%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP239-1 : 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 : n013.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 01:32:15 PM UTC 2026
% Result : Unsatisfiable 31.93s 12.26s
% Output : CNFRefutation 31.93s
% 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,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = inverse(sk_c4)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c5)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c6)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| inverse(sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = inverse(sk_c4)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = inverse(sk_c6)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c8 != multiply(X6,sk_c9)
| inverse(X5) != X6
| sk_c8 != multiply(X5,X6)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| sk_c9 != inverse(X2)
| multiply(X2,sk_c9) != X1
| sk_c8 != multiply(sk_c9,X1)
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X6,X4,X5] :
( sk_c8 != multiply(X6,sk_c9)
| inverse(X5) != X6
| sk_c8 != multiply(X5,X6)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(equality_resolution,[],[f90]) ).
fof(f92,plain,
! [X2,X3,X0,X4,X5] :
( sk_c8 != multiply(inverse(X5),sk_c9)
| sk_c8 != multiply(X5,inverse(X5))
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(equality_resolution,[],[f91]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( inverse(sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c9) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c9) = sk_c8 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_121,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_123,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_125,negated_conjecture,
( ( multiply(sk_c7,sk_c9) = sk_c8 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_127,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_128,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_130,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_132,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_133,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(sk_c9) != sk_c8 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c9 )
| ( multiply(X2,sk_c8) != sk_c9 )
| ( multiply(X1,sk_c8) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 )
| ( multiply(inverse(X4),sk_c9) != sk_c8 )
| ( multiply(X4,inverse(X4)) != sk_c8 )
| ( multiply(sk_c9,multiply(X3,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_141,plain,
multiply(identity,sk_c9) = sk_c9,
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_142,plain,
multiply(inverse(sk_c9),sk_c9) = identity,
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_533,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_140]) ).
tcf(c_534,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_140]) ).
tcf(c_535,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c9) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_140]) ).
tcf(c_536,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_140]) ).
tcf(c_537,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_538,definition,
iPr_def_14 = inverse(sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_539,definition,
iPr_def_15 = multiply(sk_c7,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_540,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_541,definition,
iPr_def_17 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_542,definition,
iPr_def_18 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_543,definition,
iPr_def_19 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_544,definition,
iPr_def_20 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_545,definition,
iPr_def_21 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_546,definition,
iPr_def_22 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_547,definition,
iPr_def_23 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_548,definition,
iPr_def_24 = multiply(sk_c9,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_549,definition,
iPr_def_25 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_550,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_551,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_537,c_538]) ).
tcf(c_552,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_536]) ).
tcf(c_554,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c9) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_535]) ).
tcf(c_555,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_534]) ).
tcf(c_556,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_533]) ).
tcf(c_557,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_139,c_540,c_539]) ).
tcf(c_558,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_138,c_541]) ).
tcf(c_559,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_137,c_542]) ).
tcf(c_560,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_136,c_543]) ).
tcf(c_561,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_135,c_544]) ).
tcf(c_562,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_134,c_545]) ).
tcf(c_563,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_133,c_546]) ).
tcf(c_564,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_132,c_547]) ).
tcf(c_565,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_567,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_568,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_570,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_571,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_125,c_548]) ).
tcf(c_572,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_573,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_574,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_575,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_576,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_577,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_578,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_118,c_549]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_580,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_581,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_582,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_583,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_584,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_585,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_550]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_587,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_588,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_589,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_590,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_591,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_592,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_594,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_595,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_596,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_597,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_598,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_599,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_601,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_603,plain,
( ( inverse(sk_c9) = inverse(sk_c9) )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_601]) ).
tcf(c_605,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_872,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_557,c_559]) ).
tcf(c_882,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_560,c_559]) ).
tcf(c_883,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_560,c_557]) ).
tcf(c_896,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_561,c_562]) ).
tcf(c_906,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_563,c_562]) ).
tcf(c_907,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_563,c_561]) ).
tcf(c_937,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_558,c_542]) ).
tcf(c_987,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_572,c_542]) ).
tcf(c_994,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_560,c_544]) ).
tcf(c_1019,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_561,c_547]) ).
tcf(c_1031,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_568,c_548]) ).
tcf(c_1032,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_567,c_548]) ).
tcf(c_1033,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_566,c_548]) ).
tcf(c_1035,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_564,c_548]) ).
tcf(c_1056,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_571,c_549]) ).
tcf(c_1068,plain,
multiply(iPr_def_14,sk_c9) = identity,
inference(superposition,[status(thm)],[c_538,c_96]) ).
tcf(c_1069,plain,
multiply(iPr_def_22,sk_c4) = identity,
inference(superposition,[status(thm)],[c_546,c_96]) ).
tcf(c_1070,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_543,c_96]) ).
tcf(c_1071,plain,
multiply(iPr_def_17,sk_c6) = identity,
inference(superposition,[status(thm)],[c_541,c_96]) ).
tcf(c_1072,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_550,c_96]) ).
tcf(c_1073,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_540,c_96]) ).
tcf(c_1090,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_573,c_549]) ).
tcf(c_1111,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c8 )
| ( iPr_def_14 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1114,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1115,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_1116,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_1117,plain,
( ( sk_c8 = sk_c9 )
| ( sk_c8 != sk_c8 )
| ( sk_c9 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1126,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_574,c_549]) ).
tcf(c_1127,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_574,c_545]) ).
tcf(c_1149,plain,
( ( sk_c8 = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1150,plain,
multiply(identity,sk_c8) = sk_c8,
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1154,plain,
( ( sk_c8 = iPr_def_15 )
| ( iPr_def_15 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1155,plain,
( ( sk_c8 = iPr_def_18 )
| ( iPr_def_18 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1156,plain,
( ( sk_c8 = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1165,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_575,c_549]) ).
tcf(c_1187,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_1196,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_576,c_549]) ).
tcf(c_1230,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_577,c_549]) ).
tcf(c_1252,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( X0 != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_1257,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_1258,plain,
( ( sk_c9 = sk_c8 )
| ( sk_c8 != iPr_def_15 )
| ( sk_c9 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1257]) ).
tcf(c_1259,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_1261,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_1283,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_578,c_549]) ).
tcf(c_1319,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_15 != X0 )
| ( iPr_def_14 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1321,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_18 )
| ( iPr_def_18 != X0 )
| ( iPr_def_14 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1326,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1333,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_579,c_542]) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_18 )
| ( iPr_def_18 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1358,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_580,c_578]) ).
tcf(c_1399,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_19 )
| ( iPr_def_19 != X0 )
| ( iPr_def_14 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1406,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_19 )
| ( iPr_def_19 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1411,plain,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c8 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1257]) ).
tcf(c_1412,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_1429,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_580]) ).
tcf(c_1436,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_549]) ).
tcf(c_1438,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_581,c_544]) ).
tcf(c_1472,plain,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_19 != iPr_def_19 )
| ( sk_c8 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1259]) ).
tcf(c_1473,plain,
iPr_def_19 = iPr_def_19,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_1478,plain,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_18 != iPr_def_18 )
| ( sk_c8 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_1479,plain,
iPr_def_18 = iPr_def_18,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_1485,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,sk_c8) )
| ( X1 != X0 )
| ( multiply(identity,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1501,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_582,c_547]) ).
tcf(c_1547,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_583,c_547]) ).
tcf(c_1590,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_584,c_547]) ).
tcf(c_1631,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_14 )
| ( iPr_def_14 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1319]) ).
tcf(c_1632,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_1633,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1656,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_585,c_549]) ).
tcf(c_1711,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1712,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c7,sk_c9) )
| ( X0 != multiply(sk_c7,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1326]) ).
tcf(c_1715,plain,
( ( sk_c8 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1718,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( iPr_def_18 != sk_c8 )
| ( iPr_def_14 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1321]) ).
tcf(c_1719,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_15 != sk_c8 )
| ( iPr_def_14 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1319]) ).
tcf(c_1725,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_586,c_542]) ).
tcf(c_1746,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_587,c_585]) ).
tcf(c_1792,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c9 )
| ( sk_c9 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1797,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_18 = X0 )
| ( iPr_def_18 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1800,plain,
! [X0: $i] :
( ( X0 = iPr_def_18 )
| ( iPr_def_18 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1342]) ).
tcf(c_1819,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_588,c_587]) ).
tcf(c_1820,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_588,c_585]) ).
tcf(c_1828,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_588,c_549]) ).
tcf(c_1830,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_588,c_544]) ).
tcf(c_1863,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_19 = X0 )
| ( iPr_def_19 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1864,plain,
! [X0: $i] :
( ( X0 = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c5) )
| ( X0 != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1406]) ).
tcf(c_1866,plain,
! [X0: $i] :
( ( X0 = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1406]) ).
tcf(c_1888,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_589,c_582]) ).
tcf(c_1893,plain,
( ( sk_c9 = iPr_def_20 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_589,c_538]) ).
tcf(c_1927,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c8) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1932,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c8) )
| ( X0 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1485]) ).
tcf(c_1940,plain,
multiply(identity,identity) = identity,
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1945,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_1947,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_1960,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_590,c_583]) ).
tcf(c_1964,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_26) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_590,c_547]) ).
tcf(c_1966,plain,
( ( sk_c9 = iPr_def_21 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_590,c_538]) ).
tcf(c_2034,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_18 != sk_c8 )
| ( iPr_def_15 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1800]) ).
tcf(c_2036,plain,
( ( iPr_def_19 = iPr_def_18 )
| ( iPr_def_19 != sk_c8 )
| ( iPr_def_18 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1800]) ).
tcf(c_2053,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_591,c_584]) ).
tcf(c_2058,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_26) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_591,c_547]) ).
tcf(c_2060,plain,
( ( sk_c9 = iPr_def_22 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_591,c_538]) ).
tcf(c_2093,plain,
( ( multiply(identity,sk_c8) = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1866]) ).
tcf(c_2103,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_2106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_2194,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_14 )
| ( iPr_def_14 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1399]) ).
tcf(c_2235,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_593,c_542]) ).
tcf(c_2248,plain,
( ( iPr_def_14 = sk_c8 )
| ( iPr_def_14 != iPr_def_24 )
| ( sk_c8 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1111]) ).
tcf(c_2249,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_2250,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_2251,plain,
( ( sk_c8 = sk_c9 )
| ( sk_c8 != iPr_def_24 )
| ( sk_c9 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2250]) ).
tcf(c_2252,plain,
( ( sk_c9 = sk_c8 )
| ( sk_c8 != iPr_def_24 )
| ( sk_c9 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2249]) ).
tcf(c_2270,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_594,c_592]) ).
tcf(c_2280,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_594,c_549]) ).
tcf(c_2345,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_15 )
| ( iPr_def_14 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1399]) ).
tcf(c_2350,plain,
( ( iPr_def_14 = sk_c8 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c8 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1111]) ).
tcf(c_2351,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_2352,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_2354,plain,
( ( sk_c9 = sk_c8 )
| ( sk_c8 != iPr_def_14 )
| ( sk_c9 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2351]) ).
tcf(c_2373,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_595,c_594]) ).
tcf(c_2384,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_595,c_549]) ).
tcf(c_2386,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_595,c_544]) ).
tcf(c_2521,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_575]) ).
tcf(c_2522,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_574]) ).
tcf(c_2523,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_573]) ).
tcf(c_2524,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_596,c_549]) ).
tcf(c_2527,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_571]) ).
tcf(c_2677,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_597,c_576]) ).
tcf(c_2827,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_598,c_577]) ).
tcf(c_2910,plain,
( ( multiply(sk_c7,sk_c9) = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c7,sk_c9) )
| ( multiply(sk_c7,sk_c9) != multiply(sk_c7,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1712]) ).
tcf(c_2911,plain,
multiply(sk_c7,sk_c9) = multiply(sk_c7,sk_c9),
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_2978,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_2980,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c9,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1068,c_97]) ).
tcf(c_2981,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1069,c_97]) ).
tcf(c_2982,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1070,c_97]) ).
tcf(c_2983,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1071,c_97]) ).
tcf(c_2984,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1072,c_97]) ).
tcf(c_2985,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1073,c_97]) ).
tcf(c_2987,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2985,c_95]) ).
tcf(c_2988,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2984,c_95]) ).
tcf(c_2989,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2983,c_95]) ).
tcf(c_2990,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2982,c_95]) ).
tcf(c_2991,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2981,c_95]) ).
tcf(c_2992,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c9,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2980,c_95]) ).
tcf(c_3040,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_872,c_547]) ).
tcf(c_3080,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c5) )
| ( inverse(X0) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1864]) ).
tcf(c_3081,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c5) )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_601]) ).
tcf(c_3083,plain,
( ( inverse(sk_c9) = inverse(sk_c5) )
| ( sk_c9 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_3081]) ).
tcf(c_3106,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_882,c_547]) ).
tcf(c_3154,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1633]) ).
tcf(c_3155,plain,
( ( iPr_def_14 = sk_c9 )
| ( iPr_def_14 != sk_c8 )
| ( sk_c9 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_3154]) ).
tcf(c_3160,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1633]) ).
tcf(c_3167,plain,
! [X0: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1711]) ).
tcf(c_3169,plain,
! [X0: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1711]) ).
tcf(c_3170,plain,
( ( iPr_def_15 = sk_c9 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c9 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_3169]) ).
tcf(c_3176,plain,
! [X0: $i] :
( ( iPr_def_18 = X0 )
| ( iPr_def_18 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1797]) ).
tcf(c_3250,plain,
! [X0: $i] :
( ( iPr_def_19 = X0 )
| ( iPr_def_19 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1863]) ).
tcf(c_3270,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_896,c_590]) ).
tcf(c_3271,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_896,c_589]) ).
tcf(c_3273,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_896,c_583]) ).
tcf(c_3274,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_896,c_582]) ).
tcf(c_3277,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_896,c_547]) ).
tcf(c_3279,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_896,c_538]) ).
tcf(c_3339,plain,
( ( iPr_def_15 = multiply(identity,sk_c8) )
| ( iPr_def_15 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1932]) ).
tcf(c_3365,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_551]) ).
tcf(c_3366,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_595,c_551]) ).
tcf(c_3378,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_574,c_551]) ).
tcf(c_3380,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_15 )
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_571,c_551]) ).
tcf(c_3528,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_544,c_555]) ).
tcf(c_3529,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_549,c_555]) ).
tcf(c_3530,plain,
( ~ iPr_def_11
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_555]) ).
tcf(c_3531,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_96,c_555]) ).
tcf(c_3557,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_26 )
| ( sk_c9 != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_3529,c_550]) ).
tcf(c_3561,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3528,c_543]) ).
tcf(c_3713,plain,
! [X0: $i] :
( ( multiply(identity,sk_c8) = X0 )
| ( X0 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1927]) ).
tcf(c_3777,plain,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_15 != iPr_def_18 )
| ( sk_c8 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_3779,plain,
! [X0: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1711]) ).
tcf(c_3780,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1326]) ).
tcf(c_3789,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_21 )
| ( inverse(sk_c4) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_545,c_556]) ).
tcf(c_3791,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_549,c_556]) ).
tcf(c_3819,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_26 )
| ( sk_c9 != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_3791,c_550]) ).
tcf(c_3827,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_22 )
| ( sk_c9 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3789,c_546]) ).
tcf(c_3946,plain,
! [X0: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1711]) ).
tcf(c_3947,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1326]) ).
tcf(c_3952,plain,
! [X0: $i] :
( ( iPr_def_18 = X0 )
| ( iPr_def_18 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1797]) ).
tcf(c_3993,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_2106]) ).
tcf(c_3997,plain,
( ( sk_c8 = iPr_def_24 )
| ( iPr_def_24 != multiply(identity,sk_c8) )
| ( sk_c8 != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1252]) ).
tcf(c_4028,plain,
( ~ iPr_def_13
| ( inverse(sk_c2) != sk_c9 )
| ( multiply(sk_c9,iPr_def_23) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_547,c_552]) ).
tcf(c_4029,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c9 )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_552]) ).
tcf(c_4052,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_16 )
| ( multiply(sk_c9,iPr_def_23) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_4028,c_540]) ).
tcf(c_4136,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( iPr_def_14 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_3154]) ).
tcf(c_4237,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = inverse(X0) )
| ( sk_c9 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_4246,plain,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_24 != iPr_def_24 )
| ( sk_c8 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2249]) ).
tcf(c_4247,plain,
iPr_def_24 = iPr_def_24,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_4248,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_4343,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_906,c_591]) ).
tcf(c_4344,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_906,c_590]) ).
tcf(c_4351,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_906,c_547]) ).
tcf(c_4353,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_906,c_538]) ).
tcf(c_4399,plain,
( ( multiply(identity,iPr_def_14) = sk_c8 )
| ( sk_c8 != iPr_def_14 )
| ( multiply(identity,iPr_def_14) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2351]) ).
tcf(c_4400,plain,
multiply(identity,iPr_def_14) = iPr_def_14,
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_4402,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_4403,plain,
( ( sk_c9 = iPr_def_14 )
| ( iPr_def_14 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_4451,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_907,c_591]) ).
tcf(c_4453,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_907,c_589]) ).
tcf(c_4459,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_907,c_547]) ).
tcf(c_4461,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_907,c_538]) ).
tcf(c_4871,plain,
( ( iPr_def_18 = iPr_def_15 )
| ( iPr_def_18 != iPr_def_18 )
| ( iPr_def_15 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3176]) ).
tcf(c_4878,plain,
( ( iPr_def_19 = iPr_def_18 )
| ( iPr_def_19 != iPr_def_19 )
| ( iPr_def_18 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3250]) ).
tcf(c_4903,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1746,c_1358]) ).
tcf(c_4910,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1746,c_872]) ).
tcf(c_4918,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1746,c_538]) ).
tcf(c_5007,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_16 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1819,c_882]) ).
tcf(c_5016,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1819,c_538]) ).
tcf(c_5076,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1820,c_883]) ).
tcf(c_5086,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1820,c_538]) ).
tcf(c_5178,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1888,c_538]) ).
tcf(c_5381,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1960,c_1888]) ).
tcf(c_5530,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_21 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_2053,c_1960]) ).
tcf(c_5531,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_2053,c_1888]) ).
tcf(c_5636,plain,
( ( inverse(sk_c5) = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c5) )
| ( inverse(sk_c5) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_3080]) ).
tcf(c_5637,plain,
inverse(sk_c5) = inverse(sk_c5),
inference(instantiation,[status(thm)],[c_2103]) ).
tcf(c_5641,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_5642,plain,
( ( sk_c9 = sk_c5 )
| ( sk_c5 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_5641]) ).
tcf(c_5865,plain,
( ( multiply(identity,sk_c8) = iPr_def_14 )
| ( iPr_def_14 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_3713]) ).
tcf(c_5909,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2373,c_551]) ).
tcf(c_6193,plain,
! [X0: $i] :
( ( inverse(sk_c5) = inverse(X0) )
| ( sk_c5 != X0 ) ),
inference(instantiation,[status(thm)],[c_601]) ).
tcf(c_6195,plain,
( ( inverse(sk_c5) = inverse(sk_c9) )
| ( sk_c5 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_6193]) ).
tcf(c_6304,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2521,c_538]) ).
tcf(c_6423,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2677,c_2521]) ).
tcf(c_6585,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2827,c_2521]) ).
tcf(c_6692,plain,
! [X0: $i] :
( ( iPr_def_18 = X0 )
| ( iPr_def_18 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1797]) ).
tcf(c_6745,plain,
multiply(iPr_def_16,iPr_def_23) = sk_c9,
inference(superposition,[status(thm)],[c_547,c_2987]) ).
tcf(c_6752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_6754,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_14 )
| ( iPr_def_14 != inverse(sk_c9) )
| ( inverse(X0) != inverse(sk_c9) ) ),
inference(instantiation,[status(thm)],[c_3993]) ).
tcf(c_6755,plain,
( ( inverse(sk_c9) = iPr_def_14 )
| ( iPr_def_14 != inverse(sk_c9) )
| ( inverse(sk_c9) != inverse(sk_c9) ) ),
inference(instantiation,[status(thm)],[c_6754]) ).
tcf(c_6769,plain,
multiply(iPr_def_26,iPr_def_25) = sk_c8,
inference(superposition,[status(thm)],[c_549,c_2988]) ).
tcf(c_6842,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_544,c_2990]) ).
tcf(c_6867,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( iPr_def_18 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_5909,c_1429,c_1819,c_3819,c_5909]) ).
tcf(c_7018,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_18 )
| ( iPr_def_18 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3176]) ).
tcf(c_7019,plain,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_19 != iPr_def_18 )
| ( sk_c8 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_7021,plain,
! [X0: $i] :
( ( iPr_def_19 = X0 )
| ( iPr_def_19 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1863]) ).
tcf(c_7022,plain,
! [X0: $i] :
( ( X0 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1406]) ).
tcf(c_7025,plain,
multiply(iPr_def_22,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_545,c_2991]) ).
tcf(c_7072,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != multiply(identity,sk_c8) )
| ( X0 != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1326]) ).
tcf(c_7077,plain,
multiply(iPr_def_14,iPr_def_24) = sk_c3,
inference(superposition,[status(thm)],[c_548,c_2992]) ).
tcf(c_7225,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c8) )
| ( X0 != iPr_def_19 )
| ( multiply(identity,sk_c8) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1485]) ).
tcf(c_7731,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_19 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1321]) ).
tcf(c_7733,plain,
( ( iPr_def_19 = iPr_def_14 )
| ( iPr_def_19 != iPr_def_19 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3250]) ).
tcf(c_7854,plain,
( ( iPr_def_18 = iPr_def_14 )
| ( iPr_def_18 != iPr_def_18 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3176]) ).
tcf(c_7984,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_24 )
| ( iPr_def_14 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1399]) ).
tcf(c_7987,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1633]) ).
tcf(c_7988,plain,
( ( iPr_def_14 = sk_c9 )
| ( iPr_def_14 != iPr_def_24 )
| ( sk_c9 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_7987]) ).
tcf(c_8015,plain,
! [X0: $i] :
( ( multiply(identity,sk_c8) = X0 )
| ( X0 != iPr_def_14 )
| ( multiply(identity,sk_c8) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1927]) ).
tcf(c_8016,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c8) )
| ( X0 != iPr_def_14 )
| ( multiply(identity,sk_c8) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1485]) ).
tcf(c_8383,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1019,c_2987]) ).
tcf(c_8384,plain,
( ( sk_c9 = iPr_def_20 )
| ( sk_c9 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_8383,c_6745]) ).
tcf(c_8791,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1031,c_2992]) ).
tcf(c_8792,plain,
( ( sk_c3 = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_8791,c_7077]) ).
tcf(c_8853,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_882,c_1032]) ).
tcf(c_8865,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1032,c_2992]) ).
tcf(c_8866,plain,
( ( sk_c3 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_8865,c_7077]) ).
tcf(c_8875,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_8853,c_6745]) ).
tcf(c_8970,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_883,c_1033]) ).
tcf(c_8971,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_882,c_1033]) ).
tcf(c_8972,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_872,c_1033]) ).
tcf(c_8989,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_8972,c_6745]) ).
tcf(c_8993,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_8971,c_6745]) ).
tcf(c_8997,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_8970,c_6745]) ).
tcf(c_9054,plain,
( ( iPr_def_15 = multiply(identity,iPr_def_14) )
| ( iPr_def_15 != sk_c8 )
| ( multiply(identity,iPr_def_14) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_3167]) ).
tcf(c_9061,plain,
( ( multiply(identity,iPr_def_14) = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( multiply(identity,iPr_def_14) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1866]) ).
tcf(c_9248,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_883,c_1035]) ).
tcf(c_9275,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_9248,c_6745]) ).
tcf(c_9738,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( iPr_def_19 != multiply(identity,iPr_def_14) )
| ( iPr_def_14 != multiply(identity,iPr_def_14) ) ),
inference(instantiation,[status(thm)],[c_1399]) ).
tcf(c_9739,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( iPr_def_18 != multiply(identity,iPr_def_14) )
| ( iPr_def_14 != multiply(identity,iPr_def_14) ) ),
inference(instantiation,[status(thm)],[c_1321]) ).
tcf(c_9740,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_15 != multiply(identity,iPr_def_14) )
| ( iPr_def_14 != multiply(identity,iPr_def_14) ) ),
inference(instantiation,[status(thm)],[c_1319]) ).
tcf(c_9773,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1126,c_2988]) ).
tcf(c_9774,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_9773,c_6769]) ).
tcf(c_9965,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_15 )
| ( iPr_def_15 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_3169]) ).
tcf(c_9967,plain,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_18 != iPr_def_15 )
| ( sk_c8 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1257]) ).
tcf(c_9968,plain,
( ( sk_c8 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_15 )
| ( sk_c8 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1187]) ).
tcf(c_9970,plain,
! [X0: $i] :
( ( X0 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1342]) ).
tcf(c_9971,plain,
( ( sk_c9 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_15 )
| ( sk_c9 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_9970]) ).
tcf(c_10247,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1165,c_2988]) ).
tcf(c_10248,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_10247,c_6769]) ).
tcf(c_10288,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1196,c_2988]) ).
tcf(c_10289,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_10288,c_6769]) ).
tcf(c_10350,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1230,c_2988]) ).
tcf(c_10351,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_10350,c_6769]) ).
tcf(c_10388,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1283,c_2988]) ).
tcf(c_10389,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c9 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_10388,c_6769]) ).
tcf(c_10488,plain,
( ( iPr_def_14 = multiply(identity,iPr_def_14) )
| ( iPr_def_14 != iPr_def_14 )
| ( multiply(identity,iPr_def_14) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_3160]) ).
tcf(c_10586,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_18 )
| ( iPr_def_15 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3779]) ).
tcf(c_10601,plain,
( ( iPr_def_19 = iPr_def_15 )
| ( iPr_def_19 != iPr_def_18 )
| ( iPr_def_15 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3780]) ).
tcf(c_10646,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1436,c_2988]) ).
tcf(c_10647,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_10646,c_6769]) ).
tcf(c_10695,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_19 )
| ( iPr_def_15 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3946]) ).
tcf(c_10697,plain,
( ( iPr_def_15 = iPr_def_14 )
| ( iPr_def_15 != iPr_def_19 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3946]) ).
tcf(c_10700,plain,
( ( iPr_def_15 = multiply(identity,sk_c8) )
| ( iPr_def_15 != iPr_def_19 )
| ( multiply(identity,sk_c8) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3946]) ).
tcf(c_10741,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1501,c_2987]) ).
tcf(c_10742,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_10741,c_6745]) ).
tcf(c_10951,plain,
( ( iPr_def_18 = iPr_def_14 )
| ( iPr_def_18 != iPr_def_19 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3952]) ).
tcf(c_10964,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1547,c_2987]) ).
tcf(c_10965,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_10964,c_6745]) ).
tcf(c_11174,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1590,c_2987]) ).
tcf(c_11175,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_11174,c_6745]) ).
tcf(c_11228,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1656,c_2988]) ).
tcf(c_11229,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c9 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_11228,c_6769]) ).
tcf(c_11621,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1828,c_2988]) ).
tcf(c_11622,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_11621,c_6769]) ).
tcf(c_12019,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1964,c_2987]) ).
tcf(c_12020,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_12019,c_6745]) ).
tcf(c_12114,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_2058,c_2987]) ).
tcf(c_12115,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_12114,c_6745]) ).
tcf(c_12551,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_2280,c_2988]) ).
tcf(c_12552,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_12551,c_6769]) ).
tcf(c_12583,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2384,c_2988]) ).
tcf(c_12584,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_12583,c_6769]) ).
tcf(c_12615,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2524,c_2988]) ).
tcf(c_12616,plain,
( ( sk_c8 = iPr_def_14 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_12615,c_6769]) ).
tcf(c_13702,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != multiply(sk_c9,sk_c3) )
| ( X0 != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_4248]) ).
tcf(c_13703,plain,
( ( sk_c9 = iPr_def_24 )
| ( iPr_def_24 != multiply(sk_c9,sk_c3) )
| ( sk_c9 != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_13702]) ).
tcf(c_13704,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_4248]) ).
tcf(c_13705,plain,
( ( sk_c9 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( sk_c9 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_13704]) ).
tcf(c_14558,plain,
( ( iPr_def_14 = multiply(sk_c7,sk_c9) )
| ( iPr_def_14 != sk_c8 )
| ( multiply(sk_c7,sk_c9) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_3154]) ).
tcf(c_16056,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_2522,c_574,c_595,c_1116,c_1156,c_4136]) ).
tcf(c_16141,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_16056,c_544]) ).
tcf(c_16245,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_2523,c_573,c_594,c_1116,c_1155,c_4136]) ).
tcf(c_16289,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_16245,c_16056]) ).
tcf(c_16517,plain,
( ( inverse(sk_c5) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_19 )
| ( inverse(sk_c5) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3947]) ).
tcf(c_16518,plain,
( ( iPr_def_15 = inverse(sk_c5) )
| ( iPr_def_15 != iPr_def_19 )
| ( inverse(sk_c5) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3946]) ).
tcf(c_16679,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_2527,c_571,c_592,c_1116,c_1154,c_4136]) ).
tcf(c_17006,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_17008,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_17010,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_17017,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_17018,plain,
( ( sk_c9 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_24 )
| ( sk_c9 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_17017]) ).
tcf(c_17134,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2978,c_95]) ).
tcf(c_17175,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_17134]) ).
tcf(c_17176,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_17134]) ).
tcf(c_17374,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_2992,c_17134]) ).
tcf(c_17375,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2991,c_17134]) ).
tcf(c_17376,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2990,c_17134]) ).
tcf(c_17377,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2989,c_17134]) ).
tcf(c_17378,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2988,c_17134]) ).
tcf(c_17379,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2987,c_17134]) ).
tcf(c_17437,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_17134,c_17134]) ).
tcf(c_18452,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_17176,c_17437]) ).
tcf(c_18491,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_18452,c_17175]) ).
tcf(c_18506,plain,
( ~ iPr_def_12
| ( multiply(identity,identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_18491,c_554]) ).
tcf(c_18509,plain,
( ~ iPr_def_12
| ( multiply(identity,identity) != sk_c8 )
| ( multiply(identity,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_18506,c_18491]) ).
tcf(c_18974,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_3271,c_3270]) ).
tcf(c_19586,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_3274,c_3273]) ).
tcf(c_19654,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_3557,c_3561,c_3557,c_10647,c_10742]) ).
tcf(c_19687,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_11
| ( iPr_def_14 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_598,c_19654]) ).
tcf(c_19688,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11
| ( iPr_def_14 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_597,c_19654]) ).
tcf(c_19690,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_11
| ( iPr_def_19 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_595,c_19654]) ).
tcf(c_19696,plain,
( ( sk_c9 = iPr_def_25 )
| ~ iPr_def_11
| ( iPr_def_19 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_581,c_19654]) ).
tcf(c_19699,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_11
| ( iPr_def_24 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_577,c_19654]) ).
tcf(c_19701,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( iPr_def_24 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_575,c_19654]) ).
tcf(c_19702,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_11
| ( iPr_def_24 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_574,c_19654]) ).
tcf(c_20057,plain,
multiply(sk_c9,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_17374,c_96]) ).
tcf(c_20060,plain,
! [X0: $i] : multiply(sk_c9,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_17374,c_17134]) ).
tcf(c_20061,plain,
multiply(sk_c9,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_17374,c_18452]) ).
tcf(c_20152,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11
| ( iPr_def_14 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_5531,c_19688]) ).
tcf(c_20413,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_19690,c_3561,c_12584,c_12616]) ).
tcf(c_21101,plain,
inverse(iPr_def_14) = sk_c9,
inference(demodulation,[status(thm)],[c_20061,c_18452]) ).
tcf(c_21175,plain,
multiply(sk_c9,sk_c3) = iPr_def_24,
inference(superposition,[status(thm)],[c_7077,c_20060]) ).
tcf(c_21180,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 )
| ( inverse(iPr_def_14) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_20060,c_552]) ).
tcf(c_21286,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 ) ),
inference(ground_joinability,[status(thm)],[c_21180,c_21101]) ).
tcf(c_21459,plain,
( ( iPr_def_18 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2373,c_21286]) ).
tcf(c_21461,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_598,c_21286]) ).
tcf(c_21462,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_597,c_21286]) ).
tcf(c_21474,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_576,c_21286]) ).
tcf(c_21475,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_575,c_21286]) ).
tcf(c_21477,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_573,c_21286]) ).
tcf(c_21478,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_571,c_21286]) ).
tcf(c_21590,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = iPr_def_15 )
| ( iPr_def_15 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_3993]) ).
tcf(c_21815,plain,
( ( sk_c9 = iPr_def_25 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_19696,c_3561,c_10647,c_10742]) ).
tcf(c_21863,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_4344,c_4343]) ).
tcf(c_21926,plain,
( ( iPr_def_24 != iPr_def_26 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_19699,c_3561,c_19702,c_19701]) ).
tcf(c_21927,plain,
( ~ iPr_def_11
| ( iPr_def_24 != iPr_def_26 ) ),
inference(renaming,[status(thm)],[c_21926]) ).
tcf(c_21974,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_19 )
| ( iPr_def_19 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_22184,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_907,c_21461]) ).
tcf(c_22190,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_591,c_21461]) ).
tcf(c_22264,plain,
( ( identity = sk_c8 )
| ( identity != iPr_def_18 )
| ( sk_c8 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_22342,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_907,c_21462]) ).
tcf(c_22885,plain,
( ( identity = iPr_def_15 )
| ( iPr_def_15 != iPr_def_18 )
| ( identity != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3780]) ).
tcf(c_22956,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_21863,c_5530]) ).
tcf(c_23171,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1947]) ).
tcf(c_23173,plain,
( ( sk_c9 = identity )
| ( identity != iPr_def_18 )
| ( sk_c9 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_23171]) ).
tcf(c_23338,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2106]) ).
tcf(c_23339,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c9 )
| ( sk_c9 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1792]) ).
tcf(c_23341,plain,
( ( inverse(sk_c9) = sk_c9 )
| ( sk_c9 != iPr_def_14 )
| ( inverse(sk_c9) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_23339]) ).
tcf(c_23384,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_4248]) ).
tcf(c_23386,plain,
( ( sk_c9 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_14 )
| ( sk_c9 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_23384]) ).
tcf(c_24425,plain,
( ( iPr_def_18 = inverse(sk_c5) )
| ( iPr_def_18 != iPr_def_18 )
| ( inverse(sk_c5) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3176]) ).
tcf(c_24427,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c5) )
| ( iPr_def_18 != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1864]) ).
tcf(c_24916,plain,
multiply(sk_c4,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_17375,c_18452]) ).
tcf(c_24979,plain,
inverse(iPr_def_22) = sk_c4,
inference(demodulation,[status(thm)],[c_24916,c_18452]) ).
tcf(c_26774,plain,
multiply(sk_c5,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_17376,c_96]) ).
tcf(c_26777,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_17376,c_17134]) ).
tcf(c_26778,plain,
multiply(sk_c5,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_17376,c_18452]) ).
tcf(c_26793,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_16141,c_26774]) ).
tcf(c_26794,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_2386,c_26774]) ).
tcf(c_26795,plain,
( ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1830,c_26774]) ).
tcf(c_26796,plain,
( ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1438,c_26774]) ).
tcf(c_26797,plain,
( ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_994,c_26774]) ).
tcf(c_26854,plain,
inverse(iPr_def_19) = sk_c5,
inference(demodulation,[status(thm)],[c_26778,c_18452]) ).
tcf(c_26864,plain,
multiply(sk_c5,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_6842,c_26777]) ).
tcf(c_26941,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( inverse(iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_26793,c_18491]) ).
tcf(c_26943,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_26793,c_95]) ).
tcf(c_26999,plain,
( ( identity = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_26794,c_21286]) ).
tcf(c_27467,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_26796,c_26795]) ).
tcf(c_27916,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_26797,c_26795]) ).
tcf(c_27956,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_26797,c_1035]) ).
tcf(c_27960,plain,
( ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_26797,c_1031]) ).
tcf(c_27987,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_26797,c_547]) ).
tcf(c_28033,plain,
( ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_27960,c_6745]) ).
tcf(c_28049,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_15 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_27956,c_6745]) ).
tcf(c_28282,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( inverse(iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_27467,c_18491]) ).
tcf(c_28284,plain,
! [X0: $i] :
( ( iPr_def_25 = iPr_def_26 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_27467,c_95]) ).
tcf(c_28661,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( inverse(X0) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_13704]) ).
tcf(c_28662,plain,
! [X0: $i] :
( ( sk_c9 = inverse(X0) )
| ( sk_c9 != iPr_def_24 )
| ( inverse(X0) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_4237]) ).
tcf(c_28665,plain,
( ( inverse(sk_c9) = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( inverse(sk_c9) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_28661]) ).
tcf(c_28667,plain,
( ( sk_c9 = inverse(sk_c9) )
| ( sk_c9 != iPr_def_24 )
| ( inverse(sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_28662]) ).
tcf(c_29133,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != sk_c8 )
| ( inverse(X0) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_6752]) ).
tcf(c_29139,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2351]) ).
tcf(c_29141,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != iPr_def_18 )
| ( inverse(X0) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_29143,plain,
( ( inverse(sk_c9) = sk_c8 )
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c9) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_29141]) ).
tcf(c_29145,plain,
( ( inverse(sk_c9) = sk_c8 )
| ( sk_c8 != iPr_def_14 )
| ( inverse(sk_c9) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_29139]) ).
tcf(c_29151,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_15 )
| ( inverse(X0) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_6752]) ).
tcf(c_29159,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_18 )
| ( inverse(X0) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_6752]) ).
tcf(c_29161,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = iPr_def_18 )
| ( iPr_def_18 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_1342]) ).
tcf(c_29178,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_6752]) ).
tcf(c_29228,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_4453,c_4451]) ).
tcf(c_29935,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( inverse(iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_27916,c_18491]) ).
tcf(c_30062,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_29228,c_5531]) ).
tcf(c_30508,plain,
multiply(sk_c6,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_17377,c_96]) ).
tcf(c_30525,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_2235,c_30508]) ).
tcf(c_30526,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1725,c_30508]) ).
tcf(c_30527,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1333,c_30508]) ).
tcf(c_30528,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_987,c_30508]) ).
tcf(c_30529,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_937,c_30508]) ).
tcf(c_31097,plain,
( ( identity = iPr_def_18 )
| ( inverse(iPr_def_26) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_30526,c_538]) ).
tcf(c_31677,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_30528,c_549]) ).
tcf(c_31926,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_30529,c_30526]) ).
tcf(c_31972,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_30529,c_1031]) ).
tcf(c_31999,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_30529,c_547]) ).
tcf(c_32042,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_31972,c_6745]) ).
tcf(c_33837,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_26,X0)) = X0,
inference(superposition,[status(thm)],[c_17378,c_17134]) ).
tcf(c_33838,plain,
multiply(sk_c1,identity) = inverse(iPr_def_26),
inference(superposition,[status(thm)],[c_17378,c_18452]) ).
tcf(c_34059,plain,
inverse(iPr_def_26) = sk_c1,
inference(demodulation,[status(thm)],[c_33838,c_18452]) ).
tcf(c_34061,plain,
( ( identity = iPr_def_18 )
| ( sk_c1 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_31097,c_34059]) ).
tcf(c_34063,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c1 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_5086,c_34059]) ).
tcf(c_34064,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c1 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_5016,c_34059]) ).
tcf(c_34065,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c1 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_4918,c_34059]) ).
tcf(c_34066,plain,
( ( sk_c1 = iPr_def_14 )
| ( sk_c9 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_2060,c_34059]) ).
tcf(c_34067,plain,
( ( sk_c1 = iPr_def_14 )
| ( sk_c9 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1966,c_34059]) ).
tcf(c_34068,plain,
( ( sk_c1 = iPr_def_14 )
| ( sk_c9 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1893,c_34059]) ).
tcf(c_34087,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_29228,c_34059]) ).
tcf(c_34088,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( inverse(iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_21863,c_34059]) ).
tcf(c_34089,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_18974,c_34059]) ).
tcf(c_34480,plain,
multiply(sk_c1,sk_c8) = iPr_def_25,
inference(superposition,[status(thm)],[c_6769,c_33837]) ).
tcf(c_35125,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34063,c_1090]) ).
tcf(c_35129,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34063,c_1056]) ).
tcf(c_35132,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34063,c_549]) ).
tcf(c_35139,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c3 = iPr_def_25 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_35129,c_7077]) ).
tcf(c_35143,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c3 = iPr_def_25 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_35125,c_7077]) ).
tcf(c_35233,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34064,c_1126]) ).
tcf(c_35241,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34064,c_549]) ).
tcf(c_35256,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c3 = iPr_def_25 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_35233,c_7077]) ).
tcf(c_35332,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34065,c_1090]) ).
tcf(c_35350,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c3 = iPr_def_25 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_35332,c_7077]) ).
tcf(c_35429,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34066,c_1230]) ).
tcf(c_35440,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34066,c_549]) ).
tcf(c_35445,plain,
( ( sk_c3 = iPr_def_25 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_35429,c_7077]) ).
tcf(c_35643,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34067,c_1196]) ).
tcf(c_35653,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34067,c_549]) ).
tcf(c_35658,plain,
( ( sk_c3 = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_35643,c_7077]) ).
tcf(c_35715,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34068,c_1165]) ).
tcf(c_35724,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34068,c_549]) ).
tcf(c_35729,plain,
( ( sk_c3 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_35715,c_7077]) ).
tcf(c_35812,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c9,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_35445,c_548]) ).
tcf(c_35813,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_35445,c_570]) ).
tcf(c_35957,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c9,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_35658,c_548]) ).
tcf(c_35959,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_35658,c_569]) ).
tcf(c_36157,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( inverse(iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_35813,c_538]) ).
tcf(c_36160,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c4 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_36157,c_24979]) ).
tcf(c_36369,plain,
( ( iPr_def_14 = inverse(sk_c5) )
| ( iPr_def_14 != iPr_def_14 )
| ( inverse(sk_c5) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_3160]) ).
tcf(c_36442,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = identity )
| ( identity != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_3993]) ).
tcf(c_36448,plain,
( ( inverse(sk_c9) = identity )
| ( identity != inverse(sk_c9) )
| ( inverse(sk_c9) != inverse(sk_c9) ) ),
inference(instantiation,[status(thm)],[c_36442]) ).
tcf(c_36526,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_561,c_562]) ).
tcf(c_36536,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_563,c_562]) ).
tcf(c_36537,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_563,c_561]) ).
tcf(c_36834,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_580,c_578]) ).
tcf(c_36941,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_571,c_545]) ).
tcf(c_37371,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_568,c_548]) ).
tcf(c_37448,plain,
multiply(iPr_def_14,sk_c9) = identity,
inference(superposition,[status(thm)],[c_538,c_96]) ).
tcf(c_37449,plain,
multiply(iPr_def_22,sk_c4) = identity,
inference(superposition,[status(thm)],[c_546,c_96]) ).
tcf(c_37450,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_543,c_96]) ).
tcf(c_37451,plain,
multiply(iPr_def_17,sk_c6) = identity,
inference(superposition,[status(thm)],[c_541,c_96]) ).
tcf(c_37452,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_550,c_96]) ).
tcf(c_37453,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_540,c_96]) ).
tcf(c_37782,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_594,c_592]) ).
tcf(c_37853,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_595,c_594]) ).
tcf(c_37938,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_574]) ).
tcf(c_37940,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_596,c_571]) ).
tcf(c_38251,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_545,c_97]) ).
tcf(c_38253,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_542,c_97]) ).
tcf(c_38259,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_38287,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c9,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_37448,c_97]) ).
tcf(c_38288,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c9,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_38287,c_95]) ).
tcf(c_38297,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_37449,c_97]) ).
tcf(c_38298,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_38297,c_95]) ).
tcf(c_38394,plain,
multiply(iPr_def_14,iPr_def_24) = sk_c3,
inference(superposition,[status(thm)],[c_548,c_38288]) ).
tcf(c_38432,plain,
multiply(iPr_def_22,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_545,c_38298]) ).
tcf(c_38444,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_598,c_551]) ).
tcf(c_38445,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_597,c_551]) ).
tcf(c_38447,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_595,c_551]) ).
tcf(c_38460,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_574,c_551]) ).
tcf(c_38578,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_544,c_555]) ).
tcf(c_38580,plain,
( ~ iPr_def_11
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_555]) ).
tcf(c_38581,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_96,c_555]) ).
tcf(c_38586,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_19) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_595,c_555]) ).
tcf(c_38612,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_38578,c_543]) ).
tcf(c_38718,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_549,c_556]) ).
tcf(c_38724,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,iPr_def_14) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_596,c_556]) ).
tcf(c_38747,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_26 )
| ( sk_c9 != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_38718,c_550]) ).
tcf(c_38868,plain,
( ~ iPr_def_13
| ( inverse(sk_c2) != sk_c9 )
| ( multiply(sk_c9,iPr_def_23) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_547,c_552]) ).
tcf(c_38869,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c9 )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_552]) ).
tcf(c_38893,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_16 )
| ( multiply(sk_c9,iPr_def_23) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_38868,c_540]) ).
tcf(c_38968,plain,
( ~ iPr_def_12
| ( multiply(sk_c9,iPr_def_14) != sk_c8 )
| ( multiply(inverse(sk_c9),sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_538,c_554]) ).
tcf(c_39003,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( multiply(sk_c9,iPr_def_14) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_38968,c_538,c_37448]) ).
tcf(c_39238,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c9 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_38444,c_551,c_2248,c_2827,c_3819,c_10351,c_11175,c_12115]) ).
tcf(c_39248,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_37450,c_97]) ).
tcf(c_39249,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_39248,c_95]) ).
tcf(c_39250,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_37451,c_97]) ).
tcf(c_39251,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_39250,c_95]) ).
tcf(c_39256,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_37452,c_97]) ).
tcf(c_39257,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_39256,c_95]) ).
tcf(c_39266,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_37453,c_97]) ).
tcf(c_39267,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_39266,c_95]) ).
tcf(c_39268,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c9 = iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_38445,c_551,c_2248,c_2677,c_3819,c_10289,c_10965,c_12020]) ).
tcf(c_39288,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_544,c_39249]) ).
tcf(c_39314,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_36526,c_591]) ).
tcf(c_39406,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_36536,c_591]) ).
tcf(c_39498,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_36537,c_591]) ).
tcf(c_39599,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_18 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_36834,c_591]) ).
tcf(c_39966,plain,
multiply(iPr_def_26,iPr_def_25) = sk_c8,
inference(superposition,[status(thm)],[c_549,c_39257]) ).
tcf(c_39976,plain,
multiply(iPr_def_16,iPr_def_23) = sk_c9,
inference(superposition,[status(thm)],[c_547,c_39267]) ).
tcf(c_40259,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_21 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_35959,c_35813]) ).
tcf(c_40628,plain,
( ( iPr_def_15 = identity )
| ( iPr_def_15 != iPr_def_18 )
| ( identity != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_3779]) ).
tcf(c_40713,plain,
( ( iPr_def_19 = identity )
| ( iPr_def_19 != iPr_def_18 )
| ( identity != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_7021]) ).
tcf(c_40746,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34061,c_31677]) ).
tcf(c_40758,plain,
( ( identity = iPr_def_18 )
| ( sk_c3 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_40746,c_7077]) ).
tcf(c_40864,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c9,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_35729,c_548]) ).
tcf(c_40867,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_35729,c_568]) ).
tcf(c_40954,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_36160,c_1127]) ).
tcf(c_40975,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c3 = iPr_def_21 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_40954,c_7077]) ).
tcf(c_41055,plain,
( ( identity = iPr_def_19 )
| ( iPr_def_19 != iPr_def_18 )
| ( identity != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_7022]) ).
tcf(c_41211,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_40259,c_22956]) ).
tcf(c_41518,plain,
( ( iPr_def_18 = iPr_def_15 )
| ( iPr_def_18 != multiply(identity,sk_c8) )
| ( iPr_def_15 != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_7072]) ).
tcf(c_41621,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_40758,c_565]) ).
tcf(c_41723,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_40867,c_35959]) ).
tcf(c_41724,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_40867,c_35813]) ).
tcf(c_42904,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_37782,c_595]) ).
tcf(c_42905,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_37782,c_594]) ).
tcf(c_43024,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_41723,c_19586]) ).
tcf(c_43345,plain,
( ( identity = iPr_def_14 )
| ( iPr_def_14 != iPr_def_18 )
| ( identity != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_17008]) ).
tcf(c_43587,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_41724,c_30062]) ).
tcf(c_43941,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_37853,c_551]) ).
tcf(c_43942,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_37853,c_595]) ).
tcf(c_44858,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_17379,c_96]) ).
tcf(c_44862,plain,
multiply(sk_c2,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_17379,c_18452]) ).
tcf(c_44892,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_31999,c_44858]) ).
tcf(c_44893,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_27987,c_44858]) ).
tcf(c_44894,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_4459,c_44858]) ).
tcf(c_44895,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_4351,c_44858]) ).
tcf(c_44896,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_3277,c_44858]) ).
tcf(c_44898,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_3106,c_44858]) ).
tcf(c_44899,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_3040,c_44858]) ).
tcf(c_44987,plain,
inverse(iPr_def_16) = sk_c2,
inference(demodulation,[status(thm)],[c_44862,c_18452]) ).
tcf(c_44991,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c2 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_4461,c_44987]) ).
tcf(c_44992,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c2 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_4353,c_44987]) ).
tcf(c_44993,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c2 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_3279,c_44987]) ).
tcf(c_45014,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_16,sk_c2) != sk_c8 )
| ( multiply(inverse(iPr_def_16),sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_44987,c_554]) ).
tcf(c_45016,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_23 )
| ( sk_c8 != identity ) ),
inference(light_normalisation,[status(thm)],[c_45014,c_547,c_1073,c_44987]) ).
tcf(c_45180,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_44894,c_18491]) ).
tcf(c_45223,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( inverse(iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_44895,c_18491]) ).
tcf(c_45467,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_44896,c_18491]) ).
tcf(c_46112,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != inverse(X1) )
| ( X0 != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_4248]) ).
tcf(c_46296,plain,
( ( iPr_def_18 = iPr_def_19 )
| iPr_def_11
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_43941,c_1472,c_1473,c_1478,c_1479,c_2036,c_6867,c_7018,c_8875,c_8993,c_16289,c_17018,c_21459]) ).
tcf(c_46297,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_18 = iPr_def_19 ) ),
inference(renaming,[status(thm)],[c_46296]) ).
tcf(c_46634,plain,
( ( iPr_def_15 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_35132,c_555]) ).
tcf(c_46644,plain,
( ( iPr_def_15 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_46634,c_21101]) ).
tcf(c_46712,plain,
( ( iPr_def_18 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_35241,c_555]) ).
tcf(c_46722,plain,
( ( iPr_def_18 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_46712,c_21101]) ).
tcf(c_46951,plain,
( ( iPr_def_19 = iPr_def_14 )
| ( iPr_def_19 != iPr_def_18 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_17008]) ).
tcf(c_47444,plain,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_18 != iPr_def_14 )
| ( sk_c8 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2351]) ).
tcf(c_47484,plain,
( ( sk_c8 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_14 )
| ( sk_c8 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2352]) ).
tcf(c_47621,plain,
( ( iPr_def_18 = multiply(identity,sk_c8) )
| ( iPr_def_18 != iPr_def_14 )
| ( multiply(identity,sk_c8) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_8016]) ).
tcf(c_48576,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 )
| ( inverse(iPr_def_14) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_35440,c_556]) ).
tcf(c_48605,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(ground_joinability,[status(thm)],[c_48576,c_21101]) ).
tcf(c_48667,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 )
| ( inverse(iPr_def_14) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_35653,c_556]) ).
tcf(c_48693,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(ground_joinability,[status(thm)],[c_48667,c_21101]) ).
tcf(c_48755,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 )
| ( inverse(iPr_def_14) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_35724,c_556]) ).
tcf(c_48756,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_35724,c_555]) ).
tcf(c_48773,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_25 )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_48756,c_21101]) ).
tcf(c_48778,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(ground_joinability,[status(thm)],[c_48755,c_21101]) ).
tcf(c_48886,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_20,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_26941,c_96]) ).
tcf(c_48888,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_14 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_26941,c_6304]) ).
tcf(c_49146,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_15 )
| ( iPr_def_15 != inverse(sk_c5) )
| ( inverse(X0) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_21590]) ).
tcf(c_49147,plain,
( ( inverse(sk_c9) = iPr_def_15 )
| ( iPr_def_15 != inverse(sk_c5) )
| ( inverse(sk_c9) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_49146]) ).
tcf(c_49177,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( multiply(iPr_def_20,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_28282,c_96]) ).
tcf(c_49180,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_14 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_28282,c_5178]) ).
tcf(c_49202,plain,
( ( sk_c8 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_14 )
| ( sk_c8 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2352]) ).
tcf(c_49205,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ( iPr_def_15 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_49471,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c7,sk_c9) )
| ( iPr_def_14 != multiply(sk_c7,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1319]) ).
tcf(c_49488,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_15 != inverse(sk_c5) )
| ( iPr_def_14 != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1319]) ).
tcf(c_50029,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_14 )
| ( iPr_def_15 != X0 )
| ( iPr_def_14 != X0 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_50031,plain,
( ( iPr_def_15 = iPr_def_14 )
| ( iPr_def_15 != sk_c9 )
| ( iPr_def_14 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_50029]) ).
tcf(c_50189,plain,
( ( multiply(identity,sk_c8) = iPr_def_19 )
| ( iPr_def_19 != iPr_def_14 )
| ( multiply(identity,sk_c8) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_8015]) ).
tcf(c_50539,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( multiply(iPr_def_20,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_29935,c_96]) ).
tcf(c_50612,plain,
! [X0: $i] :
( ( X0 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1342]) ).
tcf(c_50613,plain,
( ( iPr_def_18 = iPr_def_14 )
| ( iPr_def_18 != iPr_def_24 )
| ( iPr_def_14 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_17017]) ).
tcf(c_50617,plain,
( ( iPr_def_18 = iPr_def_14 )
| ( iPr_def_18 != sk_c8 )
| ( iPr_def_14 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_17006]) ).
tcf(c_50618,plain,
! [X0: $i] :
( ( iPr_def_18 = iPr_def_14 )
| ( iPr_def_18 != X0 )
| ( iPr_def_14 != X0 ) ),
inference(instantiation,[status(thm)],[c_4402]) ).
tcf(c_51567,plain,
! [X0: $i] : multiply(inverse(X0),sk_c9) = multiply(inverse(X0),sk_c9),
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_51569,plain,
multiply(inverse(sk_c9),sk_c9) = multiply(inverse(sk_c9),sk_c9),
inference(instantiation,[status(thm)],[c_51567]) ).
tcf(c_51570,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_51572,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,X2) )
| ( sk_c9 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_52837,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_26,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_589,c_37371]) ).
tcf(c_53459,plain,
! [X0: $i] :
( ( identity = inverse(X0) )
| ( identity != sk_c8 )
| ( inverse(X0) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_29133]) ).
tcf(c_53463,plain,
( ( identity = inverse(sk_c9) )
| ( identity != sk_c8 )
| ( inverse(sk_c9) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_53459]) ).
tcf(c_53492,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_34087,c_44987]) ).
tcf(c_53515,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_53492,c_44991]) ).
tcf(c_54076,plain,
( ( identity = iPr_def_14 )
| ( iPr_def_14 != iPr_def_24 )
| ( identity != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_17017]) ).
tcf(c_54423,plain,
( ( inverse(sk_c5) = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 )
| ( inverse(sk_c5) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_17010]) ).
tcf(c_54429,plain,
( ( inverse(sk_c5) = iPr_def_14 )
| ( iPr_def_14 != inverse(sk_c9) )
| ( inverse(sk_c5) != inverse(sk_c9) ) ),
inference(instantiation,[status(thm)],[c_6754]) ).
tcf(c_54480,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_34088,c_44987]) ).
tcf(c_55254,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_34089,c_44987]) ).
tcf(c_55275,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c1 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_55254,c_44993]) ).
tcf(c_57908,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( identity = iPr_def_18 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_41621,c_542]) ).
tcf(c_57913,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_57908,c_30508]) ).
tcf(c_58802,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( iPr_def_14 != iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_3366,c_551,c_1632,c_2350,c_3366,c_3827,c_39238,c_39268]) ).
tcf(c_60319,plain,
multiply(sk_c6,iPr_def_15) = multiply(iPr_def_18,sk_c9),
inference(superposition,[status(thm)],[c_539,c_38253]) ).
tcf(c_61232,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_43587,c_45180]) ).
tcf(c_61246,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c2 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_61232,c_44987]) ).
tcf(c_61342,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_61246,c_53492]) ).
tcf(c_61352,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_61246,c_44991]) ).
tcf(c_61687,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_61342,c_550]) ).
tcf(c_61688,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c2 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_61687,c_44987]) ).
tcf(c_62137,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_3378,c_3378,c_3819,c_10647,c_11622,c_16056]) ).
tcf(c_62170,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_3380,c_3380,c_3819,c_10389,c_11229,c_16679]) ).
tcf(c_62186,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3530,c_18491]) ).
tcf(c_62481,plain,
( ( iPr_def_24 = multiply(identity,sk_c8) )
| ( iPr_def_24 != iPr_def_14 )
| ( multiply(identity,sk_c8) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_8016]) ).
tcf(c_62493,plain,
( ( iPr_def_24 = iPr_def_14 )
| ( iPr_def_24 != iPr_def_24 )
| ( iPr_def_14 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_17017]) ).
tcf(c_62502,plain,
! [X0: $i] :
( ( iPr_def_24 = inverse(X0) )
| ( iPr_def_24 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_29178]) ).
tcf(c_62508,plain,
( ( iPr_def_24 = inverse(sk_c9) )
| ( iPr_def_24 != iPr_def_14 )
| ( inverse(sk_c9) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_62502]) ).
tcf(c_62977,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_61688,c_44991]) ).
tcf(c_63006,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_61688,c_1590]) ).
tcf(c_63007,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_61688,c_1547]) ).
tcf(c_63008,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_61688,c_1501]) ).
tcf(c_63056,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_63008,c_6769]) ).
tcf(c_63060,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_63007,c_6769]) ).
tcf(c_63064,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_63006,c_6769]) ).
tcf(c_63338,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_1326]) ).
tcf(c_63339,plain,
( ( sk_c9 = iPr_def_15 )
| ( iPr_def_15 != identity )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_63338]) ).
tcf(c_63684,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_62977,c_34059]) ).
tcf(c_63699,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_11
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_62977,c_21927]) ).
tcf(c_63738,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_62977,c_5531]) ).
tcf(c_63752,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_63684,c_21101]) ).
tcf(c_63993,plain,
( ( sk_c8 = iPr_def_19 )
| ( iPr_def_19 != identity )
| ( sk_c8 != identity ) ),
inference(instantiation,[status(thm)],[c_21974]) ).
tcf(c_64283,plain,
( ( sk_c8 = iPr_def_15 )
| ( iPr_def_15 != identity )
| ( sk_c8 != identity ) ),
inference(instantiation,[status(thm)],[c_49205]) ).
tcf(c_64306,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c9,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_63738,c_40864]) ).
tcf(c_64307,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c9,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_63738,c_35957]) ).
tcf(c_64308,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c9,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_63738,c_35812]) ).
tcf(c_64459,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_64308,c_20057]) ).
tcf(c_64463,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_64307,c_20057]) ).
tcf(c_64467,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_64306,c_20057]) ).
tcf(c_64838,plain,
( ( iPr_def_18 = iPr_def_14 )
| ( iPr_def_18 != iPr_def_15 )
| ( iPr_def_14 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_50618]) ).
tcf(c_65073,plain,
( ( identity = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_14)) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_30525,c_3531]) ).
tcf(c_65103,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_14)) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_597,c_3531]) ).
tcf(c_65104,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_14)) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_596,c_3531]) ).
tcf(c_65147,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(ground_joinability,[status(thm)],[c_65104,c_538,c_21101]) ).
tcf(c_65151,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(ground_joinability,[status(thm)],[c_65103,c_538,c_21101]) ).
tcf(c_65179,plain,
( ( identity = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(ground_joinability,[status(thm)],[c_65073,c_538,c_21101]) ).
tcf(c_66421,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_63752,c_53515]) ).
tcf(c_66469,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c9,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_63752,c_549]) ).
tcf(c_66700,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_18 )
| ( iPr_def_18 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_23338]) ).
tcf(c_66701,plain,
( ( inverse(sk_c9) = iPr_def_18 )
| ( iPr_def_18 != iPr_def_14 )
| ( inverse(sk_c9) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_66700]) ).
tcf(c_67297,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_38259,c_95]) ).
tcf(c_67334,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c9,
inference(superposition,[status(thm)],[c_539,c_67297]) ).
tcf(c_67338,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_67297]) ).
tcf(c_67339,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_67297]) ).
tcf(c_67528,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_39251,c_67297]) ).
tcf(c_67577,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_67297,c_67297]) ).
tcf(c_68162,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_41211,c_45223]) ).
tcf(c_68174,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c2 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_68162,c_44987]) ).
tcf(c_68436,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_18 )
| ( iPr_def_18 != iPr_def_15 )
| ( inverse(X0) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_29161]) ).
tcf(c_68717,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c1 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_68174,c_54480]) ).
tcf(c_68964,plain,
! [X0: $i] :
( ( identity = iPr_def_24 )
| ( iPr_def_24 != inverse(X0) )
| ( identity != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_46112]) ).
tcf(c_68965,plain,
( ( identity = iPr_def_24 )
| ( iPr_def_24 != inverse(sk_c9) )
| ( identity != inverse(sk_c9) ) ),
inference(instantiation,[status(thm)],[c_68964]) ).
tcf(c_69076,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_68717,c_550]) ).
tcf(c_69077,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c2 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_69076,c_44987]) ).
tcf(c_69497,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_69077,c_44992]) ).
tcf(c_69527,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_69077,c_1590]) ).
tcf(c_69585,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_69527,c_6769]) ).
tcf(c_71317,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_69497,c_34059]) ).
tcf(c_71330,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_69497,c_22190]) ).
tcf(c_71338,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_69497,c_19687]) ).
tcf(c_71372,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_69497,c_5530]) ).
tcf(c_71385,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_71317,c_21101]) ).
tcf(c_71883,plain,
( ( sk_c5 = multiply(identity,sk_c8) )
| ( sk_c5 != iPr_def_19 )
| ( multiply(identity,sk_c8) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_7225]) ).
tcf(c_72102,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c9,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_71372,c_35812]) ).
tcf(c_72252,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_72102,c_20057]) ).
tcf(c_72367,plain,
! [X0: $i] :
( ( identity = inverse(X0) )
| ( identity != iPr_def_15 )
| ( inverse(X0) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_29151]) ).
tcf(c_72368,plain,
! [X0: $i] :
( ( identity = inverse(X0) )
| ( identity != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_29178]) ).
tcf(c_72369,plain,
! [X0: $i] :
( ( identity = inverse(X0) )
| ( identity != iPr_def_18 )
| ( inverse(X0) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_29159]) ).
tcf(c_72372,plain,
( ( identity = inverse(sk_c9) )
| ( identity != iPr_def_18 )
| ( inverse(sk_c9) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_72369]) ).
tcf(c_72373,plain,
( ( identity = inverse(sk_c9) )
| ( identity != iPr_def_14 )
| ( inverse(sk_c9) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_72368]) ).
tcf(c_72374,plain,
( ( identity = inverse(sk_c9) )
| ( identity != iPr_def_15 )
| ( inverse(sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_72367]) ).
tcf(c_72888,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( multiply(sk_c9,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_71385,c_549]) ).
tcf(c_73906,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_43024,c_45467]) ).
tcf(c_73919,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c2 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_73906,c_44987]) ).
tcf(c_74024,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_67339,c_67577]) ).
tcf(c_74049,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_74024,c_67338]) ).
tcf(c_75001,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_583,c_66469]) ).
tcf(c_75338,plain,
( ( iPr_def_18 = multiply(identity,iPr_def_14) )
| ( iPr_def_18 != sk_c8 )
| ( multiply(identity,iPr_def_14) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_6692]) ).
tcf(c_75370,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c1 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_73919,c_55254]) ).
tcf(c_75669,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(iPr_def_16) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_75370,c_550]) ).
tcf(c_75670,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c2 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_75669,c_44987]) ).
tcf(c_75776,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_37938,c_16056]) ).
tcf(c_76023,plain,
( ( iPr_def_19 = multiply(identity,iPr_def_14) )
| ( iPr_def_19 != iPr_def_19 )
| ( multiply(identity,iPr_def_14) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3250]) ).
tcf(c_76067,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_75670,c_44993]) ).
tcf(c_76099,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_75670,c_1547]) ).
tcf(c_76146,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_76099,c_6769]) ).
tcf(c_77202,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_37940,c_16679]) ).
tcf(c_77252,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_77202,c_545]) ).
tcf(c_77516,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_26,sk_c8) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_591,c_72888]) ).
tcf(c_77715,plain,
( ( sk_c8 = identity )
| ( identity != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_77782,plain,
( ( sk_c8 = identity )
| ( identity != iPr_def_24 )
| ( sk_c8 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2250]) ).
tcf(c_77983,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_76067,c_34059]) ).
tcf(c_77998,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_11
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_76067,c_21927]) ).
tcf(c_78039,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_76067,c_5381]) ).
tcf(c_78051,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_77983,c_21101]) ).
tcf(c_78335,plain,
( ( sk_c5 = iPr_def_15 )
| ( iPr_def_15 != multiply(identity,sk_c8) )
| ( sk_c5 != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_7072]) ).
tcf(c_78899,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c9,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_78039,c_35957]) ).
tcf(c_79047,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_78899,c_20057]) ).
tcf(c_79308,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_78051,c_55275]) ).
tcf(c_79885,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_75001,c_551,c_2248,c_2677,c_10289,c_10965,c_20152,c_22342,c_45016,c_48693,c_61352,c_63060,c_63738,c_64463,c_77782]) ).
tcf(c_80040,plain,
( ( iPr_def_21 = iPr_def_25 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_79885,c_584]) ).
tcf(c_80042,plain,
( ( iPr_def_21 = iPr_def_25 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_79885,c_582]) ).
tcf(c_80260,plain,
( ( sk_c9 = iPr_def_22 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_80040,c_551,c_2248,c_6585,c_10351,c_11175,c_22184,c_45016,c_48605,c_61352,c_63064,c_63699,c_64459,c_77782]) ).
tcf(c_80261,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_80260]) ).
tcf(c_80801,plain,
( ( iPr_def_14 = iPr_def_24 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_75776,c_38612]) ).
tcf(c_81383,plain,
( ( sk_c9 = iPr_def_20 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_80042,c_3365,c_3827,c_4247,c_6585,c_10248,c_21475,c_23386,c_45016,c_62493,c_63056,c_63699,c_64467,c_66421,c_77782,c_79885,c_80261]) ).
tcf(c_81384,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_81383]) ).
tcf(c_81436,plain,
iPr_def_20 = iPr_def_22,
inference(superposition,[status(thm)],[c_81384,c_80261]) ).
tcf(c_81656,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(demodulation,[status(thm)],[c_7025,c_81436]) ).
tcf(c_81669,plain,
inverse(sk_c4) = iPr_def_20,
inference(demodulation,[status(thm)],[c_546,c_81436]) ).
tcf(c_81692,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c9 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_77516,c_551,c_2248,c_2827,c_10351,c_11175,c_45016,c_48605,c_69585,c_71338,c_71330,c_72252,c_77782]) ).
tcf(c_81694,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_81692,c_81436]) ).
tcf(c_81810,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_81694,c_583]) ).
tcf(c_81958,plain,
( ( sk_c9 = iPr_def_21 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_81810,c_4247,c_6423,c_10289,c_21474,c_23386,c_39268,c_45016,c_62493,c_76146,c_77782,c_77998,c_79047,c_79308]) ).
tcf(c_81959,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c9 = iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_81958]) ).
tcf(c_81995,plain,
iPr_def_20 = iPr_def_21,
inference(superposition,[status(thm)],[c_81959,c_81694]) ).
tcf(c_82192,plain,
multiply(sk_c4,sk_c8) = iPr_def_20,
inference(demodulation,[status(thm)],[c_545,c_81995]) ).
tcf(c_82441,plain,
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_4029,c_18491]) ).
tcf(c_82479,plain,
( ( identity = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(iPr_def_16,iPr_def_16) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_26797,c_82441]) ).
tcf(c_82498,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(iPr_def_20,iPr_def_20) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_561,c_82441]) ).
tcf(c_82777,plain,
multiply(iPr_def_20,iPr_def_20) = sk_c8,
inference(light_normalisation,[status(thm)],[c_81656,c_81995]) ).
tcf(c_82778,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( sk_c8 = identity ) ),
inference(demodulation,[status(thm)],[c_50539,c_82777]) ).
tcf(c_82780,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( sk_c8 = identity ) ),
inference(demodulation,[status(thm)],[c_49177,c_82777]) ).
tcf(c_82781,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = identity ) ),
inference(demodulation,[status(thm)],[c_48886,c_82777]) ).
tcf(c_82801,plain,
( ( iPr_def_25 = iPr_def_26 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82777,c_28284]) ).
tcf(c_82802,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82777,c_26943]) ).
tcf(c_82892,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c4) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_82192,c_556]) ).
tcf(c_82893,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_82192,c_555]) ).
tcf(c_82897,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_20 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_82893,c_81669]) ).
tcf(c_82901,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_82892,c_81669]) ).
tcf(c_82923,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_82901,c_10742,c_48778,c_82901]) ).
tcf(c_82926,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_551,c_82923]) ).
tcf(c_83758,plain,
( ( iPr_def_16 = iPr_def_26 )
| ~ iPr_def_13
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_82778,c_21286]) ).
tcf(c_83785,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_26 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_82778,c_555]) ).
tcf(c_83787,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_82778,c_595]) ).
tcf(c_83789,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_15 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_82778,c_592]) ).
tcf(c_83796,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82778,c_575]) ).
tcf(c_83797,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_82778,c_574]) ).
tcf(c_83798,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_82778,c_573]) ).
tcf(c_83899,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_26 )
| ~ iPr_def_11
| ( X0 != sk_c9 )
| ( inverse(X0) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_83785,c_18452]) ).
tcf(c_83906,plain,
( ( iPr_def_16 = iPr_def_26 )
| ~ iPr_def_11
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c9) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_83899]) ).
tcf(c_84542,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = X0 )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_51570]) ).
tcf(c_84543,plain,
( ( multiply(inverse(sk_c9),sk_c9) = sk_c9 )
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_84542]) ).
tcf(c_84971,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(sk_c9,sk_c3) )
| ( sk_c9 != sk_c3 )
| ( inverse(X0) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_51572]) ).
tcf(c_84972,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c9,sk_c3) )
| ( sk_c9 != sk_c3 )
| ( inverse(sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_84971]) ).
tcf(c_84977,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_83787,c_1473,c_4878,c_5007,c_31926,c_41055]) ).
tcf(c_85011,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( inverse(iPr_def_19) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_84977,c_18491]) ).
tcf(c_85016,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( sk_c5 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_85011,c_26854]) ).
tcf(c_85163,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_83789,c_4910,c_22885,c_31926]) ).
tcf(c_86059,plain,
( ( inverse(sk_c5) = iPr_def_18 )
| ( iPr_def_18 != iPr_def_14 )
| ( inverse(sk_c5) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_50612]) ).
tcf(c_86064,plain,
( ( inverse(sk_c5) = iPr_def_18 )
| ( iPr_def_18 != iPr_def_15 )
| ( inverse(sk_c5) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_68436]) ).
tcf(c_86077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86079,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,X2) )
| ( sk_c9 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_86080,plain,
! [X0: $i] :
( ( sk_c8 = identity )
| ( identity != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86083,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(inverse(X0),sk_c9) )
| ( sk_c8 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86086,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = X0 )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_86092,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = X1 )
| ( X1 != multiply(inverse(X0),sk_c9) )
| ( multiply(inverse(X0),sk_c9) != multiply(inverse(X0),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_86093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(inverse(X0),sk_c9) = X3 )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_86095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86097,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86103,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86106,plain,
( ( sk_c8 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c8 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86083]) ).
tcf(c_86112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(inverse(X0),sk_c9) )
| ( sk_c8 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_86083]) ).
tcf(c_86119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),sk_c9) )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,X2) )
| ( multiply(X1,X2) != multiply(inverse(X0),sk_c9) )
| ( multiply(inverse(X0),sk_c9) != multiply(inverse(X0),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86092]) ).
tcf(c_86122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = multiply(inverse(X1),sk_c9) )
| ( X2 != sk_c9 )
| ( X0 != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_86127,plain,
! [X0: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86095]) ).
tcf(c_86128,plain,
( ( sk_c8 = multiply(identity,sk_c9) )
| ( sk_c8 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_86127]) ).
tcf(c_86134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_86095]) ).
tcf(c_86145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,X1) )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86150,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = iPr_def_20 )
| ( iPr_def_20 != multiply(sk_c5,sk_c8) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86093]) ).
tcf(c_86151,plain,
( ( multiply(inverse(sk_c9),sk_c9) = iPr_def_20 )
| ( iPr_def_20 != multiply(sk_c5,sk_c8) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86150]) ).
tcf(c_86157,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = iPr_def_25 )
| ( iPr_def_25 != multiply(sk_c1,sk_c8) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86093]) ).
tcf(c_86158,plain,
( ( multiply(inverse(sk_c9),sk_c9) = iPr_def_25 )
| ( iPr_def_25 != multiply(sk_c1,sk_c8) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86157]) ).
tcf(c_86182,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = X1 )
| ( X1 != iPr_def_20 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_86196,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = X1 )
| ( X1 != iPr_def_23 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_86206,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = X1 )
| ( X1 != iPr_def_25 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_86210,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_86097]) ).
tcf(c_86231,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = X1 )
| ( X1 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86134]) ).
tcf(c_86236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = X2 )
| ( X2 != multiply(X0,X1) )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_86134]) ).
tcf(c_86237,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X0,X1),
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_86241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(X0,X1) = X4 )
| ( X4 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_86134]) ).
tcf(c_86253,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,X0) )
| ( X1 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_86254,plain,
( ( sk_c9 = multiply(identity,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_86253]) ).
tcf(c_86255,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(inverse(X0),X0) )
| ( X1 != identity )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_86256,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86255]) ).
tcf(c_86262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = multiply(X0,X1) )
| ( X4 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_86270,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(inverse(X0),sk_c9) )
| ( X1 != iPr_def_20 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_86271,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != iPr_def_20 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86270]) ).
tcf(c_86272,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(inverse(X0),sk_c9) )
| ( X1 != iPr_def_21 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_86274,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(inverse(X0),sk_c9) )
| ( X1 != iPr_def_23 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_86275,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != iPr_def_23 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86274]) ).
tcf(c_86287,plain,
! [X0: $i] :
( ( X0 = multiply(inverse(sk_c9),sk_c9) )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86119]) ).
tcf(c_86293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(inverse(X0),sk_c9) )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_86119]) ).
tcf(c_86349,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_86135]) ).
tcf(c_86404,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_20 )
| ( iPr_def_20 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86405,plain,
( ( sk_c8 = iPr_def_20 )
| ( iPr_def_20 != sk_c9 )
| ( sk_c8 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_86404]) ).
tcf(c_86408,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86415,plain,
! [X0: $i] :
( ( sk_c9 = sk_c3 )
| ( sk_c3 != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86433,plain,
( ( identity = multiply(inverse(sk_c9),sk_c9) )
| ( identity != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86287]) ).
tcf(c_86447,plain,
multiply(identity,iPr_def_23) = iPr_def_23,
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_86450,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86455,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(identity,X1) )
| ( multiply(identity,X1) != multiply(inverse(X0),sk_c9) )
| ( multiply(inverse(X0),sk_c9) != multiply(inverse(X0),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86121]) ).
tcf(c_86456,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(identity,X1) )
| ( sk_c9 != X1 )
| ( inverse(X0) != identity ) ),
inference(instantiation,[status(thm)],[c_86079]) ).
tcf(c_86457,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(identity,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86456]) ).
tcf(c_86458,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(identity,sk_c9) )
| ( multiply(identity,sk_c9) != multiply(inverse(sk_c9),sk_c9) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86455]) ).
tcf(c_86481,plain,
! [X0: $i] :
( ( iPr_def_21 = multiply(inverse(X0),sk_c9) )
| ( iPr_def_21 != multiply(sk_c4,sk_c8) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c4,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86293]) ).
tcf(c_86482,plain,
( ( iPr_def_21 = multiply(inverse(sk_c9),sk_c9) )
| ( iPr_def_21 != multiply(sk_c4,sk_c8) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c4,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86481]) ).
tcf(c_86529,plain,
iPr_def_23 = iPr_def_23,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_86535,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c3) = multiply(inverse(X0),sk_c9) )
| ( sk_c3 != sk_c9 )
| ( sk_c9 != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_86122]) ).
tcf(c_86536,plain,
( ( multiply(sk_c9,sk_c3) = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c3 != sk_c9 )
| ( sk_c9 != inverse(sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86535]) ).
tcf(c_86571,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != X1 )
| ( multiply(identity,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_86095]) ).
tcf(c_86598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),sk_c9) )
| ( X2 != multiply(identity,X1) )
| ( multiply(inverse(X0),sk_c9) != multiply(identity,X1) ) ),
inference(instantiation,[status(thm)],[c_86293]) ).
tcf(c_86601,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86598]) ).
tcf(c_86648,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = multiply(identity,X1) )
| ( multiply(identity,X1) != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86231]) ).
tcf(c_86649,plain,
( ( multiply(identity,sk_c9) = multiply(identity,sk_c9) )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_86648]) ).
tcf(c_86650,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = multiply(identity,X2) )
| ( multiply(identity,X2) != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_86253]) ).
tcf(c_86654,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c9,sk_c3) = multiply(X0,X1) )
| ( sk_c3 != X1 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_86742,plain,
! [X0: $i] :
( ( multiply(identity,X0) = sk_c8 )
| ( sk_c8 != multiply(identity,X0) )
| ( multiply(identity,X0) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_86236]) ).
tcf(c_86743,plain,
( ( multiply(identity,sk_c9) = sk_c8 )
| ( sk_c8 != multiply(identity,sk_c9) )
| ( multiply(identity,sk_c9) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86742]) ).
tcf(c_86789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_86241]) ).
tcf(c_86809,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_24 = multiply(X0,X1) )
| ( iPr_def_24 != multiply(sk_c9,sk_c3) )
| ( multiply(X0,X1) != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_86262]) ).
tcf(c_86810,plain,
( ( iPr_def_24 = multiply(sk_c9,sk_c9) )
| ( iPr_def_24 != multiply(sk_c9,sk_c3) )
| ( multiply(sk_c9,sk_c9) != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_86809]) ).
tcf(c_86826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,X1) )
| ( X3 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_86262]) ).
tcf(c_86905,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_20 = X0 )
| ( iPr_def_20 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86912,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_21 = X0 )
| ( iPr_def_21 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86919,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_23 = X0 )
| ( iPr_def_23 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86938,plain,
( ( sk_c8 = identity )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c8 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86080]) ).
tcf(c_86939,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( X0 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86103]) ).
tcf(c_86940,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( X0 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86097]) ).
tcf(c_86941,plain,
( ( identity = sk_c9 )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86940]) ).
tcf(c_86942,plain,
( ( sk_c9 = identity )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86939]) ).
tcf(c_86946,plain,
! [X0: $i,X1: $i] :
( ( identity = multiply(X0,X1) )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( multiply(X0,X1) != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86262]) ).
tcf(c_86956,plain,
( ( sk_c8 = multiply(identity,identity) )
| ( sk_c8 != identity )
| ( multiply(identity,identity) != identity ) ),
inference(instantiation,[status(thm)],[c_86127]) ).
tcf(c_86965,plain,
! [X0: $i,X1: $i] :
( ( sk_c3 = X0 )
| ( sk_c3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_86967,plain,
! [X0: $i] :
( ( sk_c3 = multiply(identity,X0) )
| ( sk_c3 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86253]) ).
tcf(c_87056,plain,
! [X0: $i,X1: $i] :
( ( sk_c5 = X0 )
| ( sk_c5 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_87083,plain,
! [X0: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != sk_c3 )
| ( X0 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_86450]) ).
tcf(c_87084,plain,
( ( sk_c9 = iPr_def_23 )
| ( iPr_def_23 != sk_c3 )
| ( sk_c9 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_87083]) ).
tcf(c_87149,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = multiply(inverse(X1),sk_c9) )
| ( identity != inverse(X1) )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_86122]) ).
tcf(c_87150,plain,
( ( multiply(identity,sk_c9) = multiply(inverse(sk_c9),sk_c9) )
| ( identity != inverse(sk_c9) )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_87149]) ).
tcf(c_87225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(identity,X0) = multiply(X2,X1) )
| ( identity != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_87226,plain,
( ( multiply(identity,sk_c9) = multiply(sk_c9,sk_c9) )
| ( identity != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_87225]) ).
tcf(c_87578,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c7,sk_c9) )
| ( X0 != iPr_def_15 )
| ( multiply(sk_c7,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_87579,plain,
! [X0: $i] :
( ( multiply(sk_c7,sk_c9) = X0 )
| ( X0 != iPr_def_15 )
| ( multiply(sk_c7,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_86134]) ).
tcf(c_87586,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c5,sk_c8) )
| ( X0 != iPr_def_20 )
| ( multiply(sk_c5,sk_c8) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_87587,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c8) = X0 )
| ( X0 != iPr_def_20 )
| ( multiply(sk_c5,sk_c8) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86134]) ).
tcf(c_87590,plain,
( ( sk_c9 = multiply(sk_c5,sk_c8) )
| ( sk_c9 != iPr_def_20 )
| ( multiply(sk_c5,sk_c8) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_87586]) ).
tcf(c_87634,plain,
( ( sk_c8 = multiply(sk_c9,sk_c3) )
| ( sk_c8 != iPr_def_24 )
| ( multiply(sk_c9,sk_c3) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_86095]) ).
tcf(c_87637,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c1,sk_c8) )
| ( X0 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_86145]) ).
tcf(c_87638,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c8) = X0 )
| ( X0 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_86134]) ).
tcf(c_87640,plain,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( sk_c9 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_87638]) ).
tcf(c_87641,plain,
( ( sk_c9 = multiply(sk_c1,sk_c8) )
| ( sk_c9 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_87637]) ).
tcf(c_87694,plain,
sk_c3 = sk_c3,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_87829,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c9,sk_c3) )
| ( X1 != sk_c3 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_87830,plain,
( ( multiply(sk_c9,sk_c9) = multiply(sk_c9,sk_c3) )
| ( sk_c9 != sk_c3 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_87829]) ).
tcf(c_88865,plain,
! [X0: $i] :
( ( sk_c8 = sk_c3 )
| ( sk_c3 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_88920,plain,
! [X0: $i] :
( ( sk_c8 = multiply(inverse(X0),sk_c9) )
| ( sk_c8 != multiply(sk_c9,sk_c3) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_86112]) ).
tcf(c_88923,plain,
( ( sk_c8 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c8 != multiply(sk_c9,sk_c3) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_88920]) ).
tcf(c_88983,plain,
! [X0: $i] :
( ( iPr_def_20 = X0 )
| ( iPr_def_20 != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86905]) ).
tcf(c_88984,plain,
iPr_def_20 = iPr_def_20,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_88985,plain,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_20 != iPr_def_20 )
| ( sk_c9 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_88983]) ).
tcf(c_89001,plain,
! [X0: $i] :
( ( iPr_def_21 = X0 )
| ( iPr_def_21 != iPr_def_21 )
| ( X0 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_86912]) ).
tcf(c_89002,plain,
iPr_def_21 = iPr_def_21,
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_89003,plain,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_21 != iPr_def_21 )
| ( sk_c9 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_89001]) ).
tcf(c_89024,plain,
! [X0: $i] :
( ( iPr_def_23 = X0 )
| ( iPr_def_23 != sk_c3 )
| ( X0 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_86919]) ).
tcf(c_89026,plain,
! [X0: $i] :
( ( iPr_def_23 = X0 )
| ( iPr_def_23 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86919]) ).
tcf(c_89359,plain,
( ( sk_c3 = iPr_def_23 )
| ( iPr_def_23 != sk_c3 )
| ( sk_c3 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_87083]) ).
tcf(c_89534,plain,
( ( multiply(identity,identity) = sk_c8 )
| ( sk_c8 != multiply(identity,identity) )
| ( multiply(identity,identity) != multiply(identity,identity) ) ),
inference(instantiation,[status(thm)],[c_86742]) ).
tcf(c_89553,plain,
multiply(identity,identity) = multiply(identity,identity),
inference(instantiation,[status(thm)],[c_86237]) ).
tcf(c_89741,plain,
( ( sk_c5 = multiply(sk_c7,sk_c9) )
| ( sk_c5 != iPr_def_15 )
| ( multiply(sk_c7,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_87578]) ).
tcf(c_89760,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(inverse(X0),sk_c9) )
| ( X1 != multiply(sk_c7,sk_c9) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c7,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86293]) ).
tcf(c_89808,plain,
( ( multiply(sk_c7,sk_c9) = identity )
| ( identity != iPr_def_15 )
| ( multiply(sk_c7,sk_c9) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_87579]) ).
tcf(c_89812,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c7,sk_c9) )
| ( multiply(sk_c7,sk_c9) != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86086]) ).
tcf(c_90059,plain,
( ( multiply(sk_c5,sk_c8) = identity )
| ( identity != iPr_def_20 )
| ( multiply(sk_c5,sk_c8) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_87587]) ).
tcf(c_90063,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c5,sk_c8) )
| ( multiply(sk_c5,sk_c8) != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86086]) ).
tcf(c_90148,plain,
! [X0: $i] :
( ( multiply(identity,X0) = iPr_def_21 )
| ( iPr_def_21 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86231]) ).
tcf(c_90150,plain,
( ( multiply(identity,sk_c9) = iPr_def_21 )
| ( iPr_def_21 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_90148]) ).
tcf(c_90287,plain,
( ( sk_c8 = identity )
| ( identity != multiply(sk_c9,sk_c3) )
| ( sk_c8 != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_86080]) ).
tcf(c_90425,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c3) = multiply(inverse(X0),sk_c9) )
| ( multiply(sk_c9,sk_c3) != iPr_def_23 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86274]) ).
tcf(c_90428,plain,
( ( multiply(sk_c9,sk_c3) = multiply(inverse(sk_c9),sk_c9) )
| ( multiply(sk_c9,sk_c3) != iPr_def_23 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_90425]) ).
tcf(c_90442,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c9,sk_c3) )
| ( X1 != multiply(identity,X0) )
| ( multiply(sk_c9,sk_c3) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_86826]) ).
tcf(c_90450,plain,
( ( sk_c9 = multiply(sk_c9,sk_c3) )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( multiply(sk_c9,sk_c3) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_90442]) ).
tcf(c_90466,plain,
( ( multiply(sk_c9,sk_c3) = iPr_def_23 )
| ( iPr_def_23 != sk_c3 )
| ( multiply(sk_c9,sk_c3) != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_87083]) ).
tcf(c_90511,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(inverse(X0),sk_c9) )
| ( X1 != multiply(sk_c1,sk_c8) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86293]) ).
tcf(c_90514,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(sk_c1,sk_c8) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_90511]) ).
tcf(c_90555,plain,
( ( iPr_def_23 = multiply(sk_c1,sk_c8) )
| ( iPr_def_23 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_87637]) ).
tcf(c_90558,plain,
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != multiply(sk_c1,sk_c8) )
| ( sk_c8 != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86408]) ).
tcf(c_90559,plain,
( ( sk_c3 = multiply(sk_c1,sk_c8) )
| ( sk_c3 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_87637]) ).
tcf(c_90560,plain,
( ( sk_c9 = sk_c3 )
| ( sk_c3 != multiply(sk_c1,sk_c8) )
| ( sk_c9 != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86415]) ).
tcf(c_90592,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c8) = multiply(identity,X0) )
| ( multiply(sk_c1,sk_c8) != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_86650]) ).
tcf(c_90595,plain,
! [X0: $i] :
( ( sk_c8 = multiply(sk_c1,sk_c8) )
| ( sk_c8 != X0 )
| ( multiply(sk_c1,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_86095]) ).
tcf(c_90596,plain,
( ( sk_c8 = multiply(sk_c1,sk_c8) )
| ( sk_c8 != sk_c9 )
| ( multiply(sk_c1,sk_c8) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_90595]) ).
tcf(c_90598,plain,
( ( multiply(sk_c1,sk_c8) = multiply(identity,sk_c9) )
| ( multiply(identity,sk_c9) != sk_c9 )
| ( multiply(sk_c1,sk_c8) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_90592]) ).
tcf(c_90616,plain,
( ( multiply(sk_c1,sk_c8) = iPr_def_23 )
| ( iPr_def_23 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_87638]) ).
tcf(c_90618,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(sk_c1,sk_c8) )
| ( multiply(sk_c1,sk_c8) != iPr_def_23 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86196]) ).
tcf(c_90619,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c1,sk_c8) )
| ( multiply(sk_c1,sk_c8) != iPr_def_23 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_90618]) ).
tcf(c_90637,plain,
! [X0: $i] :
( ( sk_c8 = multiply(sk_c1,sk_c8) )
| ( sk_c8 != multiply(identity,X0) )
| ( multiply(sk_c1,sk_c8) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_86349]) ).
tcf(c_90639,plain,
( ( sk_c8 = multiply(sk_c1,sk_c8) )
| ( sk_c8 != multiply(identity,sk_c9) )
| ( multiply(sk_c1,sk_c8) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_90637]) ).
tcf(c_90657,plain,
( ( multiply(sk_c1,sk_c8) = sk_c3 )
| ( sk_c3 != iPr_def_25 )
| ( multiply(sk_c1,sk_c8) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_87638]) ).
tcf(c_90717,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_90737,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = iPr_def_21 )
| ( iPr_def_21 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_90738,plain,
( ( multiply(inverse(sk_c9),sk_c9) = iPr_def_21 )
| ( iPr_def_21 != sk_c9 )
| ( multiply(inverse(sk_c9),sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_90737]) ).
tcf(c_90743,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(sk_c1,sk_c8) )
| ( multiply(sk_c1,sk_c8) != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_86077]) ).
tcf(c_90744,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c1,sk_c8) )
| ( multiply(sk_c1,sk_c8) != sk_c9 )
| ( multiply(inverse(sk_c9),sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_90743]) ).
tcf(c_90779,plain,
( ( multiply(inverse(sk_c9),sk_c9) = iPr_def_23 )
| ( iPr_def_23 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_86086]) ).
tcf(c_90919,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(sk_c4,sk_c8) )
| ( multiply(sk_c4,sk_c8) != iPr_def_20 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86182]) ).
tcf(c_90920,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c4,sk_c8) )
| ( multiply(sk_c4,sk_c8) != iPr_def_20 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_90919]) ).
tcf(c_90925,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = iPr_def_23 )
| ( iPr_def_23 != iPr_def_20 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_86182]) ).
tcf(c_90926,plain,
( ( multiply(inverse(sk_c9),sk_c9) = iPr_def_23 )
| ( iPr_def_23 != iPr_def_20 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_90925]) ).
tcf(c_91092,plain,
! [X0: $i] :
( ( identity = sk_c3 )
| ( identity != X0 )
| ( sk_c3 != X0 ) ),
inference(instantiation,[status(thm)],[c_86097]) ).
tcf(c_91121,plain,
! [X0: $i] :
( ( iPr_def_23 = identity )
| ( iPr_def_23 != X0 )
| ( identity != X0 ) ),
inference(instantiation,[status(thm)],[c_86103]) ).
tcf(c_91124,plain,
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != identity )
| ( sk_c8 != identity ) ),
inference(instantiation,[status(thm)],[c_86408]) ).
tcf(c_91211,plain,
! [X0: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != iPr_def_21 )
| ( multiply(identity,X0) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_86571]) ).
tcf(c_91212,plain,
( ( sk_c8 = multiply(identity,sk_c9) )
| ( sk_c8 != iPr_def_21 )
| ( multiply(identity,sk_c9) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_91211]) ).
tcf(c_91452,plain,
( ( sk_c8 = identity )
| ( identity != iPr_def_23 )
| ( sk_c8 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86080]) ).
tcf(c_92071,plain,
( ( iPr_def_23 = multiply(sk_c5,sk_c8) )
| ( iPr_def_23 != iPr_def_20 )
| ( multiply(sk_c5,sk_c8) != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_87586]) ).
tcf(c_92074,plain,
! [X0: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != multiply(sk_c5,sk_c8) )
| ( X0 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_86450]) ).
tcf(c_92075,plain,
( ( sk_c9 = iPr_def_23 )
| ( iPr_def_23 != multiply(sk_c5,sk_c8) )
| ( sk_c9 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_92074]) ).
tcf(c_92333,plain,
! [X0: $i] :
( ( sk_c3 = X0 )
| ( sk_c3 != sk_c3 )
| ( X0 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_86965]) ).
tcf(c_92334,plain,
( ( sk_c3 = sk_c9 )
| ( sk_c3 != sk_c3 )
| ( sk_c9 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_92333]) ).
tcf(c_92335,plain,
! [X0: $i,X1: $i] :
( ( sk_c3 = X0 )
| ( sk_c3 != multiply(inverse(X1),sk_c9) )
| ( X0 != multiply(inverse(X1),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86965]) ).
tcf(c_92337,plain,
( ( sk_c3 = sk_c9 )
| ( sk_c3 != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_92335]) ).
tcf(c_92394,plain,
! [X0: $i] :
( ( sk_c5 = X0 )
| ( sk_c5 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_87056]) ).
tcf(c_92398,plain,
( ( sk_c5 = sk_c9 )
| ( sk_c5 != identity )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_92394]) ).
tcf(c_92405,plain,
! [X0: $i,X1: $i] :
( ( sk_c5 = X0 )
| ( sk_c5 != multiply(inverse(X1),sk_c9) )
| ( X0 != multiply(inverse(X1),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_87056]) ).
tcf(c_92407,plain,
( ( sk_c5 = sk_c9 )
| ( sk_c5 != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_92405]) ).
tcf(c_92690,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_90717]) ).
tcf(c_92700,plain,
( ( sk_c3 = multiply(identity,iPr_def_23) )
| ( sk_c3 != iPr_def_23 )
| ( multiply(identity,iPr_def_23) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86967]) ).
tcf(c_92704,plain,
! [X0: $i] :
( ( sk_c3 = X0 )
| ( sk_c3 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_86965]) ).
tcf(c_92705,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c3) = multiply(X0,iPr_def_23) )
| ( sk_c3 != iPr_def_23 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_86654]) ).
tcf(c_92707,plain,
( ( sk_c3 = sk_c9 )
| ( sk_c3 != iPr_def_23 )
| ( sk_c9 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_92704]) ).
tcf(c_92727,plain,
( ( iPr_def_23 = multiply(sk_c1,sk_c8) )
| ( iPr_def_23 != sk_c3 )
| ( multiply(sk_c1,sk_c8) != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_89024]) ).
tcf(c_92816,plain,
( ( identity = sk_c3 )
| ( identity != iPr_def_23 )
| ( sk_c3 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_91092]) ).
tcf(c_92915,plain,
( ( identity = sk_c8 )
| ( identity != identity )
| ( sk_c8 != identity ) ),
inference(instantiation,[status(thm)],[c_86210]) ).
tcf(c_92916,plain,
! [X0: $i] :
( ( identity = sk_c8 )
| ( identity != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_86097]) ).
tcf(c_93324,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = iPr_def_23 )
| ( iPr_def_23 != iPr_def_25 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_86206]) ).
tcf(c_93325,plain,
( ( multiply(inverse(sk_c9),sk_c9) = iPr_def_23 )
| ( iPr_def_23 != iPr_def_25 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_93324]) ).
tcf(c_93686,plain,
! [X0: $i] :
( ( sk_c3 = multiply(inverse(X0),sk_c9) )
| ( sk_c3 != iPr_def_21 )
| ( multiply(inverse(X0),sk_c9) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_86272]) ).
tcf(c_93693,plain,
( ( sk_c3 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c3 != iPr_def_21 )
| ( multiply(inverse(sk_c9),sk_c9) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_93686]) ).
tcf(c_93812,plain,
( ( identity = multiply(sk_c9,sk_c3) )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( multiply(sk_c9,sk_c3) != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86946]) ).
tcf(c_95101,plain,
( ( iPr_def_23 = identity )
| ( iPr_def_23 != iPr_def_23 )
| ( identity != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_91121]) ).
tcf(c_95360,plain,
( ( sk_c5 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c5 != multiply(sk_c7,sk_c9) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c7,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_89760]) ).
tcf(c_97546,plain,
( ( iPr_def_20 = sk_c3 )
| ( iPr_def_20 != iPr_def_20 )
| ( sk_c3 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_88983]) ).
tcf(c_97547,plain,
( ( iPr_def_23 = iPr_def_20 )
| ( iPr_def_23 != sk_c3 )
| ( iPr_def_20 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_89024]) ).
tcf(c_97684,plain,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_23 != iPr_def_23 )
| ( sk_c3 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_89026]) ).
tcf(c_98159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(identity,X0) = iPr_def_24 )
| ( iPr_def_24 != multiply(X1,X2) )
| ( multiply(identity,X0) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_86241]) ).
tcf(c_98160,plain,
( ( multiply(identity,sk_c9) = iPr_def_24 )
| ( iPr_def_24 != multiply(sk_c9,sk_c9) )
| ( multiply(identity,sk_c9) != multiply(sk_c9,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_98159]) ).
tcf(c_98242,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = sk_c3 )
| ( sk_c3 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_86789]) ).
tcf(c_101587,plain,
( ( sk_c8 = multiply(sk_c9,sk_c3) )
| ( sk_c8 != sk_c8 )
| ( multiply(sk_c9,sk_c3) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_92690]) ).
tcf(c_101590,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_101868,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_38747,c_10742,c_48778,c_82901]) ).
tcf(c_101870,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_551,c_101868]) ).
tcf(c_101914,plain,
( ( identity = sk_c8 )
| ( identity != multiply(sk_c9,sk_c3) )
| ( sk_c8 != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_92916]) ).
tcf(c_102355,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = sk_c3 )
| ( sk_c3 != multiply(X0,X1) )
| ( sk_c8 != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_88865]) ).
tcf(c_102374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != multiply(X1,X2) )
| ( X0 != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_90717]) ).
tcf(c_102874,plain,
( ( sk_c8 = identity )
| ( identity != sk_c3 )
| ( sk_c8 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_86080]) ).
tcf(c_103145,plain,
( ( multiply(sk_c9,sk_c3) = sk_c3 )
| ( sk_c3 != multiply(identity,iPr_def_23) )
| ( multiply(sk_c9,sk_c3) != multiply(identity,iPr_def_23) ) ),
inference(instantiation,[status(thm)],[c_98242]) ).
tcf(c_103146,plain,
( ( multiply(sk_c9,sk_c3) = multiply(identity,iPr_def_23) )
| ( sk_c3 != iPr_def_23 )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_92705]) ).
tcf(c_109037,plain,
! [X0: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != iPr_def_24 )
| ( multiply(identity,X0) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_86571]) ).
tcf(c_109040,plain,
( ( sk_c8 = multiply(identity,sk_c9) )
| ( sk_c8 != iPr_def_24 )
| ( multiply(identity,sk_c9) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_109037]) ).
tcf(c_109239,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_21 )
| ( iPr_def_21 != multiply(inverse(X0),sk_c9) )
| ( sk_c8 != multiply(inverse(X0),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_102374]) ).
tcf(c_109240,plain,
( ( sk_c8 = iPr_def_21 )
| ( iPr_def_21 != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c8 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_109239]) ).
tcf(c_110349,plain,
( ( sk_c8 = sk_c3 )
| ( sk_c3 != multiply(sk_c1,sk_c8) )
| ( sk_c8 != multiply(sk_c1,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_102355]) ).
tcf(c_111469,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != multiply(sk_c9,sk_c3) )
| ( X0 != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_101590]) ).
tcf(c_111470,plain,
( ( sk_c9 = sk_c8 )
| ( sk_c8 != multiply(sk_c9,sk_c3) )
| ( sk_c9 != multiply(sk_c9,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_111469]) ).
tcf(c_112432,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_592,c_101870]) ).
tcf(c_112667,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c3) = multiply(identity,X0) )
| ( sk_c3 != X0 )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_86654]) ).
tcf(c_112670,plain,
( ( multiply(sk_c9,sk_c3) = multiply(identity,sk_c9) )
| ( sk_c3 != sk_c9 )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_112667]) ).
tcf(c_113304,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( iPr_def_25 = iPr_def_26 )
| ( iPr_def_14 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82801,c_82926]) ).
tcf(c_113307,plain,
( ( iPr_def_25 = iPr_def_26 )
| ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c9 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82801,c_62186]) ).
tcf(c_113322,plain,
( ( iPr_def_25 = iPr_def_26 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82801,c_21286]) ).
tcf(c_113767,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_14 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82802,c_82926]) ).
tcf(c_113785,plain,
( ( iPr_def_14 = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_82802,c_21286]) ).
tcf(c_114043,plain,
( ( iPr_def_16 = iPr_def_26 )
| ( identity = iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_83797,c_141,c_142,c_603,c_605,c_538,c_539,c_543,c_544,c_545,c_1150,c_1473,c_1940,c_2093,c_2521,c_2677,c_2910,c_2911,c_3083,c_3339,c_3777,c_4247,c_4878,c_4910,c_5007,c_5076,c_5636,c_5637,c_5642,c_6755,c_7019,c_16518,c_18509,c_26793,c_26864,c_27916,c_48888,c_49147,c_62493,c_62508,c_68965,c_71883,c_72374,c_78335,c_80801,c_82192,c_82781,c_83798,c_83796,c_85016,c_85163,c_86106,c_86151,c_86271,c_86482,c_86649,c_86743,c_86956,c_89003,c_89002,c_89534,c_89553,c_89741,c_89808,c_89812,c_90059,c_90063,c_90150,c_90920,c_91212,c_92407,c_95360,c_109240,c_113785,c_113767]) ).
tcf(c_114066,plain,
( ( iPr_def_19 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_114043,c_84977]) ).
tcf(c_114073,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_114043,c_31926]) ).
tcf(c_114464,plain,
iPr_def_20 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_39314,c_81995]) ).
tcf(c_114470,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_77252,c_114464]) ).
tcf(c_114493,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_20,X0),
inference(demodulation,[status(thm)],[c_38251,c_114464]) ).
tcf(c_114525,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_36941,c_114464]) ).
tcf(c_114540,plain,
multiply(iPr_def_22,iPr_def_20) = sk_c8,
inference(demodulation,[status(thm)],[c_38432,c_114464]) ).
tcf(c_114647,plain,
iPr_def_14 = iPr_def_24,
inference(global_subsumption_just,[status(thm)],[c_114470,c_141,c_142,c_544,c_545,c_1940,c_2521,c_2677,c_18509,c_26793,c_26864,c_48888,c_80801,c_82192,c_82781,c_86106,c_86151,c_86482,c_86649,c_86743,c_86956,c_89003,c_89002,c_89534,c_89553,c_90059,c_90063,c_90150,c_90920,c_91212,c_109240,c_113785,c_113767]) ).
tcf(c_114678,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_26,iPr_def_23) = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_52837,c_114647]) ).
tcf(c_114710,plain,
multiply(iPr_def_14,iPr_def_14) = sk_c3,
inference(demodulation,[status(thm)],[c_38394,c_114647]) ).
tcf(c_114876,plain,
iPr_def_16 = iPr_def_26,
inference(global_subsumption_just,[status(thm)],[c_39406,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_1117,c_1116,c_1258,c_1479,c_1940,c_1945,c_2521,c_2677,c_4871,c_4910,c_6755,c_7984,c_9968,c_12616,c_18509,c_26793,c_26864,c_29143,c_29145,c_31926,c_36448,c_40628,c_44893,c_44892,c_45016,c_48888,c_50613,c_51569,c_53463,c_54076,c_58802,c_63339,c_64283,c_66701,c_72373,c_80801,c_82192,c_82781,c_82778,c_83758,c_83906,c_86106,c_86128,c_86151,c_86254,c_86271,c_86433,c_86457,c_86458,c_86482,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_89003,c_89002,c_89534,c_89553,c_90059,c_90063,c_90150,c_90920,c_91124,c_91212,c_92915,c_95101,c_109240,c_113785,c_113767,c_114043,c_114073,c_114066]) ).
tcf(c_114921,plain,
multiply(iPr_def_16,iPr_def_25) = sk_c8,
inference(demodulation,[status(thm)],[c_39966,c_114876]) ).
tcf(c_115008,plain,
iPr_def_20 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_39498,c_81436]) ).
tcf(c_115010,plain,
multiply(iPr_def_20,iPr_def_20) = sk_c8,
inference(demodulation,[status(thm)],[c_114540,c_115008]) ).
tcf(c_115028,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(demodulation,[status(thm)],[c_38298,c_115008]) ).
tcf(c_115077,plain,
iPr_def_25 = iPr_def_26,
inference(global_subsumption_just,[status(thm)],[c_39599,c_141,c_142,c_603,c_605,c_538,c_544,c_1117,c_1116,c_1258,c_1888,c_1940,c_1945,c_4903,c_6755,c_12616,c_18509,c_26864,c_29145,c_40628,c_44893,c_44892,c_45016,c_49180,c_51569,c_53463,c_63339,c_64283,c_82780,c_86128,c_86151,c_86254,c_86271,c_86433,c_86458,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_89534,c_89553,c_90059,c_90063,c_91124,c_92915,c_95101,c_113322,c_113304,c_113307]) ).
tcf(c_115079,plain,
iPr_def_16 = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_115077,c_114876]) ).
tcf(c_115080,plain,
multiply(iPr_def_16,iPr_def_16) = sk_c8,
inference(demodulation,[status(thm)],[c_114921,c_115079]) ).
tcf(c_115286,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_42904,c_551,c_566,c_567,c_573,c_574,c_1116,c_1358,c_1429,c_1472,c_1473,c_1478,c_1479,c_1632,c_1715,c_2194,c_2251,c_2252,c_2270,c_2350,c_2373,c_4399,c_4400,c_4878,c_8875,c_8989,c_9061,c_9739,c_9738,c_10488,c_10695,c_10742,c_21477,c_34480,c_35256,c_35350,c_44899,c_44898,c_45016,c_46297,c_46644,c_46722,c_46951,c_48778,c_75338,c_76023,c_82901,c_87640,c_87694,c_89359,c_90558,c_90559,c_90596,c_90657,c_91452,c_92727,c_92816,c_102874,c_110349]) ).
tcf(c_115308,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_42905,c_551,c_566,c_573,c_1116,c_1358,c_1478,c_1479,c_1632,c_1715,c_2251,c_2252,c_2270,c_2350,c_4399,c_4400,c_7731,c_8989,c_9739,c_10488,c_10742,c_21477,c_34480,c_35350,c_44899,c_45016,c_46722,c_48778,c_75338,c_82901,c_87640,c_87694,c_89359,c_90558,c_90559,c_90596,c_90657,c_92727,c_92816,c_102874,c_110349,c_115286]) ).
tcf(c_115310,plain,
iPr_def_15 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_115308,c_141,c_142,c_544,c_545,c_551,c_564,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1940,c_2034,c_2251,c_2252,c_2270,c_2350,c_2521,c_2677,c_3997,c_4247,c_5865,c_7733,c_7854,c_9275,c_9965,c_10700,c_10742,c_18509,c_21478,c_26793,c_26864,c_34480,c_35139,c_41518,c_44899,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_50189,c_62481,c_62493,c_80801,c_82192,c_82781,c_82901,c_86106,c_86151,c_86482,c_86649,c_86743,c_86956,c_87640,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90558,c_90559,c_90596,c_90657,c_90920,c_91212,c_92727,c_92816,c_102874,c_109240,c_110349,c_113785,c_113767,c_115286,c_115308]) ).
tcf(c_115322,plain,
multiply(sk_c6,iPr_def_15) = multiply(iPr_def_15,sk_c9),
inference(demodulation,[status(thm)],[c_60319,c_115310]) ).
tcf(c_115398,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_43942,c_567,c_574,c_1116,c_1429,c_1472,c_1473,c_1632,c_1715,c_2251,c_2252,c_2373,c_4399,c_4400,c_8875,c_9061,c_9738,c_10488,c_34480,c_35256,c_44898,c_45016,c_46297,c_46722,c_76023,c_87640,c_90558,c_90596,c_90657,c_91452,c_92727]) ).
tcf(c_115400,plain,
iPr_def_18 = iPr_def_19,
inference(global_subsumption_just,[status(thm)],[c_115398,c_543,c_566,c_1116,c_1149,c_1150,c_1429,c_1478,c_1479,c_1632,c_2251,c_2252,c_2350,c_2373,c_3997,c_4247,c_4871,c_5636,c_5637,c_5865,c_8997,c_16517,c_24425,c_24427,c_34480,c_35143,c_44898,c_45016,c_46297,c_46722,c_50617,c_54423,c_62481,c_62493,c_86059,c_86064,c_87640,c_90558,c_90596,c_90657,c_91452,c_92727,c_114647,c_115310,c_115398]) ).
tcf(c_115402,plain,
iPr_def_15 = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_115400,c_115310]) ).
tcf(c_115403,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( sk_c9 != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_38612,c_115402]) ).
tcf(c_115413,plain,
multiply(iPr_def_15,iPr_def_20) = sk_c8,
inference(demodulation,[status(thm)],[c_39288,c_115402]) ).
tcf(c_115415,plain,
multiply(iPr_def_15,sk_c5) = identity,
inference(demodulation,[status(thm)],[c_37450,c_115402]) ).
tcf(c_115504,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c4,multiply(iPr_def_15,X0)) = multiply(iPr_def_20,X0) ) ),
inference(superposition,[status(thm)],[c_592,c_114493]) ).
tcf(c_115574,plain,
( iPr_def_13
| iPr_def_12
| ( iPr_def_14 != iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_38447,c_141,c_142,c_603,c_605,c_538,c_543,c_544,c_545,c_551,c_564,c_566,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1429,c_1473,c_1478,c_1479,c_1632,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2373,c_2521,c_2677,c_3997,c_4247,c_4871,c_4878,c_5636,c_5637,c_5865,c_6755,c_7733,c_7854,c_8997,c_9275,c_9965,c_10248,c_10586,c_10697,c_10700,c_10742,c_10951,c_16517,c_18509,c_20413,c_21478,c_21815,c_24425,c_24427,c_26793,c_26864,c_32042,c_34480,c_35143,c_35139,c_36448,c_41518,c_44899,c_44898,c_45016,c_46297,c_46644,c_46722,c_47444,c_47621,c_48778,c_48773,c_48888,c_49202,c_50189,c_50617,c_54423,c_58802,c_62481,c_62493,c_65147,c_66701,c_72372,c_80801,c_82192,c_82781,c_82901,c_86059,c_86064,c_86106,c_86151,c_86254,c_86433,c_86457,c_86482,c_86601,c_86649,c_86743,c_86942,c_86956,c_87640,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90558,c_90559,c_90596,c_90657,c_90920,c_91212,c_91452,c_92727,c_92816,c_102874,c_109240,c_110349,c_113785,c_113767,c_115286,c_115308,c_115398,c_115403]) ).
tcf(c_115670,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_114525,c_114647]) ).
tcf(c_115688,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_38460,c_62137]) ).
tcf(c_115690,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_115688,c_115402]) ).
tcf(c_115734,plain,
( ~ iPr_def_11
| ( sk_c9 != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_38580,c_1117,c_1116,c_3561,c_10647,c_10742,c_48773,c_82897,c_86405,c_88985,c_88984]) ).
tcf(c_115740,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_596,c_115734]) ).
tcf(c_115749,plain,
( ( sk_c9 = iPr_def_20 )
| ( sk_c9 != iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_115740,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_1940,c_1945,c_2251,c_2521,c_2677,c_4247,c_6755,c_10248,c_10742,c_12616,c_18509,c_21175,c_21475,c_23341,c_23386,c_26793,c_26864,c_34480,c_35729,c_40867,c_45016,c_48888,c_62493,c_80801,c_82192,c_82781,c_82926,c_84972,c_86106,c_86151,c_86433,c_86482,c_86649,c_86743,c_86938,c_86956,c_87634,c_87640,c_87641,c_88923,c_89003,c_89002,c_89534,c_89553,c_90059,c_90063,c_90150,c_90555,c_90558,c_90559,c_90560,c_90596,c_90920,c_91212,c_109240,c_113785,c_113767,c_115740]) ).
tcf(c_115768,plain,
( ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_38581,c_141,c_142,c_605,c_543,c_544,c_545,c_548,c_549,c_551,c_564,c_566,c_567,c_1116,c_1149,c_1150,c_1156,c_1358,c_1411,c_1412,c_1429,c_1473,c_1478,c_1479,c_1632,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2354,c_2373,c_2521,c_2677,c_3561,c_3997,c_4247,c_4871,c_4878,c_5636,c_5637,c_5865,c_7733,c_7854,c_8866,c_8997,c_9275,c_9774,c_9965,c_10647,c_10700,c_10742,c_12584,c_12616,c_13703,c_16517,c_17018,c_18509,c_21175,c_21478,c_24425,c_24427,c_26793,c_26864,c_34480,c_35143,c_35139,c_40713,c_40975,c_41518,c_44899,c_44898,c_45016,c_46297,c_46644,c_46722,c_47444,c_47621,c_48778,c_48888,c_50189,c_50617,c_54423,c_62481,c_62493,c_63993,c_65179,c_65151,c_65147,c_80801,c_82192,c_82781,c_82901,c_84543,c_86059,c_86064,c_86106,c_86151,c_86158,c_86254,c_86256,c_86433,c_86447,c_86482,c_86649,c_86743,c_86956,c_87634,c_87640,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90287,c_90428,c_90450,c_90466,c_90558,c_90559,c_90596,c_90657,c_90738,c_90744,c_90920,c_91212,c_91452,c_92337,c_92700,c_92727,c_92816,c_93325,c_93693,c_93812,c_102874,c_103145,c_103146,c_109240,c_110349,c_112670,c_113785,c_113767,c_115286,c_115308,c_115398,c_115734]) ).
tcf(c_115784,plain,
( ~ iPr_def_13
| ( multiply(sk_c9,iPr_def_23) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_38893,c_142,c_544,c_1945,c_4052,c_8384,c_26797,c_26864,c_82498,c_86151,c_86271,c_86433,c_86942,c_90059,c_90063,c_115010]) ).
tcf(c_115790,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_13
| ( multiply(iPr_def_20,iPr_def_23) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_561,c_115784]) ).
tcf(c_115794,plain,
( ~ iPr_def_12
| ( sk_c8 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_39003,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_551,c_564,c_1117,c_1116,c_1149,c_1150,c_1258,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2521,c_2677,c_3997,c_4247,c_5865,c_6755,c_7733,c_7854,c_9275,c_9965,c_10700,c_10742,c_12616,c_18509,c_21478,c_26793,c_26864,c_29145,c_34480,c_35139,c_40628,c_41518,c_44899,c_44893,c_44892,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_50189,c_51569,c_53463,c_62481,c_62493,c_63339,c_64283,c_80801,c_82192,c_82781,c_82901,c_86106,c_86128,c_86151,c_86254,c_86271,c_86433,c_86458,c_86482,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_87640,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90558,c_90559,c_90596,c_90657,c_90920,c_91124,c_91212,c_92727,c_92816,c_92915,c_95101,c_102874,c_109240,c_110349,c_113785,c_113767,c_115286,c_115308]) ).
tcf(c_115801,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_12
| ( identity != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_592,c_115794]) ).
tcf(c_115830,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_115801,c_1116,c_12552,c_22264,c_30525,c_77715,c_115794]) ).
tcf(c_115836,plain,
( iPr_def_13
| ( iPr_def_14 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_112432,c_141,c_142,c_605,c_543,c_544,c_545,c_548,c_551,c_564,c_566,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1429,c_1473,c_1478,c_1479,c_1632,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2345,c_2350,c_2373,c_2521,c_2677,c_3997,c_4247,c_4871,c_4878,c_5636,c_5637,c_5865,c_7733,c_7854,c_8997,c_9275,c_9965,c_10601,c_10700,c_10742,c_16517,c_18509,c_21478,c_22264,c_24425,c_24427,c_26793,c_26864,c_30528,c_30527,c_34480,c_35143,c_35139,c_40758,c_41518,c_44899,c_44898,c_44892,c_45016,c_46297,c_46644,c_46722,c_47444,c_47484,c_47621,c_48778,c_48888,c_50189,c_50617,c_54423,c_57913,c_62481,c_62493,c_64838,c_77715,c_80801,c_82192,c_82781,c_82901,c_86059,c_86064,c_86106,c_86151,c_86433,c_86482,c_86529,c_86649,c_86743,c_86810,c_86941,c_86956,c_87226,c_87640,c_87641,c_87694,c_87830,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90514,c_90555,c_90558,c_90559,c_90560,c_90596,c_90598,c_90616,c_90619,c_90639,c_90657,c_90779,c_90920,c_91212,c_91452,c_92727,c_92816,c_95101,c_98160,c_102874,c_109040,c_109240,c_110349,c_113785,c_113767,c_115286,c_115308,c_115398,c_115574,c_115794,c_115830]) ).
tcf(c_115966,plain,
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_38869,c_74049]) ).
tcf(c_116129,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_115790,c_142,c_544,c_1945,c_8384,c_26797,c_26864,c_82498,c_86151,c_86271,c_86433,c_86942,c_90059,c_90063,c_115010]) ).
tcf(c_116178,plain,
( ( sk_c9 = iPr_def_20 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_114678,c_39976,c_114876]) ).
tcf(c_116181,plain,
sk_c9 = iPr_def_20,
inference(forward_subsumption_resolution,[status(thm)],[c_116178,c_115749]) ).
tcf(c_116183,plain,
( ( iPr_def_16 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_116129,c_116181]) ).
tcf(c_116189,plain,
( ~ iPr_def_13
| ( identity != iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_20) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115966,c_116181]) ).
tcf(c_116194,plain,
( ~ iPr_def_11
| ( identity != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_115768,c_116181]) ).
tcf(c_116200,plain,
multiply(sk_c6,iPr_def_15) = multiply(iPr_def_15,iPr_def_20),
inference(demodulation,[status(thm)],[c_115322,c_116181]) ).
tcf(c_116205,plain,
multiply(inverse(sk_c7),iPr_def_15) = iPr_def_20,
inference(demodulation,[status(thm)],[c_67334,c_116181]) ).
tcf(c_116218,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_20,X0)) = X0,
inference(demodulation,[status(thm)],[c_38288,c_116181]) ).
tcf(c_116244,plain,
multiply(sk_c6,iPr_def_15) = sk_c8,
inference(light_normalisation,[status(thm)],[c_116200,c_115413]) ).
tcf(c_116260,plain,
( ~ iPr_def_13
| ( identity != iPr_def_20 ) ),
inference(ground_joinability,[status(thm)],[c_116189,c_115010]) ).
tcf(c_116297,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_38586,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_551,c_564,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1718,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2354,c_2521,c_2677,c_3561,c_3997,c_4247,c_4399,c_4400,c_4871,c_5865,c_6755,c_7733,c_7854,c_9054,c_9275,c_9740,c_9967,c_9965,c_10488,c_10700,c_10742,c_12584,c_12616,c_17018,c_18509,c_21478,c_26796,c_26794,c_26793,c_26864,c_26999,c_28049,c_34480,c_35139,c_41518,c_43345,c_44899,c_44893,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_50189,c_51569,c_57913,c_62481,c_62493,c_72373,c_80801,c_82192,c_82479,c_82781,c_82901,c_86106,c_86151,c_86254,c_86433,c_86458,c_86482,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_87640,c_87641,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90514,c_90558,c_90559,c_90596,c_90616,c_90619,c_90657,c_90779,c_90920,c_91212,c_92727,c_92816,c_95101,c_102874,c_109240,c_110349,c_113785,c_113767,c_115080,c_115286,c_115308,c_115734,c_115836,c_116260,c_116194]) ).
tcf(c_116300,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c8 = iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_115690,c_116297]) ).
tcf(c_116352,plain,
~ iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_116183,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_551,c_564,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1718,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2521,c_2677,c_3997,c_4247,c_4871,c_5865,c_6755,c_7733,c_7854,c_9275,c_9967,c_9965,c_10700,c_10742,c_17018,c_18509,c_21478,c_26796,c_26794,c_26793,c_26864,c_26999,c_28049,c_34480,c_35139,c_41518,c_43345,c_44899,c_44893,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_50189,c_51569,c_57913,c_62481,c_62493,c_72373,c_80801,c_82192,c_82479,c_82781,c_82901,c_86106,c_86151,c_86254,c_86433,c_86458,c_86482,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_87640,c_87641,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90514,c_90558,c_90559,c_90596,c_90616,c_90619,c_90657,c_90779,c_90920,c_91212,c_92727,c_92816,c_95101,c_102874,c_109240,c_110349,c_113785,c_113767,c_115080,c_115286,c_115308,c_116260]) ).
tcf(c_116451,plain,
( ( sk_c8 = iPr_def_15 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_116300,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_551,c_564,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1718,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2354,c_2521,c_2677,c_3561,c_3997,c_4247,c_4399,c_4400,c_4871,c_5865,c_6755,c_7733,c_7854,c_9054,c_9275,c_9740,c_9967,c_9965,c_10488,c_10700,c_10742,c_12584,c_12616,c_17018,c_18509,c_21478,c_26796,c_26794,c_26793,c_26864,c_26999,c_28049,c_34480,c_35139,c_41518,c_43345,c_44899,c_44893,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_50189,c_51569,c_57913,c_62170,c_62481,c_62493,c_72373,c_80801,c_82192,c_82479,c_82781,c_82901,c_86106,c_86151,c_86254,c_86433,c_86458,c_86482,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_87640,c_87641,c_87694,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90514,c_90558,c_90559,c_90596,c_90616,c_90619,c_90657,c_90779,c_90920,c_91212,c_92727,c_92816,c_95101,c_102874,c_109240,c_110349,c_113785,c_113767,c_115080,c_115286,c_115308,c_115734,c_115836,c_116260,c_116194]) ).
tcf(c_116452,plain,
( iPr_def_12
| ( sk_c8 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_116451]) ).
tcf(c_116489,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(iPr_def_17),iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_593,c_116205]) ).
tcf(c_116510,plain,
! [X0: $i] : multiply(sk_c4,X0) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_115028,c_116218]) ).
tcf(c_116519,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_14,iPr_def_14) = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_115670,c_116510]) ).
tcf(c_116524,plain,
( ( sk_c3 = iPr_def_20 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_116519,c_114710]) ).
tcf(c_116539,plain,
sk_c9 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_38724,c_141,c_142,c_603,c_605,c_538,c_544,c_545,c_551,c_564,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1719,c_1718,c_1940,c_1945,c_2034,c_2248,c_2251,c_2252,c_2270,c_2350,c_2521,c_2677,c_3155,c_3997,c_4247,c_4403,c_4871,c_5865,c_6755,c_7733,c_7854,c_8792,c_9275,c_9967,c_9965,c_10248,c_10700,c_10742,c_17018,c_18509,c_21175,c_21478,c_26796,c_26794,c_26793,c_26864,c_26999,c_28049,c_28033,c_34480,c_35139,c_35729,c_41518,c_43345,c_44899,c_44893,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_50189,c_51569,c_57913,c_62481,c_62493,c_72373,c_80801,c_82192,c_82479,c_82781,c_82901,c_86106,c_86151,c_86254,c_86275,c_86433,c_86458,c_86482,c_86529,c_86601,c_86649,c_86743,c_86942,c_86956,c_87084,c_87150,c_87634,c_87640,c_87641,c_87694,c_88984,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90450,c_90514,c_90558,c_90559,c_90560,c_90596,c_90616,c_90619,c_90657,c_90779,c_90920,c_90926,c_91212,c_92334,c_92727,c_92816,c_95101,c_97546,c_97547,c_97684,c_102874,c_109240,c_110349,c_111470,c_112670,c_113785,c_113767,c_115080,c_115286,c_115308,c_115749,c_115836,c_116260,c_116524]) ).
tcf(c_116543,plain,
multiply(inverse(iPr_def_17),iPr_def_15) = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_116489,c_141,c_142,c_125,c_603,c_605,c_538,c_539,c_544,c_545,c_548,c_551,c_564,c_571,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1718,c_1940,c_1945,c_2034,c_2251,c_2252,c_2270,c_2350,c_2521,c_2677,c_3997,c_4247,c_4399,c_4400,c_4871,c_5865,c_6755,c_7733,c_7854,c_9054,c_9275,c_9740,c_9967,c_9965,c_10488,c_10700,c_10742,c_13703,c_14558,c_17018,c_18509,c_21478,c_26796,c_26794,c_26793,c_26864,c_26999,c_28049,c_28665,c_28667,c_29145,c_34480,c_35139,c_41518,c_43345,c_44899,c_44893,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_49471,c_50189,c_51569,c_57913,c_62481,c_62493,c_72373,c_77715,c_80801,c_82192,c_82479,c_82781,c_82901,c_82926,c_86106,c_86151,c_86254,c_86271,c_86433,c_86458,c_86482,c_86529,c_86536,c_86601,c_86649,c_86743,c_86942,c_86956,c_87150,c_87590,c_87640,c_87641,c_87694,c_88984,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90450,c_90514,c_90558,c_90559,c_90596,c_90616,c_90619,c_90657,c_90779,c_90920,c_91212,c_92071,c_92075,c_92707,c_92727,c_92816,c_93812,c_95101,c_97546,c_97547,c_101587,c_101914,c_102874,c_109240,c_110349,c_112670,c_113785,c_113767,c_115080,c_115286,c_115308,c_115794,c_115836,c_116260,c_116297,c_116489,c_116524,c_116539]) ).
tcf(c_116545,plain,
sk_c8 = iPr_def_20,
inference(demodulation,[status(thm)],[c_116543,c_67528,c_116244]) ).
tcf(c_116547,plain,
( iPr_def_12
| ( iPr_def_15 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_116452,c_116545]) ).
tcf(c_116561,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_592,c_116545]) ).
tcf(c_116596,plain,
iPr_def_15 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_116561,c_141,c_142,c_125,c_603,c_605,c_538,c_539,c_544,c_545,c_548,c_551,c_564,c_571,c_1116,c_1149,c_1150,c_1358,c_1411,c_1412,c_1473,c_1479,c_1632,c_1719,c_1718,c_1940,c_1945,c_2034,c_2248,c_2251,c_2252,c_2270,c_2350,c_2354,c_2521,c_2677,c_3155,c_3561,c_3997,c_4247,c_4399,c_4400,c_4403,c_4871,c_5865,c_6755,c_7733,c_7854,c_8792,c_9054,c_9275,c_9740,c_9967,c_9965,c_10248,c_10488,c_10700,c_10742,c_12584,c_12616,c_13703,c_14558,c_17018,c_18509,c_21175,c_21478,c_26796,c_26794,c_26793,c_26864,c_26999,c_28049,c_28033,c_28665,c_28667,c_29145,c_34480,c_35139,c_35729,c_41518,c_43345,c_44899,c_44893,c_45016,c_46644,c_47444,c_47621,c_48778,c_48888,c_49471,c_50189,c_51569,c_57913,c_62481,c_62493,c_72373,c_77715,c_80801,c_82192,c_82479,c_82781,c_82901,c_82926,c_86106,c_86151,c_86254,c_86271,c_86275,c_86433,c_86458,c_86482,c_86529,c_86536,c_86601,c_86649,c_86743,c_86942,c_86956,c_87084,c_87150,c_87590,c_87634,c_87640,c_87641,c_87694,c_88984,c_89003,c_89002,c_89359,c_89534,c_89553,c_90059,c_90063,c_90150,c_90450,c_90514,c_90558,c_90559,c_90560,c_90596,c_90616,c_90619,c_90657,c_90779,c_90920,c_90926,c_91212,c_92071,c_92075,c_92334,c_92707,c_92727,c_92816,c_93812,c_95101,c_97546,c_97547,c_97684,c_101587,c_101914,c_102874,c_109240,c_110349,c_111470,c_112670,c_113785,c_113767,c_115080,c_115286,c_115308,c_115734,c_115749,c_115794,c_115830,c_115836,c_116260,c_116194,c_116524,c_116547]) ).
tcf(c_116598,plain,
sk_c8 = iPr_def_15,
inference(demodulation,[status(thm)],[c_116545,c_116596]) ).
tcf(c_116599,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_15,X0)) = X0,
inference(demodulation,[status(thm)],[c_116218,c_116596]) ).
tcf(c_116605,plain,
sk_c9 = iPr_def_15,
inference(demodulation,[status(thm)],[c_116181,c_116596]) ).
tcf(c_116664,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_15,X0)) = multiply(iPr_def_20,X0),
inference(global_subsumption_just,[status(thm)],[c_115504,c_1411,c_1412,c_1632,c_1719,c_2350,c_115504,c_115836,c_116352,c_116598]) ).
tcf(c_116667,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_15,X0)) = multiply(iPr_def_15,X0),
inference(light_normalisation,[status(thm)],[c_116664,c_116596]) ).
tcf(c_116668,plain,
! [X0: $i] : multiply(iPr_def_15,X0) = X0,
inference(demodulation,[status(thm)],[c_116667,c_116510,c_116599]) ).
tcf(c_116669,plain,
sk_c5 = identity,
inference(demodulation,[status(thm)],[c_115415,c_116668]) ).
tcf(c_116672,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116669,c_116598,c_116605,c_116352,c_115836,c_115400,c_115310,c_114647,c_92398,c_54429,c_50031,c_49488,c_36369,c_30528,c_23173,c_16518,c_13705,c_10586,c_9971,c_7988,c_6195,c_5637,c_5636,c_4878,c_4871,c_4247,c_4246,c_3170,c_1632,c_1631,c_1479,c_1473,c_1412,c_1258,c_543,c_538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/7.25 % Computer : n013.cluster.edu
% 0.13/7.25 % Model : x86_64 x86_64
% 0.13/7.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/7.25 % Memory : 8046.5625MB
% 0.13/7.25 % OS : Linux 6.8.0-71-generic
% 0.13/7.25 % CPULimit : 300
% 0.13/7.25 % WCLimit : 300
% 0.13/7.25 % DateTime : Wed Sep 23 14:13:54 UTC 2026
% 0.13/7.26 % CPUTime :
% 0.13/7.26 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/7.30 Running first-order theorem proving
% 0.13/7.30 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
% 0.17/7.31
% 0.17/7.31 % ======== iProver multi-core TPTP/SMT =========
% 0.17/7.31
% 0.17/7.31 % Detected problem language: tptp
% 0.17/7.32 % Proving...
% 31.93/12.26 % SZS status Started for theBenchmark.p
% 31.93/12.26 % SZS status Unsatisfiable for theBenchmark.p
% 31.93/12.26
% 31.93/12.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.93/12.26
% 31.93/12.26 % ------ iProver source info
% 31.93/12.26
% 31.93/12.26 % git: date: 2026-07-19 20:42:38 +0200
% 31.93/12.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.93/12.26 % git: non_committed_changes: false
% 31.93/12.26
% 31.93/12.26 % ------ Parsing...% successful
% 31.93/12.26
% 31.93/12.26
% 31.93/12.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.93/12.26
% 31.93/12.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 31.93/12.26
% 31.93/12.26 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.93/12.26
% 31.93/12.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 31.93/12.26 % ------ Proving...
% 31.93/12.26 % ------ Problem Properties
% 31.93/12.26
% 31.93/12.26 %
% 31.93/12.26 % clauses 63
% 31.93/12.26 % conjectures 47
% 31.93/12.26 % EPR 43
% 31.93/12.26 % Horn 20
% 31.93/12.26 % unary 16
% 31.93/12.26 % binary 42
% 31.93/12.26 % lits 117
% 31.93/12.26 % lits eq 109
% 31.93/12.26 % fd_pure 0
% 31.93/12.26 % fd_pseudo 0
% 31.93/12.26 % fd_cond 0
% 31.93/12.26 % fd_pseudo_cond 0
% 31.93/12.26 % AC symbols 0
% 31.93/12.26
% 31.93/12.26 % ------ Schedule dynamic 5 is on
% 31.93/12.26
% 31.93/12.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.93/12.26
% 31.93/12.26
% 31.93/12.26 % ------
% 31.93/12.26 % Current options:
% 31.93/12.26 % ------
% 31.93/12.26
% 31.93/12.26
% 31.93/12.26 %
% 31.93/12.26
% 31.93/12.26 % ------ Proving...
% 31.93/12.26 %
% 31.93/12.26
% 31.93/12.26 % SZS status Unsatisfiable for theBenchmark.p
% 31.93/12.26
% 31.93/12.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.93/12.29
% 31.93/12.29
%------------------------------------------------------------------------------