(c_171823,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c11 = iPr_def_20 )
| ( multiply(iPr_def_15,iPr_def_15) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_691,c_168982]) ).
tcf(c_172082,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != multiply(inverse(X2),sk_c10) )
| ( multiply(X0,X1) != multiply(inverse(X2),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_132171]) ).
tcf(c_172083,plain,
( ( sk_c11 = multiply(sk_c10,sk_c10) )
| ( sk_c11 != multiply(inverse(sk_c10),sk_c10) )
| ( multiply(sk_c10,sk_c10) != multiply(inverse(sk_c10),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_172082]) ).
tcf(c_172128,plain,
( iPr_def_14
| iPr_def_10
| ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_15 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_169501,c_165883]) ).
tcf(c_172481,plain,
sk_c10 = iPr_def_27,
inference(global_subsumption_just,[status(thm)],[c_167667,c_158,c_704,c_709,c_629,c_634,c_635,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2871,c_3523,c_3752,c_4655,c_4656,c_5497,c_5498,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_6670,c_6891,c_9741,c_11516,c_11535,c_15162,c_15259,c_15262,c_15269,c_17654,c_19474,c_19475,c_19838,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_24046,c_27454,c_27453,c_27597,c_28227,c_30304,c_30425,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_55775,c_55781,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_74039,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78308,c_78501,c_78580,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101159,c_101160,c_101172,c_101256,c_101738,c_101779,c_101791,c_101859,c_101867,c_101889,c_102216,c_102252,c_102255,c_102586,c_102587,c_102604,c_103067,c_103068,c_104339,c_106230,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_108978,c_110359,c_110778,c_113062,c_113720,c_114518,c_116751,c_117799,c_119325,c_119568,c_119569,c_123317,c_123312,c_126203,c_126228,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132040,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484,c_146887,c_150906,c_150915,c_152967,c_154433,c_154488,c_165082,c_166771,c_167520,c_172128]) ).
tcf(c_172543,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_78574,c_172481]) ).
tcf(c_172551,plain,
( ( iPr_def_27 = iPr_def_28 )
| ~ iPr_def_12 ),
inference(demodulation,[status(thm)],[c_74037,c_172481]) ).
tcf(c_172637,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c11 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_671,c_172481]) ).
tcf(c_172844,plain,
sk_c10 = iPr_def_27,
inference(global_subsumption_just,[status(thm)],[c_171712,c_172481]) ).
tcf(c_172900,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c3 = identity ) ),
inference(demodulation,[status(thm)],[c_146854,c_172844]) ).
tcf(c_173023,plain,
multiply(iPr_def_23,iPr_def_24) = iPr_def_27,
inference(demodulation,[status(thm)],[c_5690,c_172844]) ).
tcf(c_173027,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_647,c_172844]) ).
tcf(c_173030,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( sk_c9 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_694,c_172844]) ).
tcf(c_173032,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( sk_c9 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_675,c_172844]) ).
tcf(c_173039,plain,
multiply(sk_c1,iPr_def_27) = iPr_def_29,
inference(demodulation,[status(thm)],[c_641,c_172844]) ).
tcf(c_173045,plain,
multiply(iPr_def_27,sk_c11) = iPr_def_15,
inference(demodulation,[status(thm)],[c_627,c_172844]) ).
tcf(c_173305,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c11 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_173030,c_685]) ).
tcf(c_173336,plain,
iPr_def_27 = iPr_def_28,
inference(global_subsumption_just,[status(thm)],[c_172543,c_158,c_704,c_709,c_629,c_634,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2563,c_2590,c_2871,c_3523,c_3752,c_4655,c_4656,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_9741,c_11516,c_11535,c_15162,c_15262,c_15269,c_17130,c_17654,c_19474,c_19475,c_19925,c_20782,c_20868,c_21543,c_21544,c_23259,c_23464,c_24046,c_24578,c_27454,c_27453,c_27597,c_28227,c_29056,c_30304,c_30425,c_38661,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61138,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_74226,c_74907,c_76391,c_76943,c_77713,c_78032,c_78050,c_78197,c_78308,c_78501,c_84039,c_87509,c_88178,c_88353,c_88384,c_91402,c_93249,c_99083,c_100209,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101159,c_101160,c_101171,c_101172,c_101256,c_101738,c_101779,c_101791,c_101832,c_101859,c_101867,c_101889,c_102192,c_102496,c_102586,c_102587,c_102604,c_103067,c_103068,c_104339,c_106167,c_106230,c_107155,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_108979,c_110359,c_111628,c_113062,c_113720,c_113744,c_114518,c_116751,c_119325,c_123317,c_123312,c_126203,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132041,c_132040,c_132107,c_132230,c_132409,c_132410,c_132426,c_134825,c_137290,c_137484,c_142073,c_142155,c_143720,c_150368,c_151693,c_155803,c_156201,c_161561,c_167756,c_172128,c_172551,c_172637,c_172900]) ).
tcf(c_173493,plain,
iPr_def_27 = iPr_def_28,
inference(global_subsumption_just,[status(thm)],[c_173032,c_173336]) ).
tcf(c_173517,plain,
inverse(iPr_def_27) = sk_c1,
inference(demodulation,[status(thm)],[c_27653,c_173493]) ).
tcf(c_173518,plain,
multiply(sk_c1,iPr_def_27) = identity,
inference(demodulation,[status(thm)],[c_27403,c_173493]) ).
tcf(c_173526,plain,
identity = iPr_def_29,
inference(light_normalisation,[status(thm)],[c_173518,c_173039]) ).
tcf(c_173570,plain,
( ( iPr_def_20 = iPr_def_29 )
| ( sk_c11 = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_139279,c_173526]) ).
tcf(c_173573,plain,
multiply(iPr_def_20,sk_c3) = iPr_def_29,
inference(demodulation,[status(thm)],[c_137705,c_173526]) ).
tcf(c_173575,plain,
( iPr_def_14
| ( iPr_def_20 = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_137484,c_173526]) ).
tcf(c_173597,plain,
inverse(iPr_def_29) = iPr_def_29,
inference(demodulation,[status(thm)],[c_15521,c_173526]) ).
tcf(c_173598,plain,
! [X0: $i] : multiply(X0,iPr_def_29) = X0,
inference(demodulation,[status(thm)],[c_15498,c_173526]) ).
tcf(c_173602,plain,
multiply(iPr_def_23,sk_c4) = iPr_def_29,
inference(demodulation,[status(thm)],[c_1204,c_173526]) ).
tcf(c_173774,plain,
sk_c11 = iPr_def_29,
inference(global_subsumption_just,[status(thm)],[c_173305,c_8994,c_61218,c_101171,c_142155,c_173570]) ).
tcf(c_173784,plain,
multiply(sk_c3,iPr_def_29) = iPr_def_23,
inference(demodulation,[status(thm)],[c_152181,c_173774]) ).
tcf(c_173833,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( sk_c10 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_171822,c_158,c_704,c_709,c_629,c_634,c_635,c_637,c_640,c_1136,c_1412,c_1461,c_1518,c_1590,c_1593,c_1720,c_1805,c_1913,c_2260,c_2320,c_2434,c_2471,c_2511,c_2553,c_2563,c_2582,c_2590,c_2871,c_3523,c_3752,c_4654,c_4655,c_4656,c_5497,c_5498,c_5508,c_5509,c_5510,c_5595,c_5596,c_5597,c_6670,c_6891,c_7947,c_8994,c_9741,c_11516,c_11535,c_15160,c_15162,c_15259,c_15262,c_15269,c_15486,c_17654,c_19474,c_19475,c_19838,c_19925,c_20782,c_21543,c_21544,c_23259,c_23464,c_24046,c_24578,c_27454,c_27453,c_27597,c_28227,c_29056,c_30304,c_30425,c_47233,c_48565,c_50082,c_51845,c_52490,c_52397,c_53465,c_53479,c_54725,c_55775,c_55781,c_56796,c_56800,c_58255,c_58256,c_58286,c_58287,c_60186,c_60359,c_61121,c_61138,c_61207,c_61218,c_61503,c_61507,c_62080,c_62072,c_62066,c_62181,c_64811,c_65079,c_66625,c_68248,c_70028,c_74039,c_74226,c_74907,c_76391,c_76944,c_76943,c_77713,c_78032,c_78197,c_78308,c_78501,c_78580,c_84039,c_87509,c_88178,c_88353,c_88384,c_90026,c_91402,c_93249,c_99083,c_100209,c_100237,c_100302,c_100303,c_100309,c_100310,c_100550,c_100551,c_100668,c_101037,c_101150,c_101159,c_101160,c_101171,c_101172,c_101256,c_101738,c_101779,c_101791,c_101859,c_101867,c_101889,c_102216,c_102252,c_102255,c_102586,c_102587,c_102604,c_103067,c_103068,c_104339,c_106230,c_107155,c_107244,c_107386,c_107390,c_107391,c_107575,c_107653,c_108929,c_108978,c_110359,c_110778,c_113062,c_113720,c_113744,c_114518,c_116751,c_117799,c_119325,c_119568,c_119569,c_121035,c_123317,c_123312,c_126203,c_126228,c_126545,c_126703,c_126982,c_127072,c_127352,c_127638,c_127659,c_129802,c_129803,c_129804,c_131594,c_132041,c_132040,c_132039,c_132107,c_132230,c_132409,c_132410,c_132426,c_134825,c_137484,c_137819,c_142073,c_142155,c_143720,c_146887,c_150368,c_150906,c_150915,c_151693,c_154433,c_154488,c_156232,c_159367,c_163538,c_165082,c_165831,c_166771,c_167520,c_172128,c_173526,c_173570]) ).
tcf(c_173835,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_173833,c_172844]) ).
tcf(c_173850,plain,
( ( iPr_def_20 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_173835,c_137262]) ).
tcf(c_173864,plain,
iPr_def_20 = iPr_def_24,
inference(global_subsumption_just,[status(thm)],[c_171823,c_158,c_704,c_709,c_629,c_635,c_637,c_1331,c_1351,c_1352,c_1431,c_1590,c_1593,c_1805,c_1913,c_2260,c_2320,c_2434,c_2511,c_2553,c_2563,c_2590,c_2871,c_3349,c_4654,c_4655,c_4656,c_5497,c_5498,c_5508,c_5509,c_5510,c_8994,c_15162,c_15259,c_17654,c_19475,c_20782,c_21543,c_21544,c_27748,c_30304,c_38197,c_47070,c_47233,c_48734,c_48748,c_48941,c_48957,c_48958,c_50082,c_50726,c_50760,c_50761,c_51845,c_52490,c_52397,c_53465,c_54725,c_55788,c_56796,c_56800,c_60186,c_61218,c_66625,c_74226,c_74907,c_76391,c_77713,c_78032,c_78308,c_78501,c_79739,c_79780,c_79799,c_83546,c_83585,c_83622,c_84505,c_87572,c_87949,c_88034,c_88353,c_88384,c_93249,c_93270,c_93277,c_99083,c_100237,c_100632,c_100680,c_101171,c_101172,c_101364,c_101867,c_102586,c_102587,c_107386,c_107390,c_107391,c_113062,c_113720,c_114518,c_121035,c_126545,c_126982,c_127638,c_129802,c_129803,c_132040,c_132409,c_132410,c_137262,c_137256,c_142155,c_150368,c_150594,c_165133,c_165831,c_165871,c_168968,c_169322,c_169315,c_169501,c_169930,c_173526,c_173570,c_173833,c_173850]) ).
tcf(c_173875,plain,
( iPr_def_14
| iPr_def_10
| ( iPr_def_15 != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_165883,c_173864]) ).
tcf(c_173922,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_173027,c_7947,c_8994,c_61218,c_101171,c_132039,c_138739,c_142155,c_152092,c_163538,c_173526,c_173570]) ).
tcf(c_173976,plain,
multiply(iPr_def_23,iPr_def_20) = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_173023,c_173864]) ).
tcf(c_174008,plain,
multiply(iPr_def_27,iPr_def_29) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_173045,c_173774]) ).
tcf(c_174009,plain,
iPr_def_15 = iPr_def_27,
inference(demodulation,[status(thm)],[c_174008,c_173598]) ).
tcf(c_174012,plain,
multiply(iPr_def_23,iPr_def_20) = iPr_def_15,
inference(demodulation,[status(thm)],[c_173976,c_174009]) ).
tcf(c_174017,plain,
inverse(iPr_def_15) = sk_c1,
inference(demodulation,[status(thm)],[c_173517,c_174009]) ).
tcf(c_174022,plain,
sk_c10 = iPr_def_15,
inference(demodulation,[status(thm)],[c_172844,c_174009]) ).
tcf(c_174045,plain,
sk_c1 = sk_c2,
inference(demodulation,[status(thm)],[c_133095,c_174017]) ).
tcf(c_174247,plain,
multiply(sk_c3,iPr_def_29) = sk_c3,
inference(superposition,[status(thm)],[c_173573,c_137678]) ).
tcf(c_174249,plain,
sk_c3 = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_174247,c_173784]) ).
tcf(c_174267,plain,
inverse(iPr_def_23) = iPr_def_20,
inference(demodulation,[status(thm)],[c_137706,c_174249]) ).
tcf(c_174269,plain,
sk_c4 = iPr_def_20,
inference(demodulation,[status(thm)],[c_17517,c_174267]) ).
tcf(c_174270,plain,
multiply(iPr_def_23,iPr_def_20) = iPr_def_29,
inference(demodulation,[status(thm)],[c_173602,c_174269]) ).
tcf(c_174276,plain,
iPr_def_15 = iPr_def_29,
inference(light_normalisation,[status(thm)],[c_174270,c_174012]) ).
tcf(c_174285,plain,
inverse(iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_173597,c_174276]) ).
tcf(c_174286,plain,
( iPr_def_14
| ( iPr_def_15 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_173575,c_174276]) ).
tcf(c_174287,plain,
identity = iPr_def_15,
inference(demodulation,[status(thm)],[c_173526,c_174276]) ).
tcf(c_174290,plain,
sk_c1 = iPr_def_15,
inference(demodulation,[status(thm)],[c_174017,c_174285]) ).
tcf(c_174292,plain,
sk_c2 = iPr_def_15,
inference(demodulation,[status(thm)],[c_174045,c_174290]) ).
tcf(c_174297,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_174286,c_174287,c_174292,c_174022,c_173922,c_173875,c_173774,c_173526,c_172083,c_151365,c_150992,c_150368,c_133018,c_132763,c_132410,c_132409,c_132039,c_126545,c_121035,c_107391,c_107390,c_101172,c_100237,c_90026,c_61218,c_60186,c_54726,c_54725,c_17654,c_15486,c_15160,c_11535,c_4656,c_4655,c_4654,c_2471,c_1805,c_1461,c_629,c_709,c_704,c_158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP330-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:30:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 42.79/7.87 % SZS status Started for theBenchmark.p
% 42.79/7.87 % SZS status Unsatisfiable for theBenchmark.p
% 42.79/7.87
% 42.79/7.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 42.79/7.87
% 42.79/7.87 % ------ iProver source info
% 42.79/7.87
% 42.79/7.87 % git: date: 2026-07-19 20:42:38 +0200
% 42.79/7.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 42.79/7.87 % git: non_committed_changes: false
% 42.79/7.87
% 42.79/7.87 % ------ Parsing...% successful
% 42.79/7.87
% 42.79/7.87
% 42.79/7.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 42.79/7.87
% 42.79/7.87 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 42.79/7.87
% 42.79/7.87 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 42.79/7.87
% 42.79/7.87 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 42.79/7.87 % ------ Proving...
% 42.79/7.87 % ------ Problem Properties
% 42.79/7.87
% 42.79/7.87 %
% 42.79/7.87 % clauses 74
% 42.79/7.87 % conjectures 56
% 42.79/7.87 % EPR 51
% 42.79/7.87 % Horn 23
% 42.79/7.87 % unary 18
% 42.79/7.87 % binary 50
% 42.79/7.87 % lits 141
% 42.79/7.87 % lits eq 131
% 42.79/7.87 % fd_pure 0
% 42.79/7.87 % fd_pseudo 0
% 42.79/7.87 % fd_cond 0
% 42.79/7.87 % fd_pseudo_cond 0
% 42.79/7.87 % AC symbols 0
% 42.79/7.87
% 42.79/7.87 % ------ Schedule dynamic 5 is on
% 42.79/7.87
% 42.79/7.87 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 42.79/7.87
% 42.79/7.87
% 42.79/7.87 % ------
% 42.79/7.87 % Current options:
% 42.79/7.87 % ------
% 42.79/7.87
% 42.79/7.87
% 42.79/7.87 %
% 42.79/7.87
% 42.79/7.87 % ------ Proving...
% 42.79/7.87 %
% 42.79/7.87
% 42.79/7.87 % SZS status Unsatisfiable for theBenchmark.p
% 42.79/7.87
% 42.79/7.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.97/7.90
% 49.97/7.90
%------------------------------------------------------------------------------