%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP318-1 : 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 : n012.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 01:32:49 PM UTC 2026
% Result : Unsatisfiable 35.20s 7.04s
% Output : CNFRefutation 35.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 63
% Syntax : Number of formulae : 1213 ( 165 unt; 13 def)
% Number of atoms : 4952 (2707 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 2854 (1134 ~;1720 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 507 ( 0 sgn 507 !; 0 ?; 462 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c12 = inverse(sk_c4)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c11 = inverse(sk_c5)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c9 = inverse(sk_c6)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(reorient_equations,[],[f17]) ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c12 = inverse(sk_c4)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c11 = inverse(sk_c5)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = inverse(sk_c6)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| sk_c12 = multiply(sk_c1,sk_c11) ),
inference(reorient_equations,[],[f36]) ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c12 = inverse(sk_c4)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c11 = inverse(sk_c5)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = inverse(sk_c6)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f56]) ).
fof(f64,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c12 = inverse(sk_c4)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c11 = inverse(sk_c5)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c9 = inverse(sk_c6)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| sk_c11 = multiply(sk_c12,sk_c3) ),
inference(reorient_equations,[],[f76]) ).
fof(f84,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c12 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c11 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c9 = inverse(sk_c6)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f94]) ).
fof(f96,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f97,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| sk_c3 = multiply(sk_c2,sk_c12) ),
inference(reorient_equations,[],[f96]) ).
fof(f104,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c12 = inverse(sk_c4)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f106]) ).
fof(f108,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
fof(f109,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f108]) ).
fof(f110,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
fof(f111,plain,
( sk_c11 = inverse(sk_c5)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f110]) ).
fof(f112,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
fof(f115,plain,
( sk_c9 = inverse(sk_c6)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f114]) ).
fof(f116,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_57) ).
fof(f117,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| sk_c12 = inverse(sk_c2) ),
inference(reorient_equations,[],[f116]) ).
fof(f124,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| inverse(X2) != sk_c12
| multiply(X2,sk_c12) != X1
| multiply(sk_c12,X1) != sk_c11
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| sk_c12 != multiply(X6,sk_c11)
| inverse(X5) != X6
| sk_c12 != multiply(X5,X6)
| sk_c11 != inverse(X4)
| sk_c10 != multiply(X4,sk_c11)
| sk_c12 != inverse(X3)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X2)
| multiply(X2,sk_c12) != X1
| sk_c11 != multiply(sk_c12,X1)
| inverse(X0) != sk_c11
| sk_c12 != multiply(X0,sk_c11)
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(reorient_equations,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X0,X8,X6,X7,X4,X5] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| sk_c12 != multiply(X6,sk_c11)
| inverse(X5) != X6
| sk_c12 != multiply(X5,X6)
| sk_c11 != inverse(X4)
| sk_c10 != multiply(X4,sk_c11)
| sk_c12 != inverse(X3)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X2)
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| inverse(X0) != sk_c11
| sk_c12 != multiply(X0,sk_c11)
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(equality_resolution,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X0,X8,X7,X4,X5] :
( multiply(X7,inverse(X5)) != X8
| inverse(X5) != inverse(X8)
| inverse(X7) != X8
| sk_c12 != multiply(inverse(X5),sk_c11)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c11 != inverse(X4)
| sk_c10 != multiply(X4,sk_c11)
| sk_c12 != inverse(X3)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X2)
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| inverse(X0) != sk_c11
| sk_c12 != multiply(X0,sk_c11)
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(equality_resolution,[],[f126]) ).
fof(f128,plain,
! [X2,X3,X0,X7,X4,X5] :
( inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c11 != inverse(X4)
| sk_c10 != multiply(X4,sk_c11)
| sk_c12 != inverse(X3)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X2)
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| inverse(X0) != sk_c11
| sk_c12 != multiply(X0,sk_c11)
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(equality_resolution,[],[f127]) ).
tcf(c_113,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_114,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c4,sk_c12) = sk_c11 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c4) = sk_c12 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c5,sk_c11) = sk_c10 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c5) = sk_c11 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c12 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_122,negated_conjecture,
( ( multiply(sk_c9,sk_c11) = sk_c12 )
| ( multiply(sk_c11,sk_c12) = sk_c10 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_126,negated_conjecture,
( ( multiply(sk_c1,sk_c11) = sk_c12 )
| ( multiply(sk_c4,sk_c12) = sk_c11 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c4) = sk_c12 )
| ( multiply(sk_c1,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_128,negated_conjecture,
( ( multiply(sk_c1,sk_c11) = sk_c12 )
| ( multiply(sk_c5,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c5) = sk_c11 )
| ( multiply(sk_c1,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_130,negated_conjecture,
( ( multiply(sk_c1,sk_c11) = sk_c12 )
| ( multiply(sk_c6,sk_c9) = sk_c12 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_132,negated_conjecture,
( ( multiply(sk_c1,sk_c11) = sk_c12 )
| ( multiply(sk_c9,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c4,sk_c12) = sk_c11 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( inverse(sk_c4) = sk_c12 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c5,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( inverse(sk_c5) = sk_c11 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_140,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c6,sk_c9) = sk_c12 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_141,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_142,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c9,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_146,negated_conjecture,
( ( multiply(sk_c4,sk_c12) = sk_c11 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_147,negated_conjecture,
( ( inverse(sk_c4) = sk_c12 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_148,negated_conjecture,
( ( multiply(sk_c5,sk_c11) = sk_c10 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_149,negated_conjecture,
( ( inverse(sk_c5) = sk_c11 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_150,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c12 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_151,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_152,negated_conjecture,
( ( multiply(sk_c9,sk_c11) = sk_c12 )
| ( multiply(sk_c12,sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_156,negated_conjecture,
( ( multiply(sk_c2,sk_c12) = sk_c3 )
| ( multiply(sk_c4,sk_c12) = sk_c11 ) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_157,negated_conjecture,
( ( inverse(sk_c4) = sk_c12 )
| ( multiply(sk_c2,sk_c12) = sk_c3 ) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_158,negated_conjecture,
( ( multiply(sk_c2,sk_c12) = sk_c3 )
| ( multiply(sk_c5,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_159,negated_conjecture,
( ( inverse(sk_c5) = sk_c11 )
| ( multiply(sk_c2,sk_c12) = sk_c3 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_160,negated_conjecture,
( ( multiply(sk_c2,sk_c12) = sk_c3 )
| ( multiply(sk_c6,sk_c9) = sk_c12 ) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_161,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c2,sk_c12) = sk_c3 ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_162,negated_conjecture,
( ( multiply(sk_c2,sk_c12) = sk_c3 )
| ( multiply(sk_c9,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_166,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( multiply(sk_c4,sk_c12) = sk_c11 ) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_167,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( inverse(sk_c4) = sk_c12 ) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_168,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( multiply(sk_c5,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_169,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( inverse(sk_c5) = sk_c11 ) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_170,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( multiply(sk_c6,sk_c9) = sk_c12 ) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_171,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_172,negated_conjecture,
( ( inverse(sk_c2) = sk_c12 )
| ( multiply(sk_c9,sk_c11) = sk_c12 ) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_176,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c11 )
| ( inverse(X4) != sk_c12 )
| ( inverse(X3) != sk_c12 )
| ( inverse(X2) != sk_c11 )
| ( multiply(sk_c11,sk_c12) != sk_c10 )
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(X5,sk_c11) != sk_c10 )
| ( multiply(X4,sk_c12) != sk_c11 )
| ( multiply(X2,sk_c11) != sk_c12 )
| ( multiply(inverse(X1),sk_c11) != sk_c12 )
| ( multiply(X1,inverse(X1)) != sk_c12 )
| ( multiply(X0,inverse(X1)) != inverse(X0) )
| ( multiply(sk_c12,multiply(X3,sk_c12)) != sk_c11 ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_177,plain,
multiply(identity,sk_c12) = sk_c12,
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_178,plain,
multiply(inverse(sk_c12),sk_c12) = identity,
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_721,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c12 )
| ( multiply(X0,sk_c12) != sk_c11 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_176]) ).
tcf(c_722,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c12 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_176]) ).
tcf(c_723,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(inverse(X1),sk_c11) != sk_c12 )
| ( multiply(X1,inverse(X1)) != sk_c12 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_176]) ).
tcf(c_724,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_176]) ).
tcf(c_725,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c12 )
| ( multiply(sk_c12,multiply(X0,sk_c12)) != sk_c11 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_176]) ).
tcf(c_726,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c11,sk_c12) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_176]) ).
tcf(c_727,definition,
iPr_def_15 = multiply(sk_c11,sk_c12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_729,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_732,definition,
iPr_def_20 = multiply(sk_c9,sk_c11),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_733,definition,
iPr_def_21 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_734,definition,
iPr_def_22 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_735,definition,
iPr_def_23 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_736,definition,
iPr_def_24 = multiply(sk_c5,sk_c11),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_737,definition,
iPr_def_25 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_738,definition,
iPr_def_26 = multiply(sk_c4,sk_c12),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_739,definition,
iPr_def_27 = multiply(sk_c2,sk_c12),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_740,definition,
iPr_def_28 = multiply(sk_c12,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).
tcf(c_741,definition,
iPr_def_29 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_29])],[]) ).
tcf(c_742,definition,
iPr_def_30 = multiply(sk_c1,sk_c11),
introduced(definition,[new_symbols(definition,[iPr_def_30])],[]) ).
tcf(c_743,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_726,c_727]) ).
tcf(c_744,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c12 )
| ( multiply(sk_c12,multiply(X0,sk_c12)) != sk_c11 ) ),
inference(demodulation,[status(thm)],[c_725]) ).
tcf(c_745,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_724]) ).
tcf(c_746,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(inverse(X1),sk_c11) != sk_c12 )
| ( multiply(X1,inverse(X1)) != sk_c12 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(demodulation,[status(thm)],[c_723]) ).
tcf(c_747,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c12 ) ),
inference(demodulation,[status(thm)],[c_722]) ).
tcf(c_748,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c12 )
| ( multiply(X0,sk_c12) != sk_c11 ) ),
inference(demodulation,[status(thm)],[c_721]) ).
tcf(c_752,negated_conjecture,
( ( iPr_def_20 = sk_c12 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_172,c_732]) ).
tcf(c_753,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_171,c_733]) ).
tcf(c_754,negated_conjecture,
( ( iPr_def_22 = sk_c12 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_170,c_734]) ).
tcf(c_755,negated_conjecture,
( ( iPr_def_23 = sk_c11 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_169,c_735]) ).
tcf(c_756,negated_conjecture,
( ( iPr_def_24 = sk_c10 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_168,c_736]) ).
tcf(c_757,negated_conjecture,
( ( iPr_def_25 = sk_c12 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_167,c_737]) ).
tcf(c_758,negated_conjecture,
( ( iPr_def_26 = sk_c11 )
| ( iPr_def_17 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_166,c_738]) ).
tcf(c_762,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_20 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_162]) ).
tcf(c_763,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_161]) ).
tcf(c_764,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_22 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_765,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_23 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_159]) ).
tcf(c_766,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_24 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_158]) ).
tcf(c_767,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_25 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_157]) ).
tcf(c_768,negated_conjecture,
( ( iPr_def_27 = sk_c3 )
| ( iPr_def_26 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_156]) ).
tcf(c_772,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_20 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_152]) ).
tcf(c_773,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_151]) ).
tcf(c_774,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_22 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_150]) ).
tcf(c_775,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_23 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_149]) ).
tcf(c_776,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_24 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_148]) ).
tcf(c_777,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_25 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_147]) ).
tcf(c_778,negated_conjecture,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_26 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_146]) ).
tcf(c_782,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_20 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_142]) ).
tcf(c_783,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_141]) ).
tcf(c_784,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_22 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_140]) ).
tcf(c_785,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_23 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_139]) ).
tcf(c_786,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_24 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_138]) ).
tcf(c_787,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_25 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_137]) ).
tcf(c_788,negated_conjecture,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_26 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_136]) ).
tcf(c_792,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_20 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_793,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_794,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_22 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_795,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_23 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_796,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_24 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_797,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_25 = sk_c12 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_798,negated_conjecture,
( ( iPr_def_30 = sk_c12 )
| ( iPr_def_26 = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_802,negated_conjecture,
( ( iPr_def_20 = sk_c12 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_803,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_804,negated_conjecture,
( ( iPr_def_22 = sk_c12 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_805,negated_conjecture,
( ( iPr_def_23 = sk_c11 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_806,negated_conjecture,
( ( iPr_def_24 = sk_c10 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_807,negated_conjecture,
( ( iPr_def_25 = sk_c12 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_808,negated_conjecture,
( ( iPr_def_26 = sk_c11 )
| ( iPr_def_15 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_809,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_810,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_812,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_815,plain,
sk_c12 = sk_c12,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_818,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c12)) != inverse(sk_c12) )
| ( multiply(sk_c12,inverse(sk_c12)) != sk_c12 )
| ( multiply(sk_c12,inverse(sk_c12)) != inverse(sk_c12) )
| ( multiply(inverse(sk_c12),sk_c11) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_746]) ).
tcf(c_1193,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_752,c_754]) ).
tcf(c_1227,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_757,c_754]) ).
tcf(c_1240,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_26,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_758,c_727]) ).
tcf(c_1241,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_758,c_755]) ).
tcf(c_1305,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_753,c_734]) ).
tcf(c_1311,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_758,c_736]) ).
tcf(c_1312,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_755,c_736]) ).
tcf(c_1317,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_757,c_738]) ).
tcf(c_1318,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_754,c_738]) ).
tcf(c_1319,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_752,c_738]) ).
tcf(c_1338,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(sk_c12,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_764,c_740]) ).
tcf(c_1362,plain,
multiply(iPr_def_25,sk_c4) = identity,
inference(superposition,[status(thm)],[c_737,c_114]) ).
tcf(c_1363,plain,
multiply(iPr_def_23,sk_c5) = identity,
inference(superposition,[status(thm)],[c_735,c_114]) ).
tcf(c_1364,plain,
multiply(iPr_def_21,sk_c6) = identity,
inference(superposition,[status(thm)],[c_733,c_114]) ).
tcf(c_1367,plain,
multiply(iPr_def_29,sk_c1) = identity,
inference(superposition,[status(thm)],[c_741,c_114]) ).
tcf(c_1368,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_729,c_114]) ).
tcf(c_1373,plain,
( ( sk_c11 = iPr_def_23 )
| ( multiply(sk_c12,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_765,c_740]) ).
tcf(c_1391,plain,
( ( sk_c11 = iPr_def_26 )
| ( multiply(sk_c12,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_768,c_740]) ).
tcf(c_1441,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_772,c_742]) ).
tcf(c_1468,plain,
( ( sk_c11 = iPr_def_28 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_773,c_734]) ).
tcf(c_1486,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_774,c_742]) ).
tcf(c_1506,plain,
! [X0: $i] :
( ( iPr_def_15 = sk_c10 )
| ( iPr_def_15 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1509,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1510,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != sk_c10 )
| ( X0 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1509]) ).
tcf(c_1511,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_1520,plain,
( ( sk_c11 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_775,c_742]) ).
tcf(c_1542,plain,
( ( sk_c10 = multiply(identity,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1510]) ).
tcf(c_1543,plain,
multiply(identity,sk_c10) = sk_c10,
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1545,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c10 )
| ( sk_c10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1547,plain,
( ( sk_c10 = iPr_def_24 )
| ( iPr_def_24 != sk_c10 )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1510]) ).
tcf(c_1559,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_777,c_742]) ).
tcf(c_1579,plain,
( ( iPr_def_15 = sk_c10 )
| ( iPr_def_15 != iPr_def_24 )
| ( sk_c10 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1506]) ).
tcf(c_1583,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( X0 != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1509]) ).
tcf(c_1584,plain,
( ( sk_c10 = sk_c12 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( sk_c12 != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1583]) ).
tcf(c_1591,plain,
( ( sk_c11 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_28) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_778,c_742]) ).
tcf(c_1615,plain,
! [X0: $i] :
( ( X0 = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( X0 != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1545]) ).
tcf(c_1619,plain,
( ( sk_c10 = iPr_def_15 )
| ( iPr_def_15 != sk_c10 )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1510]) ).
tcf(c_1645,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,sk_c10) )
| ( X1 != X0 )
| ( multiply(identity,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1704,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_782,c_772]) ).
tcf(c_1705,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_782,c_742]) ).
tcf(c_1709,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(iPr_def_29,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_782,c_727]) ).
tcf(c_1741,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_1744,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1746,plain,
( ( iPr_def_15 = sk_c10 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1506]) ).
tcf(c_1748,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1509]) ).
tcf(c_1760,plain,
( ( sk_c11 = iPr_def_29 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_783,c_734]) ).
tcf(c_1791,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_784,c_774]) ).
tcf(c_1793,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_784,c_742]) ).
tcf(c_1797,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_29,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_784,c_727]) ).
tcf(c_1823,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c10) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1824,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(identity,sk_c10) )
| ( X2 != multiply(X0,X1) )
| ( multiply(identity,sk_c10) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_1645]) ).
tcf(c_1843,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_785,c_775]) ).
tcf(c_1846,plain,
( ( sk_c11 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_785,c_742]) ).
tcf(c_1880,plain,
multiply(identity,identity) = identity,
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1885,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_1905,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_787,c_777]) ).
tcf(c_1909,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_787,c_742]) ).
tcf(c_1913,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(iPr_def_29,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_787,c_727]) ).
tcf(c_1935,plain,
! [X0: $i,X1: $i] :
( ( sk_c12 = inverse(X0) )
| ( sk_c12 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1744]) ).
tcf(c_1954,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_788,c_778]) ).
tcf(c_1959,plain,
( ( sk_c11 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_788,c_742]) ).
tcf(c_1963,plain,
( ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_29,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_788,c_727]) ).
tcf(c_1986,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_24 != X0 )
| ( iPr_def_15 != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_1987,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_24 != sk_c12 )
| ( iPr_def_15 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_1986]) ).
tcf(c_1992,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_2022,plain,
iPr_def_24 = iPr_def_24,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_2150,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_30) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_792,c_739]) ).
tcf(c_2188,plain,
! [X0: $i] :
( ( multiply(identity,sk_c10) = X0 )
| ( X0 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1823]) ).
tcf(c_2202,plain,
( ( sk_c12 = iPr_def_30 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_793,c_734]) ).
tcf(c_2215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(identity,sk_c10) = X2 )
| ( X2 != multiply(X0,X1) )
| ( multiply(identity,sk_c10) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_1823]) ).
tcf(c_2217,plain,
( ( multiply(identity,sk_c10) = sk_c12 )
| ( sk_c12 != multiply(sk_c12,sk_c12) )
| ( multiply(identity,sk_c10) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_2215]) ).
tcf(c_2223,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_2233,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_30) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_794,c_739]) ).
tcf(c_2277,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_2305,plain,
( ( sk_c12 = iPr_def_30 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_795,c_742]) ).
tcf(c_2306,plain,
( ( sk_c12 = iPr_def_30 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_795,c_736]) ).
tcf(c_2393,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(sk_c2,iPr_def_30) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_797,c_739]) ).
tcf(c_2442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_2454,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c4) )
| ( inverse(X0) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_1941]) ).
tcf(c_2456,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_29 )
| ( iPr_def_29 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1941]) ).
tcf(c_2457,plain,
( ( inverse(sk_c12) = iPr_def_29 )
| ( iPr_def_29 != inverse(sk_c1) )
| ( inverse(sk_c12) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_2456]) ).
tcf(c_2475,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_798,c_795]) ).
tcf(c_2486,plain,
( ( sk_c12 = iPr_def_30 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_798,c_742]) ).
tcf(c_2680,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_2681,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_2779,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_24 = X0 )
| ( iPr_def_24 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_2780,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != multiply(sk_c5,sk_c11) )
| ( X0 != multiply(sk_c5,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_1992]) ).
tcf(c_2801,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c10 = iPr_def_15 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_806,c_805]) ).
tcf(c_2804,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c10 = iPr_def_15 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_806,c_802]) ).
tcf(c_2849,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c10 = iPr_def_15 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_807,c_806]) ).
tcf(c_2908,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c10 = iPr_def_15 )
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_808,c_806]) ).
tcf(c_2976,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_808,c_743]) ).
tcf(c_2978,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_806,c_743]) ).
tcf(c_3105,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_24 )
| ( inverse(sk_c5) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_736,c_745]) ).
tcf(c_3107,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_30 )
| ( inverse(sk_c1) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_742,c_745]) ).
tcf(c_3108,plain,
( ~ iPr_def_13
| ( sk_c11 != sk_c10 )
| ( inverse(identity) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_113,c_745]) ).
tcf(c_3109,plain,
( ~ iPr_def_13
| ( sk_c10 != identity )
| ( inverse(inverse(sk_c11)) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_114,c_745]) ).
tcf(c_3127,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_30 )
| ( sk_c11 != iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_3107,c_741]) ).
tcf(c_3134,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_24 )
| ( sk_c11 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3105,c_735]) ).
tcf(c_3241,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c11,sk_c12) )
| ( X0 != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_2277]) ).
tcf(c_3242,plain,
( ( sk_c12 = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c11,sk_c12) )
| ( sk_c12 != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_3241]) ).
tcf(c_3303,plain,
( ~ iPr_def_11
| ( sk_c12 != iPr_def_30 )
| ( inverse(sk_c1) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_742,c_747]) ).
tcf(c_3304,plain,
( ~ iPr_def_11
| ( sk_c11 != sk_c12 )
| ( inverse(identity) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_113,c_747]) ).
tcf(c_3305,plain,
( ~ iPr_def_11
| ( sk_c12 != identity )
| ( inverse(inverse(sk_c11)) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_114,c_747]) ).
tcf(c_3323,plain,
( ~ iPr_def_11
| ( sk_c12 != iPr_def_30 )
| ( sk_c11 != iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_3303,c_741]) ).
tcf(c_3417,plain,
( ( multiply(identity,sk_c10) = iPr_def_15 )
| ( iPr_def_15 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_2188]) ).
tcf(c_3510,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_26 )
| ( inverse(sk_c4) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_738,c_748]) ).
tcf(c_3511,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_27 )
| ( inverse(sk_c2) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_739,c_748]) ).
tcf(c_3512,plain,
( ~ iPr_def_10
| ( sk_c11 != sk_c12 )
| ( inverse(identity) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_113,c_748]) ).
tcf(c_3523,plain,
( ~ iPr_def_10
| ( sk_c12 != iPr_def_17 )
| ( sk_c11 != iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_3511,c_729]) ).
tcf(c_3527,plain,
( ~ iPr_def_10
| ( sk_c12 != iPr_def_25 )
| ( sk_c11 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_3510,c_737]) ).
tcf(c_3612,plain,
( ~ iPr_def_14
| ( inverse(identity) != sk_c12 )
| ( multiply(sk_c12,sk_c12) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_113,c_744]) ).
tcf(c_3613,plain,
( ~ iPr_def_14
| ( inverse(inverse(sk_c12)) != sk_c12 )
| ( multiply(sk_c12,identity) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_114,c_744]) ).
tcf(c_3670,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_2223]) ).
tcf(c_3671,plain,
( ( identity = sk_c12 )
| ( identity != identity )
| ( sk_c12 != identity ) ),
inference(instantiation,[status(thm)],[c_3670]) ).
tcf(c_3703,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != inverse(identity) )
| ( inverse(inverse(identity)) != inverse(X0) )
| ( multiply(inverse(X0),sk_c11) != sk_c12 )
| ( multiply(X0,inverse(X0)) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_113,c_746]) ).
tcf(c_3795,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_2442]) ).
tcf(c_4023,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1193,c_794]) ).
tcf(c_4024,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1193,c_792]) ).
tcf(c_4026,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1193,c_739]) ).
tcf(c_4113,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c11,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_736,c_115]) ).
tcf(c_4119,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c12,X0)) = multiply(iPr_def_27,X0),
inference(superposition,[status(thm)],[c_739,c_115]) ).
tcf(c_4121,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_114,c_115]) ).
tcf(c_4123,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1362,c_115]) ).
tcf(c_4124,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1363,c_115]) ).
tcf(c_4125,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1364,c_115]) ).
tcf(c_4128,plain,
! [X0: $i] : multiply(iPr_def_29,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1367,c_115]) ).
tcf(c_4129,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1368,c_115]) ).
tcf(c_4136,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4129,c_113]) ).
tcf(c_4137,plain,
! [X0: $i] : multiply(iPr_def_29,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4128,c_113]) ).
tcf(c_4140,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4125,c_113]) ).
tcf(c_4141,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4124,c_113]) ).
tcf(c_4142,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4123,c_113]) ).
tcf(c_4227,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1227,c_797]) ).
tcf(c_4228,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1227,c_794]) ).
tcf(c_4231,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1227,c_739]) ).
tcf(c_4369,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_729,c_114]) ).
tcf(c_4393,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1241,c_739]) ).
tcf(c_4527,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c4) )
| ( X0 != sk_c4 ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_4528,plain,
( ( inverse(sk_c12) = inverse(sk_c4) )
| ( sk_c12 != sk_c4 ) ),
inference(instantiation,[status(thm)],[c_4527]) ).
tcf(c_4529,plain,
( ( inverse(sk_c4) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c4) )
| ( inverse(sk_c4) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_2454]) ).
tcf(c_4530,plain,
inverse(sk_c4) = inverse(sk_c4),
inference(instantiation,[status(thm)],[c_1741]) ).
tcf(c_4541,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c1) )
| ( X0 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_4542,plain,
( ( inverse(sk_c12) = inverse(sk_c1) )
| ( sk_c12 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_4541]) ).
tcf(c_4543,plain,
( ( inverse(sk_c1) = iPr_def_29 )
| ( iPr_def_29 != inverse(sk_c1) )
| ( inverse(sk_c1) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_2456]) ).
tcf(c_4544,plain,
inverse(sk_c1) = inverse(sk_c1),
inference(instantiation,[status(thm)],[c_1741]) ).
tcf(c_4638,plain,
( ( multiply(sk_c5,sk_c11) = iPr_def_24 )
| ( iPr_def_24 != multiply(sk_c5,sk_c11) )
| ( multiply(sk_c5,sk_c11) != multiply(sk_c5,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_2780]) ).
tcf(c_4639,plain,
multiply(sk_c5,sk_c11) = multiply(sk_c5,sk_c11),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_4640,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c5,sk_c11) )
| ( X1 != X0 )
| ( multiply(sk_c5,sk_c11) != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_4928,plain,
! [X0: $i] :
( ( iPr_def_15 = X0 )
| ( iPr_def_15 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_2681]) ).
tcf(c_4929,plain,
( ( iPr_def_15 = sk_c12 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c12 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_4928]) ).
tcf(c_4933,plain,
! [X0: $i] :
( ( iPr_def_24 = X0 )
| ( iPr_def_24 != multiply(sk_c5,sk_c11) )
| ( X0 != multiply(sk_c5,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_2779]) ).
tcf(c_4934,plain,
( ( iPr_def_24 = sk_c12 )
| ( iPr_def_24 != multiply(sk_c5,sk_c11) )
| ( sk_c12 != multiply(sk_c5,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_4933]) ).
tcf(c_4937,plain,
! [X0: $i] :
( ( iPr_def_24 = X0 )
| ( iPr_def_24 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_2779]) ).
tcf(c_4957,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1791,c_1704]) ).
tcf(c_5212,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1905,c_1791]) ).
tcf(c_5327,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1954,c_1843]) ).
tcf(c_5490,plain,
! [X0: $i] :
( ( multiply(identity,sk_c10) = X0 )
| ( X0 != iPr_def_15 )
| ( multiply(identity,sk_c10) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1823]) ).
tcf(c_5841,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_17 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_2475,c_1241]) ).
tcf(c_5849,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_30,sk_c3) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_2475,c_740]) ).
tcf(c_5850,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c2,iPr_def_30) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2475,c_739]) ).
tcf(c_5979,plain,
multiply(iPr_def_17,iPr_def_27) = sk_c12,
inference(superposition,[status(thm)],[c_739,c_4136]) ).
tcf(c_5982,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_27,X0)) = multiply(sk_c12,X0),
inference(superposition,[status(thm)],[c_5979,c_115]) ).
tcf(c_5992,plain,
multiply(iPr_def_29,iPr_def_30) = sk_c11,
inference(superposition,[status(thm)],[c_742,c_4137]) ).
tcf(c_6380,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c9,
inference(superposition,[status(thm)],[c_734,c_4140]) ).
tcf(c_6385,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c11,
inference(superposition,[status(thm)],[c_736,c_4141]) ).
tcf(c_6390,plain,
multiply(iPr_def_25,iPr_def_26) = sk_c12,
inference(superposition,[status(thm)],[c_738,c_4142]) ).
tcf(c_6395,plain,
( ( multiply(sk_c11,sk_c12) = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c11,sk_c12) )
| ( multiply(sk_c11,sk_c12) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_3241]) ).
tcf(c_6396,plain,
multiply(sk_c11,sk_c12) = multiply(sk_c11,sk_c12),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_6397,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c11,sk_c12) )
| ( X1 != X0 )
| ( multiply(sk_c11,sk_c12) != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_6399,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c11,sk_c12) )
| ( multiply(X0,X1) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_3241]) ).
tcf(c_6400,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c11,sk_c12) )
| ( X1 != sk_c12 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_6401,plain,
( ( multiply(sk_c12,sk_c12) = iPr_def_15 )
| ( iPr_def_15 != multiply(sk_c11,sk_c12) )
| ( multiply(sk_c12,sk_c12) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_6399]) ).
tcf(c_6402,plain,
( ( multiply(sk_c12,sk_c12) = multiply(sk_c11,sk_c12) )
| ( sk_c12 != sk_c12 )
| ( sk_c12 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_6400]) ).
tcf(c_6701,plain,
! [X0: $i] :
( ( identity = multiply(inverse(X0),X0) )
| ( identity != identity )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_3670]) ).
tcf(c_6702,plain,
( ( identity = multiply(inverse(sk_c12),sk_c12) )
| ( identity != identity )
| ( multiply(inverse(sk_c12),sk_c12) != identity ) ),
inference(instantiation,[status(thm)],[c_6701]) ).
tcf(c_6705,plain,
( ( identity = multiply(identity,identity) )
| ( identity != identity )
| ( multiply(identity,identity) != identity ) ),
inference(instantiation,[status(thm)],[c_3670]) ).
tcf(c_7315,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1311,c_4141]) ).
tcf(c_7316,plain,
( ( sk_c12 = iPr_def_17 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_7315,c_6385]) ).
tcf(c_7327,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1312,c_4141]) ).
tcf(c_7328,plain,
( ( sk_c12 = iPr_def_17 )
| ( sk_c11 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_7327,c_6385]) ).
tcf(c_7338,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_30) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_5327,c_5992]) ).
tcf(c_7373,plain,
! [X0: $i] :
( ( sk_c12 = iPr_def_17 )
| ( multiply(sk_c4,multiply(iPr_def_25,X0)) = multiply(iPr_def_26,X0) ) ),
inference(superposition,[status(thm)],[c_1317,c_115]) ).
tcf(c_7374,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1317,c_4142]) ).
tcf(c_7375,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c12 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7374,c_6390]) ).
tcf(c_7386,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1318,c_4142]) ).
tcf(c_7387,plain,
( ( sk_c12 = iPr_def_22 )
| ( sk_c12 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7386,c_6390]) ).
tcf(c_7398,plain,
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1319,c_4142]) ).
tcf(c_7399,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c12 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7398,c_6390]) ).
tcf(c_7493,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1241,c_1338]) ).
tcf(c_7495,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1227,c_1338]) ).
tcf(c_7496,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1193,c_1338]) ).
tcf(c_7521,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_28 )
| ( sk_c12 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_7496,c_5979]) ).
tcf(c_7525,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_28 )
| ( sk_c12 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_7495,c_5979]) ).
tcf(c_7533,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_28 )
| ( sk_c12 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_7493,c_5979]) ).
tcf(c_8004,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_23 )
| ( multiply(iPr_def_30,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_2475,c_1373]) ).
tcf(c_8464,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1441,c_4137]) ).
tcf(c_8465,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c11 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_8464,c_5992]) ).
tcf(c_9046,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1486,c_4137]) ).
tcf(c_9047,plain,
( ( sk_c12 = iPr_def_22 )
| ( sk_c11 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_9046,c_5992]) ).
tcf(c_9219,plain,
( ( sk_c11 = iPr_def_23 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1520,c_4137]) ).
tcf(c_9220,plain,
( ( sk_c11 = iPr_def_28 )
| ( sk_c11 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_9219,c_5992]) ).
tcf(c_9414,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1559,c_4137]) ).
tcf(c_9415,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c11 = iPr_def_28 ) ),
inference(light_normalisation,[status(thm)],[c_9414,c_5992]) ).
tcf(c_9781,plain,
( ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_1591,c_4137]) ).
tcf(c_9782,plain,
( ( sk_c11 = iPr_def_28 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_9781,c_5992]) ).
tcf(c_10071,plain,
! [X0: $i] :
( ( inverse(sk_c4) = X0 )
| ( X0 != iPr_def_25 )
| ( inverse(sk_c4) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_1744]) ).
tcf(c_10189,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_29 )
| ( inverse(sk_c1) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_1744]) ).
tcf(c_10351,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_792,c_1709]) ).
tcf(c_10358,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c11 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_10351,c_5992]) ).
tcf(c_10698,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_794,c_1797]) ).
tcf(c_10706,plain,
( ( sk_c12 = iPr_def_22 )
| ( sk_c11 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_10698,c_5992]) ).
tcf(c_10805,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_10358,c_782]) ).
tcf(c_10968,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10706,c_784]) ).
tcf(c_10973,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10706,c_774]) ).
tcf(c_11656,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_10968,c_10805]) ).
tcf(c_11885,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( multiply(iPr_def_22,sk_c3) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_10973,c_740]) ).
tcf(c_12045,plain,
( ( sk_c11 = iPr_def_23 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1846,c_4137]) ).
tcf(c_12046,plain,
( ( sk_c11 = iPr_def_29 )
| ( sk_c11 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_12045,c_5992]) ).
tcf(c_12272,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_1909,c_4137]) ).
tcf(c_12273,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c11 = iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_12272,c_5992]) ).
tcf(c_12362,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_797,c_1913]) ).
tcf(c_12371,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c11 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_12362,c_5992]) ).
tcf(c_12536,plain,
( ( iPr_def_15 = iPr_def_29 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_12371,c_787]) ).
tcf(c_12715,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_12536,c_10968]) ).
tcf(c_13114,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c4 )
| ( sk_c4 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_13119,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_13216,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_15,iPr_def_30) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_11656,c_5992]) ).
tcf(c_13543,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_10
| ( sk_c11 != iPr_def_15 )
| ( inverse(iPr_def_29) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_1963,c_748]) ).
tcf(c_13844,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_15,iPr_def_30) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_12715,c_5992]) ).
tcf(c_14180,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_2150,c_4136]) ).
tcf(c_14181,plain,
( ( sk_c12 = iPr_def_30 )
| ( sk_c12 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_14180,c_5979]) ).
tcf(c_14434,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_807,c_743]) ).
tcf(c_14436,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_805,c_743]) ).
tcf(c_14745,plain,
( ( sk_c12 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_2233,c_4136]) ).
tcf(c_14746,plain,
( ( sk_c12 = iPr_def_30 )
| ( sk_c12 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_14745,c_5979]) ).
tcf(c_14854,plain,
( ( sk_c12 = iPr_def_30 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_2305,c_4137]) ).
tcf(c_14855,plain,
( ( sk_c12 = iPr_def_30 )
| ( sk_c11 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_14854,c_5992]) ).
tcf(c_15063,plain,
( ( sk_c12 = iPr_def_25 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_2393,c_4136]) ).
tcf(c_15064,plain,
( ( sk_c12 = iPr_def_30 )
| ( sk_c12 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_15063,c_5979]) ).
tcf(c_15163,plain,
( ( sk_c12 = iPr_def_30 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_2486,c_4137]) ).
tcf(c_15164,plain,
( ( sk_c12 = iPr_def_30 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_15163,c_5992]) ).
tcf(c_18621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(sk_c5,sk_c11) )
| ( X2 != multiply(X0,X1) )
| ( multiply(sk_c5,sk_c11) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_4640]) ).
tcf(c_18623,plain,
( ( sk_c12 = multiply(sk_c5,sk_c11) )
| ( sk_c12 != multiply(sk_c12,sk_c12) )
| ( multiply(sk_c5,sk_c11) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_18621]) ).
tcf(c_18628,plain,
multiply(sk_c2,iPr_def_28) = multiply(iPr_def_27,sk_c3),
inference(superposition,[status(thm)],[c_740,c_4119]) ).
tcf(c_19424,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_4369,c_115]) ).
tcf(c_19431,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_19424,c_113]) ).
tcf(c_21804,plain,
( ( sk_c11 = iPr_def_23 )
| ( sk_c10 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_2801,c_806,c_1511,c_1547,c_1579,c_1619,c_2801]) ).
tcf(c_21805,plain,
( ( sk_c10 = iPr_def_15 )
| ( sk_c11 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_21804]) ).
tcf(c_21866,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c10 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_2804,c_806,c_1511,c_1547,c_1579,c_1619,c_2804]) ).
tcf(c_21867,plain,
( ( sk_c10 = iPr_def_15 )
| ( sk_c12 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_21866]) ).
tcf(c_21904,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c10 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_2849,c_806,c_1511,c_1547,c_1579,c_1619,c_2849]) ).
tcf(c_21905,plain,
( ( sk_c10 = iPr_def_15 )
| ( sk_c12 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_21904]) ).
tcf(c_22236,plain,
( ( multiply(identity,sk_c10) = multiply(sk_c11,sk_c12) )
| ( multiply(identity,sk_c10) != iPr_def_15 )
| ( multiply(sk_c11,sk_c12) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_5490]) ).
tcf(c_22246,plain,
( ( sk_c11 = iPr_def_26 )
| ( sk_c10 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_2908,c_806,c_1511,c_1547,c_1579,c_1619,c_2908]) ).
tcf(c_22247,plain,
( ( sk_c10 = iPr_def_15 )
| ( sk_c11 = iPr_def_26 ) ),
inference(renaming,[status(thm)],[c_22246]) ).
tcf(c_23817,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_4024,c_4023]) ).
tcf(c_24812,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(sk_c11,sk_c12) )
| ( X2 != multiply(X0,X1) )
| ( multiply(sk_c11,sk_c12) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_6397]) ).
tcf(c_24813,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c11,sk_c12) = multiply(X0,X1) )
| ( sk_c12 != X1 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_24814,plain,
( ( sk_c12 = multiply(sk_c11,sk_c12) )
| ( sk_c12 != multiply(sk_c12,sk_c12) )
| ( multiply(sk_c11,sk_c12) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_24812]) ).
tcf(c_24815,plain,
( ( multiply(sk_c11,sk_c12) = multiply(sk_c12,sk_c12) )
| ( sk_c12 != sk_c12 )
| ( sk_c11 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_24813]) ).
tcf(c_24817,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c11,sk_c12) )
| ( X0 != iPr_def_15 )
| ( multiply(sk_c11,sk_c12) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_6397]) ).
tcf(c_24818,plain,
( ( sk_c12 = multiply(sk_c11,sk_c12) )
| ( sk_c12 != iPr_def_15 )
| ( multiply(sk_c11,sk_c12) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_24817]) ).
tcf(c_24927,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_4228,c_4227]) ).
tcf(c_25008,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_4121,c_113]) ).
tcf(c_25037,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_113,c_25008]) ).
tcf(c_25038,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_114,c_25008]) ).
tcf(c_25253,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_4142,c_25008]) ).
tcf(c_25254,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4141,c_25008]) ).
tcf(c_25255,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4140,c_25008]) ).
tcf(c_25258,plain,
! [X0: $i] : multiply(inverse(iPr_def_29),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_4137,c_25008]) ).
tcf(c_25259,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_4136,c_25008]) ).
tcf(c_25321,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_25008,c_25008]) ).
tcf(c_25836,plain,
multiply(identity,sk_c11) = sk_c11,
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_25839,plain,
sk_c11 = sk_c11,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_26201,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,identity) )
| ( X1 != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_26203,plain,
( ( multiply(sk_c12,sk_c12) = multiply(identity,identity) )
| ( sk_c12 != identity ) ),
inference(instantiation,[status(thm)],[c_26201]) ).
tcf(c_27433,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_25038,c_25321]) ).
tcf(c_27467,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_27433,c_25037]) ).
tcf(c_29189,plain,
multiply(sk_c4,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_25253,c_114]) ).
tcf(c_29193,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_25253,c_25008]) ).
tcf(c_29194,plain,
multiply(sk_c4,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_25253,c_27433]) ).
tcf(c_29446,plain,
inverse(iPr_def_25) = sk_c4,
inference(demodulation,[status(thm)],[c_29194,c_27433]) ).
tcf(c_30242,plain,
multiply(sk_c5,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_25254,c_114]) ).
tcf(c_30246,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_25254,c_25008]) ).
tcf(c_30247,plain,
multiply(sk_c5,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_25254,c_27433]) ).
tcf(c_30268,plain,
( ( identity = iPr_def_24 )
| ( sk_c12 = iPr_def_30 ) ),
inference(demodulation,[status(thm)],[c_2306,c_30242]) ).
tcf(c_30394,plain,
inverse(iPr_def_23) = sk_c5,
inference(demodulation,[status(thm)],[c_30247,c_27433]) ).
tcf(c_30712,plain,
multiply(iPr_def_17,iPr_def_27) = sk_c12,
inference(superposition,[status(thm)],[c_739,c_19431]) ).
tcf(c_31848,plain,
multiply(sk_c6,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_25255,c_114]) ).
tcf(c_31852,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_25255,c_25008]) ).
tcf(c_31871,plain,
( ( identity = iPr_def_22 )
| ( sk_c12 = iPr_def_30 ) ),
inference(demodulation,[status(thm)],[c_2202,c_31848]) ).
tcf(c_31872,plain,
( ( identity = iPr_def_22 )
| ( sk_c11 = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_1760,c_31848]) ).
tcf(c_31873,plain,
( ( identity = iPr_def_22 )
| ( sk_c11 = iPr_def_28 ) ),
inference(demodulation,[status(thm)],[c_1468,c_31848]) ).
tcf(c_31874,plain,
( ( identity = iPr_def_22 )
| ( sk_c12 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_1305,c_31848]) ).
tcf(c_31929,plain,
multiply(sk_c6,sk_c9) = iPr_def_22,
inference(superposition,[status(thm)],[c_6380,c_31852]) ).
tcf(c_32251,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_30,sk_c3) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_31871,c_740]) ).
tcf(c_32255,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c11,iPr_def_30) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_31871,c_727]) ).
tcf(c_32378,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c10) )
| ( X0 != multiply(sk_c11,sk_c12) )
| ( multiply(identity,sk_c10) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_1824]) ).
tcf(c_32379,plain,
( ( sk_c12 = multiply(identity,sk_c10) )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( multiply(identity,sk_c10) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_32378]) ).
tcf(c_32511,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_31872,c_742]) ).
tcf(c_32867,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| ( sk_c12 = iPr_def_25 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_14434,c_743,c_1746,c_2680,c_3323,c_12273,c_15064,c_21905]) ).
tcf(c_32868,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c12 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_32867]) ).
tcf(c_32884,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| ( sk_c11 = iPr_def_23 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_14436,c_743,c_1746,c_2680,c_3323,c_12046,c_14855,c_21805]) ).
tcf(c_32885,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c11 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_32884]) ).
tcf(c_32928,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_31873,c_31872]) ).
tcf(c_33367,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_31874,c_739]) ).
tcf(c_35059,plain,
( ( inverse(sk_c4) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_25 )
| ( inverse(sk_c4) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_10071]) ).
tcf(c_39548,plain,
multiply(sk_c1,iPr_def_29) = identity,
inference(superposition,[status(thm)],[c_25258,c_114]) ).
tcf(c_39552,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_29,X0)) = X0,
inference(superposition,[status(thm)],[c_25258,c_25008]) ).
tcf(c_39553,plain,
multiply(sk_c1,identity) = inverse(iPr_def_29),
inference(superposition,[status(thm)],[c_25258,c_27433]) ).
tcf(c_39609,plain,
( ( identity = iPr_def_30 )
| ( sk_c11 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1959,c_39548]) ).
tcf(c_39610,plain,
( ( identity = iPr_def_30 )
| ( sk_c12 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1909,c_39548]) ).
tcf(c_39611,plain,
( ( identity = iPr_def_30 )
| ( sk_c11 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1846,c_39548]) ).
tcf(c_39612,plain,
( ( identity = iPr_def_30 )
| ( sk_c12 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1793,c_39548]) ).
tcf(c_39613,plain,
( ( identity = iPr_def_30 )
| ( sk_c12 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1705,c_39548]) ).
tcf(c_41041,plain,
inverse(iPr_def_29) = sk_c1,
inference(demodulation,[status(thm)],[c_39553,c_27433]) ).
tcf(c_41052,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_15) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_12715,c_41041]) ).
tcf(c_41053,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_15) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_11656,c_41041]) ).
tcf(c_41054,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_28) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_5327,c_41041]) ).
tcf(c_41056,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_28) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_5212,c_41041]) ).
tcf(c_41057,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_28) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_4957,c_41041]) ).
tcf(c_41192,plain,
multiply(sk_c1,sk_c11) = iPr_def_30,
inference(superposition,[status(thm)],[c_5992,c_39552]) ).
tcf(c_41460,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_39611,c_39609]) ).
tcf(c_41816,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( identity = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_39612,c_39610]) ).
tcf(c_42197,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_39613,c_39612]) ).
tcf(c_42554,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_30) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_41460,c_27467]) ).
tcf(c_42556,plain,
! [X0: $i] :
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_30,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_41460,c_113]) ).
tcf(c_42743,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_30) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_41816,c_27467]) ).
tcf(c_42783,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_30) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_42197,c_27467]) ).
tcf(c_43772,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_25259,c_114]) ).
tcf(c_43777,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_25259,c_27433]) ).
tcf(c_43798,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_4393,c_43772]) ).
tcf(c_43800,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( identity = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_4231,c_43772]) ).
tcf(c_43801,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_4026,c_43772]) ).
tcf(c_43880,plain,
( ~ iPr_def_13
| ( sk_c11 != identity )
| ( sk_c11 != sk_c10 ) ),
inference(light_normalisation,[status(thm)],[c_3108,c_27467]) ).
tcf(c_43898,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_13
| ( sk_c11 != iPr_def_15 )
| ( sk_c11 != identity ) ),
inference(superposition,[status(thm)],[c_808,c_43880]) ).
tcf(c_43899,plain,
( ( sk_c12 = iPr_def_25 )
| ~ iPr_def_13
| ( sk_c11 != iPr_def_15 )
| ( sk_c11 != identity ) ),
inference(superposition,[status(thm)],[c_807,c_43880]) ).
tcf(c_43902,plain,
( ( sk_c12 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c11 != iPr_def_15 )
| ( sk_c11 != identity ) ),
inference(superposition,[status(thm)],[c_804,c_43880]) ).
tcf(c_43904,plain,
( ( sk_c12 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c11 != iPr_def_15 )
| ( sk_c11 != identity ) ),
inference(superposition,[status(thm)],[c_802,c_43880]) ).
tcf(c_44051,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_752,c_754]) ).
tcf(c_44091,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_757,c_754]) ).
tcf(c_44104,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_755,c_758]) ).
tcf(c_44554,plain,
( ( sk_c11 = iPr_def_26 )
| ( multiply(sk_c12,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_768,c_740]) ).
tcf(c_44614,plain,
multiply(iPr_def_29,sk_c1) = identity,
inference(superposition,[status(thm)],[c_741,c_114]) ).
tcf(c_44704,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(iPr_def_29,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_782,c_727]) ).
tcf(c_44823,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_785,c_775]) ).
tcf(c_44923,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_788,c_778]) ).
tcf(c_45415,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_798,c_795]) ).
tcf(c_45574,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c3 = iPr_def_27 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_802,c_766]) ).
tcf(c_45632,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c3 = iPr_def_27 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_804,c_766]) ).
tcf(c_45754,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c3 = iPr_def_27 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_807,c_766]) ).
tcf(c_45821,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_807,c_743]) ).
tcf(c_45823,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_805,c_743]) ).
tcf(c_45923,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_24 )
| ( inverse(sk_c5) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_736,c_745]) ).
tcf(c_45925,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_30 )
| ( inverse(sk_c1) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_742,c_745]) ).
tcf(c_45926,plain,
( ~ iPr_def_13
| ( sk_c11 != sk_c10 )
| ( inverse(identity) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_113,c_745]) ).
tcf(c_45946,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_30 )
| ( sk_c11 != iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_45925,c_741]) ).
tcf(c_45953,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_24 )
| ( sk_c11 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_45923,c_735]) ).
tcf(c_46028,plain,
( ~ iPr_def_11
| ( sk_c12 != iPr_def_30 )
| ( inverse(sk_c1) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_742,c_747]) ).
tcf(c_46049,plain,
( ~ iPr_def_11
| ( sk_c12 != iPr_def_30 )
| ( sk_c11 != iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_46028,c_741]) ).
tcf(c_46130,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_26 )
| ( inverse(sk_c4) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_738,c_748]) ).
tcf(c_46131,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_27 )
| ( inverse(sk_c2) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_739,c_748]) ).
tcf(c_46132,plain,
( ~ iPr_def_10
| ( sk_c11 != sk_c12 )
| ( inverse(identity) != sk_c12 ) ),
inference(superposition,[status(thm)],[c_113,c_748]) ).
tcf(c_46146,plain,
( ~ iPr_def_10
| ( sk_c12 != iPr_def_17 )
| ( sk_c11 != iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_46131,c_729]) ).
tcf(c_46150,plain,
( ~ iPr_def_10
| ( sk_c12 != iPr_def_25 )
| ( sk_c11 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_46130,c_737]) ).
tcf(c_46293,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_114,c_115]) ).
tcf(c_46393,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| ( sk_c12 = iPr_def_25 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_45821,c_32868]) ).
tcf(c_46394,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c12 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_46393]) ).
tcf(c_46405,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| ( sk_c11 = iPr_def_23 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_45823,c_32885]) ).
tcf(c_46406,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c11 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_46405]) ).
tcf(c_47012,plain,
! [X0: $i] : multiply(iPr_def_29,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_44614,c_115]) ).
tcf(c_47013,plain,
! [X0: $i] : multiply(iPr_def_29,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_47012,c_113]) ).
tcf(c_47493,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_44923,c_44823]) ).
tcf(c_48054,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_792,c_44704]) ).
tcf(c_48382,plain,
multiply(iPr_def_29,iPr_def_30) = sk_c11,
inference(superposition,[status(thm)],[c_742,c_47013]) ).
tcf(c_49411,plain,
( ~ iPr_def_11
| ( sk_c11 != identity )
| ( sk_c11 != sk_c12 ) ),
inference(light_normalisation,[status(thm)],[c_3304,c_27467]) ).
tcf(c_49452,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_11
| ( sk_c12 != iPr_def_29 )
| ( sk_c11 != identity ) ),
inference(superposition,[status(thm)],[c_788,c_49411]) ).
tcf(c_49585,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c11) = sk_c12 )
| ( sk_c12 != X1 )
| ( multiply(inverse(X0),sk_c11) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_49711,plain,
( ~ iPr_def_10
| ( sk_c12 != identity )
| ( sk_c11 != sk_c12 ) ),
inference(light_normalisation,[status(thm)],[c_3512,c_27467]) ).
tcf(c_49755,plain,
( ( sk_c12 = iPr_def_25 )
| ~ iPr_def_10
| ( identity != iPr_def_30 )
| ( sk_c11 != sk_c12 ) ),
inference(superposition,[status(thm)],[c_797,c_49711]) ).
tcf(c_50138,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_2978,c_743,c_1746,c_2680,c_2978]) ).
tcf(c_50377,plain,
( ( iPr_def_27 = iPr_def_30 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_43798,c_41460]) ).
tcf(c_50389,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_27) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_43798,c_27467]) ).
tcf(c_50391,plain,
! [X0: $i] :
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_43798,c_113]) ).
tcf(c_50516,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_43777,c_27433]) ).
tcf(c_50700,plain,
( ( iPr_def_27 = iPr_def_30 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_43800,c_41816]) ).
tcf(c_50714,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_27) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_43800,c_27467]) ).
tcf(c_50716,plain,
! [X0: $i] :
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_43800,c_113]) ).
tcf(c_50792,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_13
| ( sk_c10 != identity )
| ( inverse(inverse(iPr_def_29)) != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_788,c_3109]) ).
tcf(c_50794,plain,
( ( sk_c11 = iPr_def_23 )
| ~ iPr_def_13
| ( sk_c10 != identity )
| ( inverse(inverse(iPr_def_29)) != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_785,c_3109]) ).
tcf(c_50836,plain,
( ( sk_c11 = iPr_def_23 )
| ~ iPr_def_13
| ( sk_c10 != identity ) ),
inference(ground_joinability,[status(thm)],[c_50794,c_741,c_41041]) ).
tcf(c_50844,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_13
| ( sk_c10 != identity ) ),
inference(ground_joinability,[status(thm)],[c_50792,c_741,c_41041]) ).
tcf(c_50938,plain,
( ( sk_c12 = iPr_def_30 )
| ~ iPr_def_11
| ( sk_c12 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_795,c_3305]) ).
tcf(c_50995,plain,
( ( sk_c12 = iPr_def_30 )
| ~ iPr_def_11
| ( sk_c12 != identity ) ),
inference(ground_joinability,[status(thm)],[c_50938,c_735,c_30394]) ).
tcf(c_51375,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_44104,c_44554]) ).
tcf(c_51377,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_44091,c_44554]) ).
tcf(c_51378,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_44051,c_44554]) ).
tcf(c_51399,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_28 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_51378,c_30712]) ).
tcf(c_51403,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_28 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_51377,c_30712]) ).
tcf(c_51411,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_28 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_51375,c_30712]) ).
tcf(c_51451,plain,
( ( iPr_def_27 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_43801,c_42197]) ).
tcf(c_51466,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_27) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_43801,c_27467]) ).
tcf(c_51468,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_43801,c_113]) ).
tcf(c_52019,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_17 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_50377,c_5841]) ).
tcf(c_53147,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != inverse(sk_c4) )
| ( inverse(X0) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_3795]) ).
tcf(c_53148,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != inverse(sk_c4) )
| ( inverse(X0) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_1941]) ).
tcf(c_53149,plain,
( ( inverse(sk_c12) = sk_c12 )
| ( sk_c12 != inverse(sk_c4) )
| ( inverse(sk_c12) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_53148]) ).
tcf(c_53150,plain,
( ( sk_c12 = inverse(sk_c12) )
| ( sk_c12 != inverse(sk_c4) )
| ( inverse(sk_c12) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_53147]) ).
tcf(c_55737,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_31872,c_32255]) ).
tcf(c_55798,plain,
( ( identity = iPr_def_22 )
| ( sk_c11 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_55737,c_5992]) ).
tcf(c_55864,plain,
( ( identity = iPr_def_30 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_32511,c_39548]) ).
tcf(c_55909,plain,
! [X0: $i] :
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_30,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_55864,c_113]) ).
tcf(c_57531,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_55798,c_31873]) ).
tcf(c_57916,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_28 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_57531,c_113]) ).
tcf(c_58251,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_33367,c_43772]) ).
tcf(c_58298,plain,
( ( identity = iPr_def_22 )
| ( inverse(iPr_def_27) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_58251,c_27467]) ).
tcf(c_58789,plain,
( ( iPr_def_24 = iPr_def_15 )
| ( iPr_def_24 != iPr_def_24 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_4937]) ).
tcf(c_58915,plain,
( ( sk_c10 = identity )
| ( identity != sk_c10 )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1510]) ).
tcf(c_59895,plain,
! [X0: $i] :
( ( sk_c12 = inverse(X0) )
| ( sk_c12 != iPr_def_15 )
| ( inverse(X0) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1935]) ).
tcf(c_60331,plain,
( ( inverse(sk_c1) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_29 )
| ( inverse(sk_c1) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_10189]) ).
tcf(c_62113,plain,
( ( identity = sk_c10 )
| ( identity != multiply(identity,sk_c10) )
| ( sk_c10 != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1615]) ).
tcf(c_62559,plain,
! [X0: $i] :
( ( X0 = sk_c4 )
| ( sk_c4 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_13114]) ).
tcf(c_62560,plain,
( ( sk_c12 = sk_c4 )
| ( sk_c4 != iPr_def_15 )
| ( sk_c12 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_62559]) ).
tcf(c_62564,plain,
! [X0: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_13119]) ).
tcf(c_62565,plain,
( ( sk_c12 = sk_c1 )
| ( sk_c1 != iPr_def_15 )
| ( sk_c12 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_62564]) ).
tcf(c_63093,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c10) = multiply(X0,X1) )
| ( multiply(identity,sk_c10) != iPr_def_15 )
| ( multiply(X0,X1) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_5490]) ).
tcf(c_63094,plain,
( ( multiply(identity,sk_c10) = multiply(sk_c12,sk_c12) )
| ( multiply(identity,sk_c10) != iPr_def_15 )
| ( multiply(sk_c12,sk_c12) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_63093]) ).
tcf(c_64434,plain,
! [X0: $i] :
( ( identity = multiply(identity,sk_c10) )
| ( identity != X0 )
| ( multiply(identity,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_1645]) ).
tcf(c_64439,plain,
( ( identity = multiply(identity,sk_c10) )
| ( identity != sk_c12 )
| ( multiply(identity,sk_c10) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_64434]) ).
tcf(c_66008,plain,
( ( sk_c10 = iPr_def_24 )
| ( iPr_def_24 != iPr_def_15 )
| ( sk_c10 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1748]) ).
tcf(c_67451,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c3 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_42556,c_5849]) ).
tcf(c_67936,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_67451,c_768]) ).
tcf(c_67938,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_67451,c_765]) ).
tcf(c_68916,plain,
multiply(inverse(sk_c11),sk_c11) = identity,
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_68922,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c11) = sk_c12 )
| ( sk_c12 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c11) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_49585]) ).
tcf(c_68923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c11) = multiply(X1,X2) )
| ( sk_c11 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_68924,plain,
( ( multiply(inverse(sk_c12),sk_c11) = sk_c12 )
| ( sk_c12 != multiply(sk_c12,sk_c12) )
| ( multiply(inverse(sk_c12),sk_c11) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_68922]) ).
tcf(c_68925,plain,
( ( multiply(inverse(sk_c12),sk_c11) = multiply(sk_c12,sk_c12) )
| ( sk_c11 != sk_c12 )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_68923]) ).
tcf(c_68997,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_67938,c_67936]) ).
tcf(c_70761,plain,
! [X0: $i] :
( ( sk_c11 = sk_c10 )
| ( sk_c10 != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_1545]) ).
tcf(c_70762,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c10 != sk_c12 )
| ( sk_c11 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_70761]) ).
tcf(c_71211,plain,
( ( sk_c12 = inverse(sk_c1) )
| ( sk_c12 != iPr_def_15 )
| ( inverse(sk_c1) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_59895]) ).
tcf(c_72029,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_27) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_68997,c_41054]) ).
tcf(c_73011,plain,
( ( sk_c12 = inverse(sk_c4) )
| ( sk_c12 != iPr_def_15 )
| ( inverse(sk_c4) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_59895]) ).
tcf(c_73768,plain,
( ( identity = iPr_def_22 )
| ( sk_c3 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_55909,c_32251]) ).
tcf(c_74018,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_22 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_73768,c_763]) ).
tcf(c_75029,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_22 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_74018,c_734]) ).
tcf(c_75039,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_75029,c_31848]) ).
tcf(c_77187,plain,
( ( iPr_def_15 = iPr_def_28 )
| ( sk_c3 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_57916,c_11885]) ).
tcf(c_77259,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c11 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_48054,c_48382]) ).
tcf(c_77804,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_15 = iPr_def_28 )
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_77187,c_768]) ).
tcf(c_81795,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_17) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_5841,c_42554]) ).
tcf(c_81801,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c2 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_81795,c_50516]) ).
tcf(c_82671,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_17) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_24927,c_42743]) ).
tcf(c_82680,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c2 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_82671,c_50516]) ).
tcf(c_83027,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_17) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_23817,c_42783]) ).
tcf(c_83035,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c2 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_83027,c_50516]) ).
tcf(c_86980,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c11) = sk_c12 )
| ( sk_c12 != X1 )
| ( multiply(inverse(X0),sk_c11) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_86985,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c11) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c11) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_86986,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c11) = sk_c12 )
| ( sk_c12 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c11) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_86980]) ).
tcf(c_86987,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c11) = multiply(X1,X2) )
| ( sk_c11 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_86988,plain,
! [X0: $i] :
( ( sk_c12 = identity )
| ( identity != X0 )
| ( sk_c12 != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_86991,plain,
! [X0: $i,X1: $i] :
( ( sk_c12 = multiply(inverse(X0),sk_c11) )
| ( sk_c12 != X1 )
| ( multiply(inverse(X0),sk_c11) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c12 = multiply(X0,X1) )
| ( sk_c12 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87003,plain,
( ( sk_c12 = multiply(sk_c12,sk_c12) )
| ( sk_c12 != sk_c12 )
| ( multiply(sk_c12,sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_87002]) ).
tcf(c_87004,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c11) = multiply(X1,sk_c11) )
| ( sk_c11 != sk_c11 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_86987]) ).
tcf(c_87006,plain,
( ( multiply(inverse(sk_c12),sk_c11) = multiply(sk_c12,sk_c11) )
| ( sk_c11 != sk_c11 )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_87004]) ).
tcf(c_87007,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87010,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87016,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87024,plain,
( ( sk_c12 = multiply(inverse(sk_c11),sk_c11) )
| ( sk_c12 != identity )
| ( multiply(inverse(sk_c11),sk_c11) != identity ) ),
inference(instantiation,[status(thm)],[c_86991]) ).
tcf(c_87027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c11) = X2 )
| ( X2 != multiply(X1,sk_c11) )
| ( multiply(inverse(X0),sk_c11) != multiply(X1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_86985]) ).
tcf(c_87029,plain,
( ( multiply(inverse(sk_c12),sk_c11) = sk_c12 )
| ( sk_c12 != multiply(sk_c12,sk_c11) )
| ( multiply(inverse(sk_c12),sk_c11) != multiply(sk_c12,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87027]) ).
tcf(c_87034,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_87035,plain,
( ( sk_c11 = sk_c12 )
| ( sk_c12 != sk_c11 )
| ( sk_c11 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87034]) ).
tcf(c_87048,plain,
! [X0: $i] :
( ( sk_c12 = multiply(identity,X0) )
| ( sk_c12 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_87002]) ).
tcf(c_87049,plain,
( ( sk_c12 = multiply(identity,sk_c12) )
| ( sk_c12 != sk_c12 )
| ( multiply(identity,sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_87048]) ).
tcf(c_87055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c12 = multiply(X0,X1) )
| ( sk_c12 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_87002]) ).
tcf(c_87057,plain,
( ( sk_c12 = multiply(iPr_def_17,iPr_def_27) )
| ( sk_c12 != sk_c12 )
| ( multiply(iPr_def_17,iPr_def_27) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_87002]) ).
tcf(c_87065,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c11) = sk_c12 )
| ( sk_c12 != multiply(inverse(sk_c11),sk_c11) )
| ( multiply(inverse(X0),sk_c11) != multiply(inverse(sk_c11),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_86986]) ).
tcf(c_87066,plain,
( ( multiply(inverse(sk_c12),sk_c11) = sk_c12 )
| ( sk_c12 != multiply(inverse(sk_c11),sk_c11) )
| ( multiply(inverse(sk_c12),sk_c11) != multiply(inverse(sk_c11),sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87065]) ).
tcf(c_87074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(X0,sk_c11) )
| ( X2 != X1 )
| ( multiply(X0,sk_c11) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = multiply(X1,sk_c11) )
| ( X2 != sk_c11 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_87090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87091,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c11) = multiply(inverse(X1),sk_c11) )
| ( sk_c11 != sk_c11 )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_87004]) ).
tcf(c_87102,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87104,plain,
( ( sk_c11 = iPr_def_29 )
| ( iPr_def_29 != sk_c11 )
| ( sk_c11 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87034]) ).
tcf(c_87164,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = X1 )
| ( X1 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_87055]) ).
tcf(c_87169,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_87055]) ).
tcf(c_87170,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X0,X1),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_87174,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_87055]) ).
tcf(c_87184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c12 = multiply(X0,X1) )
| ( sk_c12 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_87056]) ).
tcf(c_87185,plain,
( ( sk_c12 = multiply(sk_c12,sk_c12) )
| ( sk_c12 != multiply(identity,sk_c12) )
| ( multiply(sk_c12,sk_c12) != multiply(identity,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87184]) ).
tcf(c_87186,plain,
! [X0: $i,X1: $i] :
( ( sk_c12 = multiply(X0,X1) )
| ( sk_c12 != multiply(iPr_def_17,iPr_def_27) )
| ( multiply(X0,X1) != multiply(iPr_def_17,iPr_def_27) ) ),
inference(instantiation,[status(thm)],[c_87056]) ).
tcf(c_87187,plain,
( ( sk_c12 = multiply(sk_c12,sk_c12) )
| ( sk_c12 != multiply(iPr_def_17,iPr_def_27) )
| ( multiply(sk_c12,sk_c12) != multiply(iPr_def_17,iPr_def_27) ) ),
inference(instantiation,[status(thm)],[c_87186]) ).
tcf(c_87193,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != iPr_def_28 )
| ( X0 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_87194,plain,
( ( sk_c11 = sk_c12 )
| ( sk_c12 != iPr_def_28 )
| ( sk_c11 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87193]) ).
tcf(c_87217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_87090]) ).
tcf(c_87262,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),X0) )
| ( X2 != X1 )
| ( multiply(inverse(X0),X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = multiply(inverse(X1),X1) )
| ( X2 != X1 )
| ( X0 != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_87267,plain,
( ( multiply(sk_c12,sk_c12) = multiply(inverse(sk_c12),sk_c12) )
| ( sk_c12 != sk_c12 )
| ( sk_c12 != inverse(sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87265]) ).
tcf(c_87277,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,sk_c11) )
| ( X3 != multiply(X1,X2) )
| ( multiply(X0,sk_c11) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_87074]) ).
tcf(c_87379,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,iPr_def_29) = multiply(X1,sk_c11) )
| ( iPr_def_29 != sk_c11 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_87077]) ).
tcf(c_87381,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,sk_c11) = multiply(X1,sk_c11) )
| ( sk_c11 != sk_c11 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_87077]) ).
tcf(c_87402,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c11) )
| ( X0 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87074]) ).
tcf(c_87428,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_28 )
| ( X0 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_87429,plain,
( ( sk_c12 = sk_c11 )
| ( sk_c12 != iPr_def_28 )
| ( sk_c11 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87428]) ).
tcf(c_87430,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_87492,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(iPr_def_17,iPr_def_27) )
| ( X1 != iPr_def_27 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_87493,plain,
( ( multiply(sk_c12,sk_c12) = multiply(iPr_def_17,iPr_def_27) )
| ( sk_c12 != iPr_def_27 )
| ( sk_c12 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_87492]) ).
tcf(c_87570,plain,
! [X0: $i] :
( ( multiply(identity,sk_c11) = X0 )
| ( X0 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87164]) ).
tcf(c_87571,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,sk_c11) )
| ( X1 != X0 )
| ( multiply(identity,sk_c11) != X0 ) ),
inference(instantiation,[status(thm)],[c_87074]) ).
tcf(c_87608,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = multiply(identity,X2) )
| ( X1 != X2 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_87609,plain,
( ( multiply(sk_c12,sk_c12) = multiply(identity,sk_c12) )
| ( sk_c12 != identity )
| ( sk_c12 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_87608]) ).
tcf(c_87633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,X1) )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = multiply(X2,X3) )
| ( multiply(X2,X3) != multiply(X0,X1) )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_87169]) ).
tcf(c_87642,plain,
( ( multiply(sk_c12,sk_c3) = iPr_def_28 )
| ( iPr_def_28 != multiply(sk_c12,sk_c3) )
| ( multiply(sk_c12,sk_c3) != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_87169]) ).
tcf(c_87676,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = iPr_def_28 )
| ( iPr_def_28 != multiply(sk_c12,sk_c3) )
| ( multiply(X0,X1) != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_87678,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = iPr_def_30 )
| ( iPr_def_30 != multiply(sk_c1,sk_c11) )
| ( multiply(X0,X1) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_87687,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = sk_c12 )
| ( sk_c12 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_87688,plain,
( ( multiply(sk_c12,sk_c12) = sk_c12 )
| ( sk_c12 != multiply(identity,sk_c12) )
| ( multiply(sk_c12,sk_c12) != multiply(identity,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87687]) ).
tcf(c_87733,plain,
! [X0: $i] :
( ( multiply(X0,iPr_def_29) = multiply(identity,sk_c11) )
| ( iPr_def_29 != sk_c11 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_87379]) ).
tcf(c_87734,plain,
! [X0: $i] :
( ( sk_c12 = multiply(X0,iPr_def_29) )
| ( sk_c12 != multiply(identity,sk_c11) )
| ( multiply(X0,iPr_def_29) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87184]) ).
tcf(c_87735,plain,
( ( multiply(sk_c12,iPr_def_29) = multiply(identity,sk_c11) )
| ( iPr_def_29 != sk_c11 )
| ( sk_c12 != identity ) ),
inference(instantiation,[status(thm)],[c_87733]) ).
tcf(c_87736,plain,
( ( sk_c12 = multiply(sk_c12,iPr_def_29) )
| ( sk_c12 != multiply(identity,sk_c11) )
| ( multiply(sk_c12,iPr_def_29) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87734]) ).
tcf(c_87860,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_28 )
| ( iPr_def_28 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_87888,plain,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_28 != iPr_def_28 )
| ( sk_c11 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87428]) ).
tcf(c_87889,plain,
iPr_def_28 = iPr_def_28,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_87899,plain,
iPr_def_29 = iPr_def_29,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_88454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(inverse(X0),X0) )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),X0) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_87262]) ).
tcf(c_88455,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),X0) = multiply(X1,X2) )
| ( X0 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_88456,plain,
( ( sk_c12 = multiply(inverse(sk_c12),sk_c12) )
| ( sk_c12 != multiply(sk_c12,sk_c12) )
| ( multiply(inverse(sk_c12),sk_c12) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_88454]) ).
tcf(c_88457,plain,
( ( multiply(inverse(sk_c12),sk_c12) = multiply(sk_c12,sk_c12) )
| ( sk_c12 != sk_c12 )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_88455]) ).
tcf(c_88487,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c11) = multiply(inverse(sk_c11),sk_c11) )
| ( sk_c11 != sk_c11 )
| ( inverse(X0) != inverse(sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87091]) ).
tcf(c_88489,plain,
( ( multiply(inverse(sk_c12),sk_c11) = multiply(inverse(sk_c11),sk_c11) )
| ( sk_c11 != sk_c11 )
| ( inverse(sk_c12) != inverse(sk_c11) ) ),
inference(instantiation,[status(thm)],[c_88487]) ).
tcf(c_88683,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = identity )
| ( identity != multiply(identity,identity) )
| ( multiply(X0,X1) != multiply(identity,identity) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_88684,plain,
( ( multiply(sk_c12,sk_c12) = identity )
| ( identity != multiply(identity,identity) )
| ( multiply(sk_c12,sk_c12) != multiply(identity,identity) ) ),
inference(instantiation,[status(thm)],[c_88683]) ).
tcf(c_88747,plain,
( ( iPr_def_28 = multiply(identity,sk_c11) )
| ( iPr_def_28 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87402]) ).
tcf(c_88785,plain,
( ( multiply(identity,sk_c11) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87570]) ).
tcf(c_89477,plain,
! [X0: $i] :
( ( multiply(sk_c6,sk_c9) = X0 )
| ( X0 != iPr_def_22 )
| ( multiply(sk_c6,sk_c9) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_87055]) ).
tcf(c_89478,plain,
( ( sk_c12 = multiply(sk_c6,sk_c9) )
| ( sk_c12 != iPr_def_22 )
| ( multiply(sk_c6,sk_c9) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_87002]) ).
tcf(c_89480,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c11) = X0 )
| ( X0 != iPr_def_24 )
| ( multiply(sk_c5,sk_c11) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_87055]) ).
tcf(c_89493,plain,
multiply(sk_c12,sk_c3) = multiply(sk_c12,sk_c3),
inference(instantiation,[status(thm)],[c_87170]) ).
tcf(c_89494,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c11) = X0 )
| ( X0 != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_87055]) ).
tcf(c_89495,plain,
( ( sk_c12 = multiply(sk_c1,sk_c11) )
| ( sk_c12 != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_87002]) ).
tcf(c_89497,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c1,sk_c11) )
| ( X0 != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_87074]) ).
tcf(c_89593,plain,
! [X0: $i] :
( ( sk_c12 = identity )
| ( identity != multiply(inverse(X0),X0) )
| ( sk_c12 != multiply(inverse(X0),X0) ) ),
inference(instantiation,[status(thm)],[c_86988]) ).
tcf(c_89594,plain,
( ( sk_c12 = identity )
| ( identity != multiply(inverse(sk_c12),sk_c12) )
| ( sk_c12 != multiply(inverse(sk_c12),sk_c12) ) ),
inference(instantiation,[status(thm)],[c_89593]) ).
tcf(c_89610,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = identity )
| ( identity != multiply(inverse(X2),X2) )
| ( multiply(X0,X1) != multiply(inverse(X2),X2) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_89611,plain,
( ( multiply(sk_c12,sk_c12) = identity )
| ( identity != multiply(inverse(sk_c12),sk_c12) )
| ( multiply(sk_c12,sk_c12) != multiply(inverse(sk_c12),sk_c12) ) ),
inference(instantiation,[status(thm)],[c_89610]) ).
tcf(c_89620,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_27 )
| ( iPr_def_27 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_89665,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c11,sk_c12) )
| ( X0 != iPr_def_15 )
| ( multiply(sk_c11,sk_c12) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_87633]) ).
tcf(c_89670,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c6,sk_c9) )
| ( X0 != iPr_def_22 )
| ( multiply(sk_c6,sk_c9) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_87633]) ).
tcf(c_89980,plain,
! [X0: $i] :
( ( multiply(X0,sk_c11) = multiply(sk_c1,sk_c11) )
| ( sk_c11 != sk_c11 )
| ( X0 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_87381]) ).
tcf(c_89982,plain,
( ( multiply(sk_c12,sk_c11) = multiply(sk_c1,sk_c11) )
| ( sk_c12 != sk_c1 )
| ( sk_c11 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_89980]) ).
tcf(c_90384,plain,
( ( sk_c11 = multiply(sk_c12,sk_c3) )
| ( sk_c11 != iPr_def_28 )
| ( multiply(sk_c12,sk_c3) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87193]) ).
tcf(c_90599,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = iPr_def_28 )
| ( iPr_def_28 != multiply(identity,sk_c11) )
| ( multiply(X0,X1) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_90600,plain,
( ( multiply(sk_c12,sk_c12) = iPr_def_28 )
| ( iPr_def_28 != multiply(identity,sk_c11) )
| ( multiply(sk_c12,sk_c12) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_90599]) ).
tcf(c_90622,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c11) )
| ( X0 != iPr_def_28 )
| ( multiply(identity,sk_c11) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87571]) ).
tcf(c_90623,plain,
( ( sk_c12 = multiply(identity,sk_c11) )
| ( sk_c12 != iPr_def_28 )
| ( multiply(identity,sk_c11) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_90622]) ).
tcf(c_91211,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(sk_c12,sk_c3) )
| ( X0 != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_91212,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(sk_c12,sk_c3) )
| ( X0 != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_91213,plain,
( ( sk_c11 = sk_c12 )
| ( sk_c12 != multiply(sk_c12,sk_c3) )
| ( sk_c11 != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_91212]) ).
tcf(c_91214,plain,
( ( sk_c12 = sk_c11 )
| ( sk_c12 != multiply(sk_c12,sk_c3) )
| ( sk_c11 != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_91211]) ).
tcf(c_91440,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c11) )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_91441,plain,
( ( inverse(sk_c12) = inverse(sk_c11) )
| ( sk_c12 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_91440]) ).
tcf(c_91580,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c1) )
| ( X0 != iPr_def_29 )
| ( inverse(sk_c1) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_87277]) ).
tcf(c_91583,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_29 )
| ( inverse(sk_c1) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_87090]) ).
tcf(c_91654,plain,
! [X0: $i] :
( ( X0 = iPr_def_28 )
| ( iPr_def_28 != multiply(sk_c12,sk_c3) )
| ( X0 != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_87860]) ).
tcf(c_91655,plain,
( ( sk_c12 = iPr_def_28 )
| ( iPr_def_28 != multiply(sk_c12,sk_c3) )
| ( sk_c12 != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_91654]) ).
tcf(c_91656,plain,
! [X0: $i] :
( ( X0 = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87860]) ).
tcf(c_91657,plain,
( ( sk_c12 = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( sk_c12 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_91656]) ).
tcf(c_92392,plain,
! [X0: $i,X1: $i] :
( ( sk_c12 = multiply(X0,X1) )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( multiply(X0,X1) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87056]) ).
tcf(c_92393,plain,
( ( sk_c12 = multiply(sk_c12,sk_c12) )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( multiply(sk_c12,sk_c12) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_92392]) ).
tcf(c_92394,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = sk_c12 )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( multiply(X0,X1) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_92395,plain,
( ( multiply(sk_c12,sk_c12) = sk_c12 )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( multiply(sk_c12,sk_c12) != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_92394]) ).
tcf(c_94350,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_22 )
| ( iPr_def_22 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_94351,plain,
( ( sk_c12 = iPr_def_22 )
| ( iPr_def_22 != sk_c12 )
| ( sk_c12 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_94350]) ).
tcf(c_94487,plain,
( ( multiply(sk_c1,sk_c11) = identity )
| ( identity != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_89494]) ).
tcf(c_94654,plain,
( ( identity = multiply(sk_c1,sk_c11) )
| ( identity != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_89497]) ).
tcf(c_94658,plain,
( ( sk_c12 = identity )
| ( identity != multiply(sk_c1,sk_c11) )
| ( sk_c12 != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_86988]) ).
tcf(c_94669,plain,
( ( sk_c11 = multiply(sk_c1,sk_c11) )
| ( sk_c11 != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_89497]) ).
tcf(c_94671,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(sk_c1,sk_c11) )
| ( X0 != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_94672,plain,
( ( sk_c11 = sk_c12 )
| ( sk_c12 != multiply(sk_c1,sk_c11) )
| ( sk_c11 != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_94671]) ).
tcf(c_94688,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(X0,sk_c11) )
| ( X1 != multiply(sk_c1,sk_c11) )
| ( multiply(X0,sk_c11) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87362]) ).
tcf(c_94689,plain,
( ( sk_c12 = multiply(sk_c12,sk_c11) )
| ( sk_c12 != multiply(sk_c1,sk_c11) )
| ( multiply(sk_c12,sk_c11) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_94688]) ).
tcf(c_94857,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( iPr_def_20 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_94858,plain,
( ( sk_c12 = iPr_def_20 )
| ( iPr_def_20 != sk_c12 )
| ( sk_c12 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_94857]) ).
tcf(c_95831,plain,
! [X0: $i] :
( ( X0 = iPr_def_27 )
| ( iPr_def_27 != sk_c3 )
| ( X0 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_89620]) ).
tcf(c_95833,plain,
! [X0: $i] :
( ( X0 = iPr_def_27 )
| ( iPr_def_27 != multiply(sk_c1,sk_c11) )
| ( X0 != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_89620]) ).
tcf(c_95834,plain,
( ( iPr_def_27 = multiply(sk_c1,sk_c11) )
| ( iPr_def_27 != iPr_def_30 )
| ( multiply(sk_c1,sk_c11) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_89497]) ).
tcf(c_95835,plain,
( ( sk_c12 = iPr_def_27 )
| ( iPr_def_27 != multiply(sk_c1,sk_c11) )
| ( sk_c12 != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_95833]) ).
tcf(c_96309,plain,
( ( sk_c3 = iPr_def_27 )
| ( iPr_def_27 != sk_c3 )
| ( sk_c3 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_95831]) ).
tcf(c_96310,plain,
sk_c3 = sk_c3,
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_96311,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c3 )
| ( sk_c3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_97791,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c11 )
| ( sk_c11 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_87217]) ).
tcf(c_97792,plain,
( ( inverse(sk_c12) = sk_c11 )
| ( sk_c11 != inverse(sk_c1) )
| ( inverse(sk_c12) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_97791]) ).
tcf(c_99155,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_25 )
| ( iPr_def_25 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_99156,plain,
( ( sk_c12 = iPr_def_25 )
| ( iPr_def_25 != sk_c12 )
| ( sk_c12 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_99155]) ).
tcf(c_99289,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c5,sk_c11) = multiply(X0,X1) )
| ( multiply(sk_c5,sk_c11) != multiply(sk_c5,sk_c11) )
| ( multiply(X0,X1) != multiply(sk_c5,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87634]) ).
tcf(c_99291,plain,
( ( multiply(sk_c5,sk_c11) = multiply(sk_c12,sk_c12) )
| ( multiply(sk_c5,sk_c11) != multiply(sk_c5,sk_c11) )
| ( multiply(sk_c12,sk_c12) != multiply(sk_c5,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_99289]) ).
tcf(c_101041,plain,
( ( iPr_def_29 = sk_c11 )
| ( iPr_def_29 != iPr_def_28 )
| ( sk_c11 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87428]) ).
tcf(c_101043,plain,
( ( inverse(sk_c1) = iPr_def_28 )
| ( iPr_def_28 != iPr_def_29 )
| ( inverse(sk_c1) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_91583]) ).
tcf(c_101044,plain,
( ( iPr_def_28 = inverse(sk_c1) )
| ( iPr_def_28 != iPr_def_29 )
| ( inverse(sk_c1) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_91580]) ).
tcf(c_101046,plain,
( ( iPr_def_28 = sk_c11 )
| ( iPr_def_28 != iPr_def_29 )
| ( sk_c11 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_87430]) ).
tcf(c_101051,plain,
! [X0: $i] :
( ( X0 = iPr_def_28 )
| ( iPr_def_28 != iPr_def_29 )
| ( X0 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_87860]) ).
tcf(c_101192,plain,
( ( multiply(sk_c6,sk_c9) = identity )
| ( identity != iPr_def_22 )
| ( multiply(sk_c6,sk_c9) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_89477]) ).
tcf(c_101260,plain,
( ( sk_c11 = multiply(sk_c6,sk_c9) )
| ( sk_c11 != sk_c11 )
| ( multiply(sk_c6,sk_c9) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87034]) ).
tcf(c_101398,plain,
! [X0: $i] :
( ( multiply(X0,sk_c3) = multiply(iPr_def_17,iPr_def_27) )
| ( sk_c3 != iPr_def_27 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_87492]) ).
tcf(c_101399,plain,
( ( multiply(sk_c12,sk_c3) = multiply(iPr_def_17,iPr_def_27) )
| ( sk_c3 != iPr_def_27 )
| ( sk_c12 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_101398]) ).
tcf(c_101405,plain,
! [X0: $i] :
( ( sk_c3 = sk_c12 )
| ( sk_c3 != X0 )
| ( sk_c12 != X0 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_101510,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c1) )
| ( X0 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87277]) ).
tcf(c_101513,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87090]) ).
tcf(c_101515,plain,
( ( inverse(sk_c1) = sk_c12 )
| ( sk_c12 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_101513]) ).
tcf(c_101516,plain,
( ( sk_c12 = inverse(sk_c1) )
| ( sk_c12 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_101510]) ).
tcf(c_101521,plain,
( ( sk_c11 = inverse(sk_c1) )
| ( sk_c11 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87193]) ).
tcf(c_103221,plain,
( ( sk_c11 = multiply(sk_c11,sk_c12) )
| ( sk_c11 != iPr_def_15 )
| ( multiply(sk_c11,sk_c12) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_89665]) ).
tcf(c_103223,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(sk_c11,sk_c12) )
| ( X0 != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_103224,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(sk_c11,sk_c12) )
| ( X0 != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_103225,plain,
( ( sk_c11 = sk_c12 )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( sk_c11 != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_103224]) ).
tcf(c_103226,plain,
( ( sk_c12 = sk_c11 )
| ( sk_c12 != multiply(sk_c11,sk_c12) )
| ( sk_c11 != multiply(sk_c11,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_103223]) ).
tcf(c_103432,plain,
( ( identity = multiply(sk_c6,sk_c9) )
| ( identity != iPr_def_22 )
| ( multiply(sk_c6,sk_c9) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_89670]) ).
tcf(c_103439,plain,
( ( sk_c12 = identity )
| ( identity != multiply(sk_c6,sk_c9) )
| ( sk_c12 != multiply(sk_c6,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_86988]) ).
tcf(c_103462,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(sk_c6,sk_c9) )
| ( X0 != multiply(sk_c6,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_103463,plain,
( ( sk_c11 = sk_c12 )
| ( sk_c12 != multiply(sk_c6,sk_c9) )
| ( sk_c11 != multiply(sk_c6,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_103462]) ).
tcf(c_103800,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( inverse(X0) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_91656]) ).
tcf(c_103806,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_28 )
| ( inverse(X0) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87277]) ).
tcf(c_103811,plain,
( ( inverse(sk_c12) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( inverse(sk_c12) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_103800]) ).
tcf(c_103902,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_27 )
| ( inverse(X0) != iPr_def_27 ) ),
inference(instantiation,[status(thm)],[c_87277]) ).
tcf(c_104035,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_28 )
| ( iPr_def_28 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_87217]) ).
tcf(c_104036,plain,
( ( inverse(sk_c12) = iPr_def_28 )
| ( iPr_def_28 != inverse(sk_c1) )
| ( inverse(sk_c12) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_104035]) ).
tcf(c_104049,plain,
! [X0: $i] :
( ( X0 = iPr_def_28 )
| ( iPr_def_28 != inverse(sk_c1) )
| ( X0 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_87860]) ).
tcf(c_104050,plain,
( ( sk_c12 = iPr_def_28 )
| ( iPr_def_28 != inverse(sk_c1) )
| ( sk_c12 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_104049]) ).
tcf(c_104066,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = inverse(X0) )
| ( sk_c11 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_87007]) ).
tcf(c_104476,plain,
! [X0: $i] :
( ( X0 = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_96311]) ).
tcf(c_105397,plain,
( ( multiply(sk_c5,sk_c11) = identity )
| ( identity != iPr_def_24 )
| ( multiply(sk_c5,sk_c11) != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_89480]) ).
tcf(c_105489,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != identity )
| ( inverse(X0) != identity ) ),
inference(instantiation,[status(thm)],[c_87090]) ).
tcf(c_105764,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = sk_c12 )
| ( sk_c12 != X1 )
| ( multiply(X0,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_87055]) ).
tcf(c_108303,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_27,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_58298,c_114]) ).
tcf(c_109189,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c11 )
| ( sk_c11 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_109190,plain,
( ( inverse(sk_c12) = sk_c11 )
| ( sk_c11 != sk_c12 )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_109189]) ).
tcf(c_109232,plain,
! [X0: $i] :
( ( multiply(sk_c6,sk_c9) = sk_c11 )
| ( sk_c11 != X0 )
| ( multiply(sk_c6,sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_109735,plain,
! [X0: $i] :
( ( X0 = iPr_def_27 )
| ( iPr_def_27 != iPr_def_28 )
| ( X0 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_89620]) ).
tcf(c_109736,plain,
( ( sk_c12 = iPr_def_27 )
| ( iPr_def_27 != iPr_def_28 )
| ( sk_c12 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_109735]) ).
tcf(c_109738,plain,
! [X0: $i] :
( ( X0 = sk_c3 )
| ( sk_c3 != iPr_def_28 )
| ( X0 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_96311]) ).
tcf(c_109739,plain,
( ( sk_c12 = sk_c3 )
| ( sk_c3 != iPr_def_28 )
| ( sk_c12 != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_109738]) ).
tcf(c_110211,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(X0,sk_c11) )
| ( X1 != identity )
| ( multiply(X0,sk_c11) != identity ) ),
inference(instantiation,[status(thm)],[c_87074]) ).
tcf(c_110449,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( multiply(X0,X1) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_91656]) ).
tcf(c_110450,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = sk_c11 )
| ( sk_c11 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_87055]) ).
tcf(c_110452,plain,
( ( multiply(sk_c12,sk_c12) = sk_c11 )
| ( sk_c11 != sk_c12 )
| ( multiply(sk_c12,sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_110450]) ).
tcf(c_110851,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != iPr_def_28 )
| ( multiply(X0,X1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_87193]) ).
tcf(c_110853,plain,
( ( sk_c11 = multiply(sk_c12,sk_c12) )
| ( sk_c11 != iPr_def_28 )
| ( multiply(sk_c12,sk_c12) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_110851]) ).
tcf(c_111493,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_17) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_52019,c_72029]) ).
tcf(c_111495,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_72029,c_114]) ).
tcf(c_111504,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c1 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_72029,c_50389]) ).
tcf(c_111508,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_111493,c_50516]) ).
tcf(c_111698,plain,
! [X0: $i] :
( ( sk_c11 = identity )
| ( identity != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_87016]) ).
tcf(c_111700,plain,
( ( sk_c11 = identity )
| ( identity != sk_c12 )
| ( sk_c11 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_111698]) ).
tcf(c_111768,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_111504,c_742]) ).
tcf(c_111769,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_27) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_111504,c_741]) ).
tcf(c_112487,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_17) = iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_52019,c_111769]) ).
tcf(c_112505,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c2 = iPr_def_29 ) ),
inference(light_normalisation,[status(thm)],[c_112487,c_50516]) ).
tcf(c_112853,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c1 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_111508,c_81801]) ).
tcf(c_113148,plain,
( ( iPr_def_29 = iPr_def_28 )
| ( iPr_def_29 != iPr_def_29 )
| ( iPr_def_28 != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_101051]) ).
tcf(c_113464,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,sk_c11) )
| ( X1 != sk_c11 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_87077]) ).
tcf(c_113465,plain,
( ( multiply(sk_c12,sk_c12) = multiply(identity,sk_c11) )
| ( sk_c12 != identity )
| ( sk_c12 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_113464]) ).
tcf(c_113687,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_29,iPr_def_30) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_112505,c_5850]) ).
tcf(c_113710,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_113687,c_5992]) ).
tcf(c_114431,plain,
( ~ iPr_def_14
| ( sk_c12 != identity )
| ( multiply(sk_c12,sk_c12) != sk_c11 ) ),
inference(light_normalisation,[status(thm)],[c_3612,c_27467]) ).
tcf(c_116104,plain,
( ~ iPr_def_14
| ( sk_c11 != sk_c12 )
| ( inverse(inverse(sk_c12)) != sk_c12 ) ),
inference(demodulation,[status(thm)],[c_3613,c_27433]) ).
tcf(c_116518,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c3 = iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_45574,c_815,c_762,c_94858,c_96309,c_96310]) ).
tcf(c_116519,plain,
( ( sk_c3 = iPr_def_27 )
| ( sk_c12 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_116518]) ).
tcf(c_116715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = sk_c12 )
| ( sk_c12 != multiply(X1,X2) )
| ( multiply(X0,inverse(X0)) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_87174]) ).
tcf(c_116716,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = sk_c12 )
| ( sk_c12 != multiply(sk_c12,sk_c12) )
| ( multiply(sk_c12,inverse(sk_c12)) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_116715]) ).
tcf(c_117472,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_27,sk_c12) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_113710,c_727]) ).
tcf(c_118344,plain,
( ( sk_c12 = iPr_def_22 )
| ( sk_c3 = iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_45632,c_815,c_764,c_94351,c_96309,c_96310]) ).
tcf(c_118345,plain,
( ( sk_c3 = iPr_def_27 )
| ( sk_c12 = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_118344]) ).
tcf(c_118520,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_46293,c_113]) ).
tcf(c_118549,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_113,c_118520]) ).
tcf(c_118550,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_114,c_118520]) ).
tcf(c_118551,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_115,c_118520]) ).
tcf(c_118840,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_118520,c_118520]) ).
tcf(c_119847,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_87217]) ).
tcf(c_119848,plain,
( ( inverse(sk_c12) = sk_c12 )
| ( sk_c12 != inverse(sk_c1) )
| ( inverse(sk_c12) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_119847]) ).
tcf(c_120390,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = sk_c11 )
| ( sk_c11 != X1 )
| ( multiply(X0,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_120683,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = multiply(X2,X1) )
| ( X0 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_120684,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = multiply(sk_c12,sk_c12) )
| ( sk_c12 != sk_c12 )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_120683]) ).
tcf(c_121358,plain,
( ( sk_c12 = multiply(sk_c12,sk_c3) )
| ( sk_c12 != multiply(iPr_def_17,iPr_def_27) )
| ( multiply(sk_c12,sk_c3) != multiply(iPr_def_17,iPr_def_27) ) ),
inference(instantiation,[status(thm)],[c_87186]) ).
tcf(c_121925,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = multiply(X0,X1) )
| ( sk_c11 != sk_c11 )
| ( multiply(X0,X1) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87034]) ).
tcf(c_121927,plain,
( ( sk_c11 = multiply(sk_c12,sk_c12) )
| ( sk_c11 != sk_c11 )
| ( multiply(sk_c12,sk_c12) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_121925]) ).
tcf(c_125760,plain,
! [X0: $i] :
( ( sk_c3 = sk_c11 )
| ( sk_c3 != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_87102]) ).
tcf(c_125763,plain,
( ( sk_c3 = sk_c11 )
| ( sk_c3 != sk_c12 )
| ( sk_c11 != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_125760]) ).
tcf(c_130389,plain,
! [X0: $i] :
( ( sk_c12 = iPr_def_17 )
| ( multiply(iPr_def_26,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_7373,c_29193]) ).
tcf(c_130422,plain,
( ( sk_c12 = iPr_def_17 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_130389,c_1240]) ).
tcf(c_131297,plain,
( ( sk_c12 = iPr_def_15 )
| ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_130422,c_1391]) ).
tcf(c_131314,plain,
( ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_25 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_130422,c_797]) ).
tcf(c_131315,plain,
( ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_22 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_130422,c_794]) ).
tcf(c_131316,plain,
( ( iPr_def_17 = iPr_def_30 )
| ( sk_c12 = iPr_def_20 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_130422,c_792]) ).
tcf(c_131408,plain,
( ( sk_c12 = iPr_def_28 )
| ( sk_c12 = iPr_def_15 )
| ( sk_c11 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_131297,c_5979]) ).
tcf(c_132747,plain,
( ( sk_c11 = iPr_def_23 )
| ( iPr_def_23 != sk_c11 )
| ( sk_c11 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_87034]) ).
tcf(c_133840,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c3 = iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_45754,c_815,c_767,c_96309,c_96310,c_99156]) ).
tcf(c_133841,plain,
( ( sk_c3 = iPr_def_27 )
| ( sk_c12 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_133840]) ).
tcf(c_133870,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_118550,c_118840]) ).
tcf(c_133900,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_133870,c_118549]) ).
tcf(c_133981,plain,
! [X0: $i] :
( ( identity = iPr_def_20 )
| ( iPr_def_20 != X0 )
| ( identity != X0 ) ),
inference(instantiation,[status(thm)],[c_87010]) ).
tcf(c_133982,plain,
( ( identity = iPr_def_20 )
| ( iPr_def_20 != sk_c12 )
| ( identity != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_133981]) ).
tcf(c_134210,plain,
( ( sk_c12 = iPr_def_15 )
| ( sk_c12 = iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_131314,c_177,c_815,c_727,c_740,c_3242,c_5979,c_7375,c_9415,c_15064,c_24814,c_24815,c_39610,c_41192,c_87049,c_87057,c_87185,c_87609,c_87642,c_89493,c_89495,c_90384,c_91213,c_94654,c_94658,c_101399,c_121358,c_133841]) ).
tcf(c_134211,plain,
( ( sk_c12 = iPr_def_25 )
| ( sk_c12 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_134210]) ).
tcf(c_135149,plain,
( ( sk_c12 = iPr_def_15 )
| ( sk_c12 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_131315,c_177,c_815,c_727,c_740,c_3242,c_5979,c_7387,c_9047,c_14746,c_24814,c_24815,c_39612,c_41192,c_87049,c_87057,c_87185,c_87609,c_87642,c_89493,c_89495,c_90384,c_91213,c_94654,c_94658,c_101399,c_118345,c_121358]) ).
tcf(c_135150,plain,
( ( sk_c12 = iPr_def_22 )
| ( sk_c12 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_135149]) ).
tcf(c_135193,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_135150,c_134211]) ).
tcf(c_135764,plain,
( ( sk_c3 = sk_c12 )
| ( sk_c3 != iPr_def_27 )
| ( sk_c12 != iPr_def_27 ) ),
inference(instantiation,[status(thm)],[c_101405]) ).
tcf(c_135804,plain,
( ( sk_c3 = sk_c12 )
| ( sk_c3 != sk_c3 )
| ( sk_c12 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_101405]) ).
tcf(c_136113,plain,
( ( sk_c12 = iPr_def_15 )
| ( sk_c12 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_131316,c_177,c_815,c_727,c_740,c_3242,c_5979,c_7399,c_8465,c_14181,c_24814,c_24815,c_39613,c_41192,c_87049,c_87057,c_87185,c_87609,c_87642,c_89493,c_89495,c_90384,c_91213,c_94654,c_94658,c_101399,c_116519,c_121358]) ).
tcf(c_136114,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c12 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_136113]) ).
tcf(c_136158,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_136114,c_135150]) ).
tcf(c_136700,plain,
( ( inverse(sk_c1) = iPr_def_27 )
| ( iPr_def_27 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_101513]) ).
tcf(c_136702,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c1) )
| ( X0 != iPr_def_27 )
| ( inverse(sk_c1) != iPr_def_27 ) ),
inference(instantiation,[status(thm)],[c_103902]) ).
tcf(c_136711,plain,
( ( sk_c12 = inverse(sk_c1) )
| ( sk_c12 != iPr_def_27 )
| ( inverse(sk_c1) != iPr_def_27 ) ),
inference(instantiation,[status(thm)],[c_136702]) ).
tcf(c_137586,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_30 ) ),
inference(global_subsumption_just,[status(thm)],[c_45946,c_786,c_1511,c_1547,c_3134,c_3127,c_12046,c_25839,c_87104]) ).
tcf(c_137600,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_808,c_137586]) ).
tcf(c_137601,plain,
( ( sk_c12 = iPr_def_25 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_807,c_137586]) ).
tcf(c_137603,plain,
( ( sk_c11 = iPr_def_23 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_805,c_137586]) ).
tcf(c_137604,plain,
( ( sk_c12 = iPr_def_22 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_804,c_137586]) ).
tcf(c_137606,plain,
( ( sk_c12 = iPr_def_20 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_802,c_137586]) ).
tcf(c_138007,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_45953,c_177,c_815,c_727,c_740,c_765,c_1511,c_1542,c_1543,c_1746,c_1885,c_2217,c_2680,c_3134,c_3417,c_3671,c_5979,c_6401,c_6402,c_7328,c_9220,c_14855,c_21805,c_25839,c_39611,c_41192,c_50836,c_58915,c_62113,c_63094,c_64439,c_87049,c_87057,c_87185,c_87609,c_87642,c_89493,c_89495,c_90384,c_91214,c_94654,c_94658,c_96309,c_96310,c_101399,c_121358,c_132747]) ).
tcf(c_138023,plain,
( ( sk_c10 = iPr_def_15 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_806,c_138007]) ).
tcf(c_138026,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_803,c_138007]) ).
tcf(c_138029,plain,
( ( sk_c12 = iPr_def_30 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_796,c_138007]) ).
tcf(c_138031,plain,
( ( sk_c11 = iPr_def_28 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_776,c_138007]) ).
tcf(c_138032,plain,
( ( sk_c3 = iPr_def_27 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_766,c_138007]) ).
tcf(c_138033,plain,
( ( sk_c12 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_756,c_138007]) ).
tcf(c_138473,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c3 )
| ( sk_c3 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_96311]) ).
tcf(c_138485,plain,
( ( inverse(sk_c12) = sk_c3 )
| ( sk_c3 != sk_c12 )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_138473]) ).
tcf(c_139054,plain,
( ~ iPr_def_11
| ( sk_c11 != iPr_def_29 ) ),
inference(global_subsumption_just,[status(thm)],[c_46049,c_3323,c_14746,c_31871,c_31929,c_50995,c_89478,c_103432,c_103439]) ).
tcf(c_139072,plain,
( ( sk_c12 = iPr_def_30 )
| ~ iPr_def_11
| ( iPr_def_26 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_798,c_139054]) ).
tcf(c_139074,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_788,c_139054]) ).
tcf(c_139076,plain,
( ( sk_c11 = iPr_def_23 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_785,c_139054]) ).
tcf(c_139077,plain,
( ( sk_c12 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_784,c_139054]) ).
tcf(c_139078,plain,
( ( sk_c12 = iPr_def_20 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_782,c_139054]) ).
tcf(c_140512,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_27 ) ),
inference(global_subsumption_just,[status(thm)],[c_46146,c_741,c_1905,c_3527,c_3523,c_4543,c_4544,c_7316,c_9415,c_12536,c_39610,c_49755,c_60331,c_71211,c_87194,c_101044,c_104050,c_134211]) ).
tcf(c_140532,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_10
| ( iPr_def_27 != iPr_def_29 ) ),
inference(superposition,[status(thm)],[c_788,c_140512]) ).
tcf(c_140537,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_10
| ( iPr_def_27 != iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_778,c_140512]) ).
tcf(c_141667,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_110449]) ).
tcf(c_141670,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( multiply(sk_c12,inverse(sk_c12)) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_141667]) ).
tcf(c_142071,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_46150,c_741,c_1905,c_3527,c_4543,c_4544,c_9415,c_12536,c_39610,c_49755,c_60331,c_71211,c_87194,c_101044,c_104050,c_134211]) ).
tcf(c_142083,plain,
( ( iPr_def_28 = iPr_def_29 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_44923,c_142071]) ).
tcf(c_142089,plain,
( ( sk_c12 = iPr_def_30 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_798,c_142071]) ).
tcf(c_143907,plain,
! [X0: $i] :
( ( sk_c11 = inverse(sk_c1) )
| ( sk_c11 != X0 )
| ( inverse(sk_c1) != X0 ) ),
inference(instantiation,[status(thm)],[c_104066]) ).
tcf(c_143908,plain,
( ( sk_c11 = inverse(sk_c1) )
| ( sk_c11 != sk_c12 )
| ( inverse(sk_c1) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_143907]) ).
tcf(c_144310,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_137600,c_177,c_815,c_727,c_740,c_1511,c_1542,c_1543,c_1746,c_1885,c_2217,c_2680,c_3417,c_3671,c_5979,c_6401,c_6402,c_39609,c_41192,c_50844,c_58915,c_62113,c_63094,c_64439,c_87049,c_87057,c_87185,c_87609,c_87642,c_89493,c_89495,c_90384,c_91214,c_94654,c_94658,c_101399,c_121358,c_138033,c_138032,c_138031,c_138029,c_138023]) ).
tcf(c_144321,plain,
( ( sk_c12 = iPr_def_25 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_137601,c_815,c_740,c_1885,c_3671,c_5979,c_12371,c_39610,c_41192,c_43899,c_87057,c_87642,c_89493,c_89495,c_90384,c_91213,c_94654,c_94658,c_101399,c_111700,c_121358,c_138033,c_138032,c_138031,c_138029]) ).
tcf(c_144327,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c12 = iPr_def_25 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_46394,c_144321]) ).
tcf(c_144334,plain,
( ( sk_c11 = iPr_def_23 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_137603,c_177,c_815,c_727,c_740,c_1511,c_1542,c_1543,c_1746,c_1885,c_2217,c_2680,c_3417,c_3671,c_5979,c_6401,c_6402,c_39611,c_41192,c_50836,c_58915,c_62113,c_63094,c_64439,c_87049,c_87057,c_87185,c_87609,c_87642,c_89493,c_89495,c_90384,c_91214,c_94654,c_94658,c_101399,c_121358,c_138033,c_138032,c_138031,c_138029,c_138023]) ).
tcf(c_144340,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c11 = iPr_def_23 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_46406,c_144334]) ).
tcf(c_145829,plain,
( ( sk_c12 = iPr_def_22 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_137604,c_815,c_740,c_1885,c_3671,c_5979,c_10706,c_39612,c_41192,c_43902,c_87057,c_87642,c_89493,c_89495,c_90384,c_91213,c_94654,c_94658,c_101399,c_111700,c_121358,c_138033,c_138032,c_138031,c_138029]) ).
tcf(c_145912,plain,
( ( sk_c12 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_137606,c_815,c_740,c_1885,c_3671,c_5979,c_10358,c_39613,c_41192,c_43904,c_87057,c_87642,c_89493,c_89495,c_90384,c_91213,c_94654,c_94658,c_101399,c_111700,c_121358,c_138033,c_138032,c_138031,c_138029]) ).
tcf(c_146180,plain,
( ( iPr_def_22 = iPr_def_25 )
| ~ iPr_def_14
| ( sk_c12 != identity )
| ( multiply(iPr_def_15,iPr_def_15) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_135193,c_114431]) ).
tcf(c_146302,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_30 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_135193,c_797]) ).
tcf(c_146303,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_30 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_135193,c_794]) ).
tcf(c_146993,plain,
( ( iPr_def_15 != iPr_def_24 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_138026,c_2022,c_58789,c_66008,c_138007,c_138023]) ).
tcf(c_146994,plain,
( ~ iPr_def_13
| ( iPr_def_15 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_146993]) ).
tcf(c_149323,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = multiply(X1,sk_c3) )
| ( X0 != X1 )
| ( inverse(X0) != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_120683]) ).
tcf(c_149336,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = multiply(sk_c12,sk_c3) )
| ( sk_c12 != sk_c12 )
| ( inverse(sk_c12) != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_149323]) ).
tcf(c_149918,plain,
( ( sk_c12 = iPr_def_30 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_139072,c_31872,c_31929,c_50995,c_89478,c_103432,c_103439,c_139054,c_139077]) ).
tcf(c_150135,plain,
( ( iPr_def_27 != iPr_def_29 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_140532,c_741,c_1905,c_3527,c_4543,c_4544,c_9415,c_12536,c_39610,c_49755,c_60331,c_71211,c_87194,c_101044,c_104050,c_134211,c_140532]) ).
tcf(c_150136,plain,
( ~ iPr_def_10
| ( iPr_def_27 != iPr_def_29 ) ),
inference(renaming,[status(thm)],[c_150135]) ).
tcf(c_150145,plain,
( ( iPr_def_23 = iPr_def_26 )
| ~ iPr_def_10
| ( iPr_def_27 != iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_47493,c_150136]) ).
tcf(c_150786,plain,
( ( inverse(sk_c1) = iPr_def_15 )
| ( iPr_def_15 != iPr_def_28 )
| ( inverse(sk_c1) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_101513]) ).
tcf(c_151393,plain,
( ( iPr_def_27 != iPr_def_28 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_140537,c_140537,c_142071]) ).
tcf(c_151394,plain,
( ~ iPr_def_10
| ( iPr_def_27 != iPr_def_28 ) ),
inference(renaming,[status(thm)],[c_151393]) ).
tcf(c_152464,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_14
| ( sk_c12 != identity )
| ( multiply(iPr_def_15,iPr_def_15) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_136158,c_114431]) ).
tcf(c_152587,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_30 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_136158,c_794]) ).
tcf(c_152588,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_30 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_136158,c_792]) ).
tcf(c_154085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,inverse(X0)) = sk_c11 )
| ( sk_c11 != multiply(X1,X2) )
| ( multiply(X0,inverse(X0)) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_120390]) ).
tcf(c_154090,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = sk_c11 )
| ( sk_c11 != multiply(sk_c12,sk_c12) )
| ( multiply(sk_c12,inverse(sk_c12)) != multiply(sk_c12,sk_c12) ) ),
inference(instantiation,[status(thm)],[c_154085]) ).
tcf(c_159004,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_17,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_112853,c_111495]) ).
tcf(c_159034,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = identity ) ),
inference(light_normalisation,[status(thm)],[c_159004,c_5979]) ).
tcf(c_159593,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( inverse(X0) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_104476]) ).
tcf(c_159594,plain,
( ( inverse(sk_c12) = sk_c3 )
| ( sk_c3 != sk_c11 )
| ( inverse(sk_c12) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_159593]) ).
tcf(c_160097,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c2,identity) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_159034,c_739]) ).
tcf(c_162264,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_15 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_146303,c_146302]) ).
tcf(c_163605,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c11 ) ),
inference(global_subsumption_just,[status(thm)],[c_45926,c_177,c_815,c_727,c_740,c_1511,c_1542,c_1543,c_1584,c_1746,c_2680,c_3108,c_3417,c_5979,c_6395,c_6396,c_22236,c_24814,c_24815,c_31929,c_32379,c_70762,c_75039,c_87049,c_87057,c_87185,c_87187,c_87493,c_87609,c_87642,c_89478,c_89493,c_90384,c_91213,c_91655,c_101399,c_103432,c_103439,c_109736,c_121358,c_138033,c_138032,c_138031,c_138023,c_145829]) ).
tcf(c_164671,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_51399,c_741,c_4543,c_4544,c_4957,c_11656,c_60331,c_71211,c_101044,c_104050,c_136158]) ).
tcf(c_164772,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_164671,c_794]) ).
tcf(c_164773,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_164671,c_792]) ).
tcf(c_166407,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_111768,c_50391]) ).
tcf(c_167388,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = sk_c12 )
| ( sk_c12 != iPr_def_15 )
| ( multiply(X0,inverse(X0)) != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_105764]) ).
tcf(c_168241,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_15) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_162264,c_42743]) ).
tcf(c_168533,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c5,sk_c11) )
| ( multiply(sk_c5,sk_c11) != identity )
| ( multiply(X0,X1) != identity ) ),
inference(instantiation,[status(thm)],[c_110211]) ).
tcf(c_168534,plain,
( ( multiply(sk_c12,sk_c12) = multiply(sk_c5,sk_c11) )
| ( multiply(sk_c5,sk_c11) != identity )
| ( multiply(sk_c12,sk_c12) != identity ) ),
inference(instantiation,[status(thm)],[c_168533]) ).
tcf(c_168558,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_51403,c_741,c_4543,c_4544,c_5212,c_12715,c_60331,c_71211,c_101044,c_104050,c_135193]) ).
tcf(c_168658,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_168558,c_797]) ).
tcf(c_168659,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_168558,c_794]) ).
tcf(c_168989,plain,
( ( multiply(sk_c6,sk_c9) = multiply(sk_c1,sk_c11) )
| ( multiply(sk_c1,sk_c11) != identity )
| ( multiply(sk_c6,sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_110211]) ).
tcf(c_169200,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_23 = iPr_def_26 )
| ( sk_c11 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_166407,c_778]) ).
tcf(c_169468,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) = iPr_def_28 )
| ( iPr_def_28 != multiply(sk_c12,sk_c3) )
| ( multiply(X0,inverse(X0)) != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_87676]) ).
tcf(c_169480,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = iPr_def_28 )
| ( iPr_def_28 != multiply(sk_c12,sk_c3) )
| ( multiply(sk_c12,inverse(sk_c12)) != multiply(sk_c12,sk_c3) ) ),
inference(instantiation,[status(thm)],[c_169468]) ).
tcf(c_170776,plain,
( ( multiply(sk_c6,sk_c9) = sk_c11 )
| ( sk_c11 != iPr_def_30 )
| ( multiply(sk_c6,sk_c9) != iPr_def_30 ) ),
inference(instantiation,[status(thm)],[c_109232]) ).
tcf(c_170777,plain,
( ( multiply(sk_c6,sk_c9) = iPr_def_30 )
| ( iPr_def_30 != multiply(sk_c1,sk_c11) )
| ( multiply(sk_c6,sk_c9) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_87678]) ).
tcf(c_170996,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_152588,c_152587]) ).
tcf(c_174960,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_15) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_170996,c_42783]) ).
tcf(c_175706,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_51411,c_741,c_2475,c_4543,c_4544,c_5327,c_41192,c_50377,c_68997,c_89495,c_95835,c_95834,c_101044,c_101043,c_104050,c_136700,c_136711]) ).
tcf(c_175792,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_175706,c_45415]) ).
tcf(c_178059,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_117472,c_50391]) ).
tcf(c_179533,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_178059,c_159034]) ).
tcf(c_181715,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_23 = iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_169200,c_175792]) ).
tcf(c_181754,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_28,iPr_def_28) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_181715,c_7338]) ).
tcf(c_182220,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_164773,c_164772]) ).
tcf(c_184147,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_179533,c_43798]) ).
tcf(c_184165,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_15) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_179533,c_27467]) ).
tcf(c_184594,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_168659,c_168658]) ).
tcf(c_189726,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( inverse(iPr_def_15) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_184147,c_72029]) ).
tcf(c_192918,plain,
( ~ iPr_def_10
| ( inverse(identity) != sk_c12 ) ),
inference(global_subsumption_just,[status(thm)],[c_46132,c_741,c_3512,c_4543,c_4544,c_9782,c_25839,c_71211,c_77804,c_87035,c_87429,c_101044,c_101043,c_104050,c_131408,c_142071,c_142083,c_150786,c_151394]) ).
tcf(c_192920,plain,
( ~ iPr_def_10
| ( sk_c12 != identity ) ),
inference(light_normalisation,[status(thm)],[c_192918,c_133900]) ).
tcf(c_192956,plain,
( ( sk_c12 = iPr_def_20 )
| ~ iPr_def_10
| ( identity != iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_792,c_192920]) ).
tcf(c_193780,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(identity) )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_193781,plain,
( ( inverse(sk_c12) = inverse(identity) )
| ( sk_c12 != identity ) ),
inference(instantiation,[status(thm)],[c_193780]) ).
tcf(c_195655,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_43898,c_144310]) ).
tcf(c_195661,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c11 = iPr_def_26 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2976,c_195655]) ).
tcf(c_196380,plain,
( iPr_def_14
| iPr_def_12
| ( sk_c11 = iPr_def_26 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_195661,c_743,c_1746,c_2680,c_22247,c_139074,c_144310]) ).
tcf(c_196381,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c11 = iPr_def_26 ) ),
inference(renaming,[status(thm)],[c_196380]) ).
tcf(c_197482,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_7521,c_164671]) ).
tcf(c_197738,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_197482,c_1193]) ).
tcf(c_197743,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_197482,c_797]) ).
tcf(c_197747,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_28) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_197482,c_739]) ).
tcf(c_197761,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,sk_c3) = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_197747,c_18628]) ).
tcf(c_198290,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_17) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_197738,c_41057]) ).
tcf(c_198378,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_198290,c_50516]) ).
tcf(c_199017,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c11)),multiply(X0,iPr_def_15)) = sk_c12,
inference(superposition,[status(thm)],[c_727,c_118551]) ).
tcf(c_201735,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_198378,c_83035]) ).
tcf(c_201945,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_197743,c_182220]) ).
tcf(c_202022,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_201945,c_51451]) ).
tcf(c_202413,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_7525,c_741,c_4543,c_4544,c_5212,c_12715,c_60331,c_71211,c_101044,c_104050,c_135193]) ).
tcf(c_202668,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_28 ) ),
inference(superposition,[status(thm)],[c_202413,c_1227]) ).
tcf(c_202674,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_202413,c_797]) ).
tcf(c_202678,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c2,iPr_def_28) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_202413,c_739]) ).
tcf(c_202692,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,sk_c3) = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_202678,c_18628]) ).
tcf(c_203534,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_27) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_202022,c_41057]) ).
tcf(c_203813,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_17) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_202668,c_41056]) ).
tcf(c_203900,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_203813,c_50516]) ).
tcf(c_204658,plain,
( ( iPr_def_28 = iPr_def_30 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_202674,c_184594]) ).
tcf(c_204736,plain,
( ( iPr_def_27 = iPr_def_28 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_204658,c_50700]) ).
tcf(c_205228,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_49452,c_139074]) ).
tcf(c_206762,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c1 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_203900,c_82680]) ).
tcf(c_207160,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( inverse(iPr_def_27) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_204736,c_41056]) ).
tcf(c_207969,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = multiply(X1,iPr_def_29) )
| ( X0 != X1 )
| ( inverse(X0) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_120683]) ).
tcf(c_207983,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = multiply(sk_c12,iPr_def_29) )
| ( sk_c12 != sk_c12 )
| ( inverse(sk_c12) != iPr_def_29 ) ),
inference(instantiation,[status(thm)],[c_207969]) ).
tcf(c_208582,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c12 = iPr_def_28 ) ),
inference(global_subsumption_just,[status(thm)],[c_7533,c_741,c_2475,c_4543,c_4544,c_5327,c_41192,c_50377,c_68997,c_89495,c_95835,c_95834,c_101044,c_101043,c_104050,c_136700,c_136711]) ).
tcf(c_208721,plain,
( ( iPr_def_23 = iPr_def_26 )
| ~ iPr_def_14
| ( sk_c12 != identity )
| ( multiply(iPr_def_28,iPr_def_28) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_208582,c_114431]) ).
tcf(c_217473,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c1 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_168241,c_41052]) ).
tcf(c_217676,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_15,sk_c11) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_217473,c_742]) ).
tcf(c_217938,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_174960,c_41053]) ).
tcf(c_220254,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c1 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_189726,c_184165]) ).
tcf(c_221758,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_203534,c_114]) ).
tcf(c_221770,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c1 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_203534,c_51466]) ).
tcf(c_221897,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_221770,c_742]) ).
tcf(c_223599,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_207160,c_114]) ).
tcf(c_223613,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c1 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_207160,c_50714]) ).
tcf(c_223744,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_27,sk_c11) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_223613,c_742]) ).
tcf(c_224121,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( sk_c2 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_160097,c_27433]) ).
tcf(c_224211,plain,
! [X0: $i] :
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(iPr_def_17,multiply(iPr_def_27,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_224121,c_4136]) ).
tcf(c_224221,plain,
! [X0: $i] :
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c12,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_224211,c_5982]) ).
tcf(c_224278,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( multiply(sk_c12,sk_c12) = sk_c12 ) ),
inference(instantiation,[status(thm)],[c_224221]) ).
tcf(c_230543,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_15,iPr_def_15) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_170996,c_13216]) ).
tcf(c_230730,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_15,iPr_def_15) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_162264,c_13844]) ).
tcf(c_231038,plain,
( ( inverse(iPr_def_29) != sk_c12 )
| ( sk_c11 != iPr_def_15 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_13543,c_741,c_1905,c_3527,c_4543,c_4544,c_9415,c_12536,c_13543,c_39610,c_49755,c_60331,c_71211,c_87194,c_101044,c_104050,c_134211]) ).
tcf(c_231039,plain,
( ~ iPr_def_10
| ( sk_c11 != iPr_def_15 )
| ( inverse(iPr_def_29) != sk_c12 ) ),
inference(renaming,[status(thm)],[c_231038]) ).
tcf(c_231040,plain,
( ~ iPr_def_10
| ( sk_c12 != sk_c1 )
| ( sk_c11 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_231039,c_41041]) ).
tcf(c_231092,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_10
| ( iPr_def_15 != iPr_def_29 )
| ( sk_c12 != sk_c1 ) ),
inference(superposition,[status(thm)],[c_788,c_231040]) ).
tcf(c_231097,plain,
( ( sk_c11 = iPr_def_26 )
| ~ iPr_def_10
| ( iPr_def_15 != iPr_def_28 )
| ( sk_c12 != sk_c1 ) ),
inference(superposition,[status(thm)],[c_778,c_231040]) ).
tcf(c_231701,plain,
( ( sk_c12 != sk_c1 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_231092,c_741,c_1905,c_3527,c_4543,c_4544,c_9415,c_12536,c_39610,c_49755,c_60331,c_71211,c_77804,c_87194,c_101044,c_104050,c_134211,c_151394,c_231097]) ).
tcf(c_231702,plain,
( ~ iPr_def_10
| ( sk_c12 != sk_c1 ) ),
inference(renaming,[status(thm)],[c_231701]) ).
tcf(c_231717,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c12 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_217938,c_231702]) ).
tcf(c_231718,plain,
( ( iPr_def_22 = iPr_def_25 )
| ~ iPr_def_10
| ( sk_c12 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_217473,c_231702]) ).
tcf(c_231725,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c12 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_201735,c_231702]) ).
tcf(c_239372,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c3 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_197761,c_51468]) ).
tcf(c_241025,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c3 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_202692,c_50716]) ).
tcf(c_245210,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X0)) = sk_c12 )
| ( sk_c12 != multiply(X1,iPr_def_29) )
| ( multiply(X0,inverse(X0)) != multiply(X1,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_116715]) ).
tcf(c_245212,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = sk_c12 )
| ( sk_c12 != multiply(sk_c12,iPr_def_29) )
| ( multiply(sk_c12,inverse(sk_c12)) != multiply(sk_c12,iPr_def_29) ) ),
inference(instantiation,[status(thm)],[c_245210]) ).
tcf(c_248308,plain,
multiply(inverse(multiply(inverse(iPr_def_15),sk_c11)),identity) = sk_c12,
inference(superposition,[status(thm)],[c_114,c_199017]) ).
tcf(c_249683,plain,
inverse(multiply(inverse(iPr_def_15),sk_c11)) = sk_c12,
inference(demodulation,[status(thm)],[c_248308,c_133870]) ).
tcf(c_249711,plain,
multiply(sk_c12,multiply(inverse(iPr_def_15),sk_c11)) = identity,
inference(superposition,[status(thm)],[c_249683,c_114]) ).
tcf(c_249714,plain,
multiply(sk_c12,multiply(inverse(iPr_def_15),iPr_def_15)) = sk_c12,
inference(superposition,[status(thm)],[c_249683,c_199017]) ).
tcf(c_251397,plain,
! [X0: $i,X1: $i] :
( ( inverse(inverse(X0)) = inverse(X1) )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_251398,plain,
( ( inverse(inverse(sk_c12)) = inverse(sk_c12) )
| ( inverse(sk_c12) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_251397]) ).
tcf(c_251458,plain,
( ( sk_c12 = iPr_def_20 )
| ( multiply(sk_c12,multiply(inverse(iPr_def_15),iPr_def_15)) = identity ) ),
inference(superposition,[status(thm)],[c_77259,c_249711]) ).
tcf(c_251539,plain,
( ( sk_c12 = iPr_def_20 )
| ( sk_c12 = identity ) ),
inference(light_normalisation,[status(thm)],[c_251458,c_249714]) ).
tcf(c_251981,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_26 )
| ( multiply(iPr_def_15,iPr_def_29) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_788,c_217676]) ).
tcf(c_252073,plain,
! [X0: $i] :
( ( inverse(identity) = sk_c11 )
| ( sk_c11 != X0 )
| ( inverse(identity) != X0 ) ),
inference(instantiation,[status(thm)],[c_87090]) ).
tcf(c_252074,plain,
( ( inverse(identity) = sk_c11 )
| ( sk_c11 != sk_c12 )
| ( inverse(identity) != sk_c12 ) ),
inference(instantiation,[status(thm)],[c_252073]) ).
tcf(c_254183,plain,
( ( inverse(identity) = iPr_def_28 )
| ( iPr_def_28 != sk_c11 )
| ( inverse(identity) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_103800]) ).
tcf(c_255239,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_201735,c_221758]) ).
tcf(c_255280,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = identity ) ),
inference(light_normalisation,[status(thm)],[c_255239,c_5979]) ).
tcf(c_256008,plain,
! [X0: $i] :
( ( inverse(identity) = X0 )
| ( X0 != identity )
| ( inverse(identity) != identity ) ),
inference(instantiation,[status(thm)],[c_105489]) ).
tcf(c_256009,plain,
( ( inverse(identity) = sk_c12 )
| ( sk_c12 != identity )
| ( inverse(identity) != identity ) ),
inference(instantiation,[status(thm)],[c_256008]) ).
tcf(c_257148,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,inverse(X1)) = inverse(X0) )
| ( inverse(X0) != iPr_def_28 )
| ( multiply(X0,inverse(X1)) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_103806]) ).
tcf(c_257149,plain,
( ( multiply(sk_c12,inverse(sk_c12)) = inverse(sk_c12) )
| ( inverse(sk_c12) != iPr_def_28 )
| ( multiply(sk_c12,inverse(sk_c12)) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_257148]) ).
tcf(c_257421,plain,
( ( sk_c12 = inverse(identity) )
| ( sk_c12 != iPr_def_28 )
| ( inverse(identity) != iPr_def_28 ) ),
inference(instantiation,[status(thm)],[c_103806]) ).
tcf(c_257508,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_251981,c_815,c_818,c_740,c_741,c_1954,c_2457,c_2976,c_3512,c_4542,c_4543,c_4544,c_9782,c_12715,c_15164,c_25836,c_25839,c_27467,c_39609,c_41192,c_60331,c_62565,c_68916,c_71211,c_77804,c_87024,c_87035,c_87066,c_87194,c_87429,c_87735,c_87736,c_87888,c_87889,c_87899,c_88489,c_88785,c_89495,c_90623,c_91441,c_94654,c_94658,c_97792,c_101041,c_101044,c_101043,c_101521,c_104036,c_104050,c_109736,c_113148,c_119848,c_125763,c_131408,c_135193,c_135764,c_139074,c_142071,c_142083,c_144310,c_146180,c_149336,c_150786,c_151394,c_159594,c_168558,c_169480,c_204736,c_207983,c_217473,c_230730,c_241025,c_245212,c_251398,c_256009,c_257149]) ).
tcf(c_257706,plain,
( ( iPr_def_26 = iPr_def_29 )
| ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_257508,c_787]) ).
tcf(c_257707,plain,
( ( iPr_def_26 = iPr_def_29 )
| ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_257508,c_785]) ).
tcf(c_258413,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_221897,c_51468]) ).
tcf(c_258641,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(iPr_def_17,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_206762,c_223599]) ).
tcf(c_258677,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = identity ) ),
inference(light_normalisation,[status(thm)],[c_258641,c_5979]) ).
tcf(c_258778,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_223744,c_50716]) ).
tcf(c_259006,plain,
( ( sk_c12 = iPr_def_25 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_257706,c_177,c_815,c_818,c_740,c_741,c_4542,c_4543,c_4544,c_5212,c_9415,c_12715,c_60331,c_62565,c_68924,c_68925,c_71211,c_87049,c_87185,c_87194,c_87609,c_101044,c_104036,c_109736,c_116716,c_119848,c_120684,c_135193,c_135764,c_138485,c_144327,c_146180,c_149336,c_168558,c_169480,c_204736,c_217473,c_230730,c_231718,c_241025,c_251398,c_257149,c_258677]) ).
tcf(c_259007,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c12 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_259006]) ).
tcf(c_259255,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_259007,c_738]) ).
tcf(c_259267,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( identity = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_259255,c_29189]) ).
tcf(c_259563,plain,
( ( sk_c11 = iPr_def_23 )
| ( iPr_def_22 = iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_257707,c_177,c_815,c_818,c_740,c_741,c_4542,c_4543,c_4544,c_5212,c_9220,c_12715,c_60331,c_62565,c_68924,c_68925,c_71211,c_87049,c_87185,c_87194,c_87609,c_101044,c_104036,c_109736,c_116716,c_119848,c_120684,c_135193,c_135764,c_138485,c_144340,c_146180,c_149336,c_168558,c_169480,c_204736,c_217473,c_230730,c_231718,c_241025,c_251398,c_257149,c_258677]) ).
tcf(c_259564,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c11 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_259563]) ).
tcf(c_259680,plain,
( ( iPr_def_22 = iPr_def_25 )
| ~ iPr_def_11
| ( sk_c12 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_259564,c_3305]) ).
tcf(c_259760,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_259564,c_736]) ).
tcf(c_259770,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_259760,c_30242]) ).
tcf(c_259955,plain,
( ( iPr_def_22 = iPr_def_25 )
| ~ iPr_def_11
| ( sk_c12 != identity ) ),
inference(ground_joinability,[status(thm)],[c_259680,c_735,c_30394]) ).
tcf(c_260150,plain,
iPr_def_22 = iPr_def_25,
inference(global_subsumption_just,[status(thm)],[c_259267,c_177,c_815,c_818,c_736,c_740,c_741,c_742,c_1880,c_1885,c_1987,c_2680,c_4542,c_4543,c_4544,c_4638,c_4639,c_4929,c_4934,c_5212,c_6705,c_9047,c_12715,c_18623,c_25839,c_26203,c_31873,c_31929,c_41192,c_41816,c_50138,c_60331,c_62565,c_68924,c_68925,c_71211,c_87049,c_87185,c_87194,c_87609,c_88684,c_89478,c_94487,c_99291,c_101044,c_101192,c_101260,c_103463,c_104036,c_105397,c_109736,c_116716,c_119848,c_120684,c_135193,c_135764,c_138485,c_146180,c_146994,c_149336,c_168534,c_168558,c_168989,c_169480,c_170776,c_170777,c_204736,c_217473,c_230730,c_231718,c_241025,c_251398,c_257149,c_258677,c_258778,c_259770,c_259955]) ).
tcf(c_260346,plain,
inverse(iPr_def_22) = sk_c4,
inference(demodulation,[status(thm)],[c_29446,c_260150]) ).
tcf(c_260347,plain,
multiply(sk_c4,iPr_def_22) = identity,
inference(demodulation,[status(thm)],[c_29189,c_260150]) ).
tcf(c_260397,plain,
multiply(iPr_def_22,iPr_def_26) = sk_c12,
inference(demodulation,[status(thm)],[c_6390,c_260150]) ).
tcf(c_261209,plain,
( ( iPr_def_26 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_258413,c_798]) ).
tcf(c_261212,plain,
( ( iPr_def_29 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_258413,c_785]) ).
tcf(c_261213,plain,
( ( iPr_def_29 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_258413,c_784]) ).
tcf(c_261410,plain,
( ( sk_c12 = iPr_def_30 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_261209,c_177,c_815,c_818,c_736,c_740,c_741,c_742,c_743,c_1193,c_1746,c_1880,c_1885,c_1987,c_2680,c_2978,c_4542,c_4543,c_4544,c_4638,c_4639,c_4929,c_4934,c_4957,c_6705,c_11656,c_14746,c_18623,c_25839,c_26203,c_30268,c_31871,c_31929,c_41192,c_42197,c_60331,c_62565,c_68924,c_68925,c_71211,c_87049,c_87185,c_87609,c_88684,c_89478,c_94487,c_99291,c_101044,c_101192,c_101260,c_103463,c_104036,c_105397,c_109736,c_116716,c_119848,c_120684,c_135764,c_136158,c_138029,c_138485,c_149336,c_149918,c_152464,c_164671,c_168534,c_168989,c_169480,c_170776,c_170777,c_202022,c_217938,c_230543,c_231725,c_239372,c_251398,c_255280,c_257149,c_258413]) ).
tcf(c_261411,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c12 = iPr_def_30 ) ),
inference(renaming,[status(thm)],[c_261410]) ).
tcf(c_262218,plain,
( ( sk_c11 = iPr_def_23 )
| ( iPr_def_20 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_261212,c_177,c_815,c_818,c_740,c_741,c_1193,c_4542,c_4543,c_4544,c_4957,c_9220,c_11656,c_60331,c_62565,c_68924,c_68925,c_71211,c_87049,c_87185,c_87194,c_87609,c_101044,c_104036,c_109736,c_116716,c_119848,c_120684,c_135764,c_136158,c_138485,c_144340,c_149336,c_152464,c_164671,c_169480,c_202022,c_217938,c_230543,c_231725,c_239372,c_251398,c_255280,c_257149]) ).
tcf(c_262219,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c11 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_262218]) ).
tcf(c_262315,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c12 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_262219,c_3305]) ).
tcf(c_262383,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_262219,c_736]) ).
tcf(c_262395,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_262383,c_30242]) ).
tcf(c_262540,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c12 != identity ) ),
inference(ground_joinability,[status(thm)],[c_262315,c_735,c_30394]) ).
tcf(c_262582,plain,
iPr_def_20 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_261213,c_177,c_815,c_818,c_736,c_740,c_741,c_743,c_1746,c_1880,c_1885,c_1987,c_2680,c_2978,c_4542,c_4543,c_4544,c_4638,c_4639,c_4929,c_4934,c_4957,c_6705,c_11656,c_18623,c_26203,c_27467,c_41192,c_60331,c_62565,c_68924,c_68925,c_71211,c_87049,c_87185,c_87609,c_88684,c_89495,c_94669,c_94672,c_99291,c_101044,c_104036,c_105397,c_109736,c_116716,c_119848,c_120684,c_135764,c_136158,c_138485,c_149336,c_152464,c_163605,c_164671,c_168534,c_169480,c_202022,c_217938,c_230543,c_231717,c_239372,c_251398,c_252074,c_255280,c_256009,c_257149,c_258413,c_261411,c_262395,c_262540]) ).
tcf(c_262594,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_260346,c_262582]) ).
tcf(c_262595,plain,
multiply(iPr_def_20,iPr_def_26) = sk_c12,
inference(demodulation,[status(thm)],[c_260397,c_262582]) ).
tcf(c_262596,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(demodulation,[status(thm)],[c_260347,c_262582]) ).
tcf(c_262598,plain,
iPr_def_20 = iPr_def_25,
inference(demodulation,[status(thm)],[c_260150,c_262582]) ).
tcf(c_262685,plain,
( ( identity = iPr_def_20 )
| ( multiply(iPr_def_27,iPr_def_27) = identity ) ),
inference(demodulation,[status(thm)],[c_108303,c_262582]) ).
tcf(c_262769,plain,
( ( identity = iPr_def_20 )
| ( sk_c11 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_55798,c_262582]) ).
tcf(c_262776,plain,
( ( identity = iPr_def_30 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_55864,c_262582]) ).
tcf(c_262795,plain,
( ( iPr_def_28 = iPr_def_29 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_32928,c_262582]) ).
tcf(c_262797,plain,
( ( identity = iPr_def_20 )
| ( sk_c12 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_31874,c_262582]) ).
tcf(c_262798,plain,
( ( identity = iPr_def_20 )
| ( sk_c11 = iPr_def_28 ) ),
inference(demodulation,[status(thm)],[c_31873,c_262582]) ).
tcf(c_262799,plain,
( ( identity = iPr_def_20 )
| ( sk_c11 = iPr_def_29 ) ),
inference(demodulation,[status(thm)],[c_31872,c_262582]) ).
tcf(c_262800,plain,
( ( identity = iPr_def_20 )
| ( sk_c12 = iPr_def_30 ) ),
inference(demodulation,[status(thm)],[c_31871,c_262582]) ).
tcf(c_264145,plain,
( ( identity = iPr_def_20 )
| ~ iPr_def_14
| ( sk_c11 != sk_c12 )
| ( inverse(inverse(iPr_def_17)) != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_262797,c_116104]) ).
tcf(c_264370,plain,
( ( identity = iPr_def_20 )
| ~ iPr_def_14
| ( sk_c11 != sk_c12 ) ),
inference(ground_joinability,[status(thm)],[c_264145,c_729,c_50516]) ).
tcf(c_269347,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c12 )
| ( sk_c12 != inverse(identity) )
| ( inverse(X0) != inverse(identity) ) ),
inference(instantiation,[status(thm)],[c_87217]) ).
tcf(c_269348,plain,
( ( inverse(sk_c12) = sk_c12 )
| ( sk_c12 != inverse(identity) )
| ( inverse(sk_c12) != inverse(identity) ) ),
inference(instantiation,[status(thm)],[c_269347]) ).
tcf(c_269926,plain,
sk_c11 = iPr_def_23,
inference(global_subsumption_just,[status(thm)],[c_8004,c_177,c_815,c_818,c_740,c_743,c_765,c_1746,c_2680,c_3612,c_5979,c_7328,c_9220,c_14855,c_21805,c_25839,c_27467,c_39611,c_41192,c_68916,c_87024,c_87049,c_87057,c_87066,c_87185,c_87609,c_87642,c_87688,c_87888,c_87889,c_88489,c_89493,c_89495,c_90384,c_91213,c_91214,c_91441,c_91655,c_94654,c_94658,c_96309,c_96310,c_101399,c_103811,c_109190,c_110452,c_116716,c_120684,c_121358,c_121927,c_132747,c_139076,c_141670,c_144334,c_154090,c_192918,c_193781,c_251398,c_252074,c_254183,c_256009,c_257149,c_257421,c_269348]) ).
tcf(c_269948,plain,
( ( iPr_def_23 = iPr_def_26 )
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_205228,c_269926]) ).
tcf(c_269953,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( iPr_def_23 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_196381,c_269926]) ).
tcf(c_269999,plain,
( ~ iPr_def_11
| ( sk_c12 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_3305,c_269926]) ).
tcf(c_270043,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_23,X0)) = multiply(iPr_def_24,X0),
inference(demodulation,[status(thm)],[c_4113,c_269926]) ).
tcf(c_270097,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c12 )
| ( multiply(X0,sk_c12) != iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_748,c_269926]) ).
tcf(c_270098,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != iPr_def_23 )
| ( multiply(X0,iPr_def_23) != sk_c12 ) ),
inference(demodulation,[status(thm)],[c_747,c_269926]) ).
tcf(c_270108,plain,
( ( iPr_def_23 = iPr_def_29 )
| ( sk_c12 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_782,c_269926]) ).
tcf(c_270121,plain,
multiply(sk_c5,iPr_def_23) = iPr_def_24,
inference(demodulation,[status(thm)],[c_736,c_269926]) ).
tcf(c_270124,plain,
multiply(iPr_def_23,sk_c12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_727,c_269926]) ).
tcf(c_270229,plain,
! [X0: $i] : multiply(iPr_def_24,X0) = X0,
inference(light_normalisation,[status(thm)],[c_270043,c_30246]) ).
tcf(c_270338,plain,
( ~ iPr_def_11
| ( sk_c12 != identity ) ),
inference(ground_joinability,[status(thm)],[c_269999,c_735,c_30394]) ).
tcf(c_270404,plain,
identity = iPr_def_24,
inference(demodulation,[status(thm)],[c_30242,c_270121]) ).
tcf(c_270410,plain,
multiply(sk_c4,iPr_def_20) = iPr_def_24,
inference(demodulation,[status(thm)],[c_262596,c_270404]) ).
tcf(c_270492,plain,
inverse(iPr_def_24) = iPr_def_24,
inference(demodulation,[status(thm)],[c_27467,c_270404]) ).
tcf(c_270493,plain,
! [X0: $i] : multiply(X0,iPr_def_24) = X0,
inference(demodulation,[status(thm)],[c_27433,c_270404]) ).
tcf(c_270927,plain,
iPr_def_23 = iPr_def_26,
inference(global_subsumption_just,[status(thm)],[c_269948,c_815,c_818,c_740,c_741,c_2475,c_4542,c_4543,c_4544,c_5327,c_25839,c_41192,c_62565,c_67451,c_68997,c_87003,c_87006,c_87029,c_89495,c_89982,c_94669,c_94672,c_94689,c_96310,c_97792,c_101044,c_101043,c_101515,c_101516,c_104036,c_109739,c_116716,c_119848,c_120684,c_125763,c_135804,c_143908,c_149336,c_150145,c_159034,c_159594,c_166407,c_169480,c_175706,c_178059,c_181754,c_208721,c_220254,c_224278,c_251398,c_257149,c_269953]) ).
tcf(c_270939,plain,
multiply(iPr_def_20,iPr_def_23) = sk_c12,
inference(demodulation,[status(thm)],[c_262595,c_270927]) ).
tcf(c_271157,plain,
sk_c12 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_270108,c_177,c_815,c_818,c_727,c_743,c_1746,c_2680,c_3612,c_6395,c_6396,c_8465,c_10358,c_21867,c_24818,c_25839,c_27467,c_39613,c_68916,c_87024,c_87049,c_87066,c_87185,c_87609,c_87688,c_87888,c_87889,c_88489,c_91441,c_91657,c_103221,c_103225,c_103226,c_103811,c_109190,c_110452,c_116716,c_120684,c_121927,c_136114,c_139078,c_141670,c_145912,c_154090,c_192956,c_193781,c_251398,c_251539,c_252074,c_254183,c_256009,c_257149,c_257421,c_269348]) ).
tcf(c_271502,plain,
multiply(iPr_def_23,iPr_def_20) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_270124,c_271157]) ).
tcf(c_271725,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_270097,c_741,c_1905,c_3527,c_3512,c_4543,c_4544,c_9415,c_9782,c_12536,c_25839,c_27467,c_39610,c_39609,c_41192,c_49755,c_60331,c_71211,c_77804,c_87035,c_87194,c_87429,c_89495,c_94654,c_94658,c_101044,c_101043,c_104050,c_131408,c_134211,c_142071,c_142089,c_142083,c_150786,c_151394,c_256009]) ).
tcf(c_271831,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_270098,c_31872,c_31929,c_89478,c_103432,c_103439,c_139054,c_139077,c_270338]) ).
tcf(c_271975,plain,
multiply(iPr_def_20,iPr_def_23) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_270939,c_271157]) ).
tcf(c_271976,plain,
multiply(inverse(iPr_def_20),iPr_def_20) = iPr_def_23,
inference(superposition,[status(thm)],[c_271975,c_25008]) ).
tcf(c_271979,plain,
iPr_def_23 = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_271976,c_262594,c_270410]) ).
tcf(c_271988,plain,
! [X0: $i] : multiply(X0,iPr_def_23) = X0,
inference(demodulation,[status(thm)],[c_270493,c_271979]) ).
tcf(c_271997,plain,
! [X0: $i] : multiply(iPr_def_23,X0) = X0,
inference(demodulation,[status(thm)],[c_270229,c_271979]) ).
tcf(c_272003,plain,
inverse(iPr_def_23) = iPr_def_23,
inference(demodulation,[status(thm)],[c_270492,c_271979]) ).
tcf(c_272004,plain,
identity = iPr_def_23,
inference(demodulation,[status(thm)],[c_270404,c_271979]) ).
tcf(c_272026,plain,
iPr_def_15 = iPr_def_20,
inference(demodulation,[status(thm)],[c_271502,c_271997]) ).
tcf(c_272034,plain,
sk_c12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_271157,c_272026]) ).
tcf(c_272042,plain,
inverse(iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_262594,c_272026]) ).
tcf(c_272044,plain,
iPr_def_15 = iPr_def_25,
inference(demodulation,[status(thm)],[c_262598,c_272026]) ).
tcf(c_272454,plain,
identity = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_262685,c_177,c_815,c_818,c_727,c_740,c_743,c_802,c_1511,c_1542,c_1543,c_1584,c_1746,c_1885,c_2680,c_3108,c_3417,c_3671,c_5979,c_6395,c_6396,c_22236,c_24814,c_24815,c_24818,c_25836,c_25839,c_27467,c_31929,c_32379,c_41192,c_68916,c_70762,c_75039,c_87024,c_87049,c_87057,c_87066,c_87185,c_87187,c_87493,c_87609,c_87642,c_88489,c_88747,c_89478,c_89493,c_89495,c_90384,c_90600,c_91213,c_91441,c_91655,c_91657,c_94654,c_94658,c_101046,c_101399,c_103221,c_103225,c_103226,c_103432,c_103439,c_103811,c_109190,c_109736,c_110853,c_113465,c_116716,c_120684,c_121358,c_133982,c_138033,c_138032,c_138031,c_138023,c_141670,c_145829,c_154090,c_193781,c_251398,c_252074,c_254183,c_256009,c_257149,c_257421,c_262800,c_262799,c_262798,c_262795,c_262776,c_262769,c_264370,c_269348,c_271725,c_271831,c_272034]) ).
tcf(c_272456,plain,
identity = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_272454,c_272004,c_272026]) ).
tcf(c_272457,plain,
iPr_def_15 = iPr_def_23,
inference(demodulation,[status(thm)],[c_272004,c_272456]) ).
tcf(c_272462,plain,
inverse(iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_272003,c_272457]) ).
tcf(c_272475,plain,
sk_c11 = iPr_def_15,
inference(demodulation,[status(thm)],[c_269926,c_272457]) ).
tcf(c_272490,plain,
sk_c4 = iPr_def_15,
inference(demodulation,[status(thm)],[c_272042,c_272462]) ).
tcf(c_272783,plain,
! [X0: $i] : multiply(X0,iPr_def_15) = X0,
inference(light_normalisation,[status(thm)],[c_271988,c_272457]) ).
tcf(c_272788,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_15,
inference(superposition,[status(thm)],[c_272783,c_25008]) ).
tcf(c_275521,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_15,
inference(superposition,[status(thm)],[c_25321,c_272788]) ).
tcf(c_276669,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c11) != sk_c12 )
| ( inverse(inverse(identity)) != inverse(X0) )
| ( inverse(X0) != inverse(identity) ) ),
inference(global_subsumption_just,[status(thm)],[c_3703,c_178,c_815,c_727,c_736,c_737,c_741,c_1885,c_1905,c_1987,c_2680,c_3527,c_3512,c_3612,c_3703,c_4528,c_4529,c_4530,c_4543,c_4544,c_4638,c_4639,c_4929,c_4934,c_6395,c_6396,c_6402,c_6702,c_9415,c_9782,c_12536,c_18623,c_24818,c_25839,c_27467,c_31872,c_31929,c_35059,c_39610,c_39609,c_41192,c_49755,c_50138,c_53149,c_53150,c_60331,c_62560,c_71211,c_73011,c_77804,c_87035,c_87194,c_87267,c_87429,c_88456,c_88457,c_89478,c_89495,c_89594,c_89611,c_92393,c_92395,c_94654,c_94658,c_99291,c_101044,c_101043,c_103221,c_103225,c_103226,c_103432,c_103439,c_104050,c_105397,c_110452,c_131408,c_134211,c_139054,c_139077,c_142071,c_142089,c_142083,c_146994,c_150786,c_151394,c_167388,c_168534,c_256009,c_270404,c_270338,c_272044,c_272034,c_272490,c_272475,c_275521]) ).
tcf(c_276670,plain,
! [X0: $i] :
( ( inverse(X0) != inverse(identity) )
| ( inverse(inverse(identity)) != inverse(X0) )
| ( multiply(inverse(X0),sk_c11) != sk_c12 ) ),
inference(renaming,[status(thm)],[c_276669]) ).
tcf(c_276672,plain,
! [X0: $i] :
( ( inverse(X0) != iPr_def_15 )
| ( multiply(inverse(X0),iPr_def_15) != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_276670,c_272034,c_272456,c_272462,c_272475]) ).
tcf(c_276673,plain,
! [X0: $i] : inverse(X0) != iPr_def_15,
inference(demodulation,[status(thm)],[c_276672,c_272783]) ).
tcf(c_276674,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_272462,c_276673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Wed Sep 23 14:27:11 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.08/0.34
% 0.08/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.34
% 0.08/0.34 % Detected problem language: tptp
% 0.08/0.35 % Proving...
% 35.20/7.04 % SZS status Started for theBenchmark.p
% 35.20/7.04 ERROR - "ProverProcess:heur/330959:296.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( sk_c11 != sk_c12 | ~iPr_def_14 )")
% 35.20/7.04 Fatal error: exception Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( sk_c11 != sk_c12 | ~iPr_def_14 )")
% 35.20/7.04 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_af_restrict_to_split_sk false --abstr_ref_prep false --abstr_ref_sig_restrict funpre --abstr_ref_under "[]" --abstr_ref_until_sat false --add_important_lit false --bc_imp_inh "[conj_cone]" --brand_transform false --clause_weak_htbl true --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --gc_record_bc_elim false --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_sos_phase true --inst_sos_sth_lit_sel "[+prop;+non_prol_conj_symb;-eq;+ground;-num_var]" --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --large_theory_mode true --lt_threshold 2000 --min_unsat_core false --non_eq_to_eq false --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sem_filter_out false --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessed_out false --preprocessed_stats false --preprocessing_flag true --prolific_symb_bound 256 --prop_impl_unit "[]" --prop_impl_unit_size 0 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_orphan_elimination true --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300. --res_to_prop_solver active --reset_solvers false --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --soft_assumptions false --soft_lemma_size 3 --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[BwDemod;BwUnitSubsAndRes]" --sup_full_fw "[FwDemodLightNormLoopTriv;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[BwUnitSubsAndRes]" --sup_immed_bw_main "[BwUnitSubsAndRes]" --sup_immed_fw_immed "[ACNormalisation;FwDemodLightNormLoopTriv;FwUnitSubsAndRes]" --sup_immed_fw_main "[FwUnitSubsAndRes]" --sup_immed_triv "[]" --sup_indices_passive "[LightNormIndex;UnitSubsumptionIndex]" --sup_input_bw "[BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]" --sup_input_fw "[ACNormalisation;FwDemodLightNormLoopTriv;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --out_options none --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 98.67" --time_out_real 296.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_es2dleu9/p89gn8k7 2>> /export/starexec/sandbox2/tmp/iprover_out_es2dleu9/p89gn8k7_error
% 35.20/7.04 % SZS status Unsatisfiable for theBenchmark.p
% 35.20/7.04
% 35.20/7.04 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.20/7.04
% 35.20/7.04 % ------ iProver source info
% 35.20/7.04
% 35.20/7.04 % git: date: 2026-07-19 20:42:38 +0200
% 35.20/7.04 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.20/7.04 % git: non_committed_changes: false
% 35.20/7.04
% 35.20/7.04 % ------ Parsing...% successful
% 35.20/7.04
% 35.20/7.04
% 35.20/7.04 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.20/7.04
% 35.20/7.04 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 35.20/7.04
% 35.20/7.04 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.20/7.04
% 35.20/7.04 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 35.20/7.04 % ------ Proving...
% 35.20/7.04 % ------ Problem Properties
% 35.20/7.04
% 35.20/7.04 %
% 35.20/7.04 % clauses 85
% 35.20/7.04 % conjectures 66
% 35.20/7.04 % EPR 61
% 35.20/7.04 % Horn 24
% 35.20/7.04 % unary 19
% 35.20/7.04 % binary 60
% 35.20/7.04 % lits 162
% 35.20/7.04 % lits eq 152
% 35.20/7.04 % fd_pure 0
% 35.20/7.04 % fd_pseudo 0
% 35.20/7.04 % fd_cond 0
% 35.20/7.04 % fd_pseudo_cond 0
% 35.20/7.04 % AC symbols 0
% 35.20/7.04
% 35.20/7.04 % ------ Schedule dynamic 5 is on
% 35.20/7.04
% 35.20/7.04 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 35.20/7.04
% 35.20/7.04
% 35.20/7.04 % ------
% 35.20/7.04 % Current options:
% 35.20/7.04 % ------
% 35.20/7.04
% 35.20/7.04
% 35.20/7.04 %
% 35.20/7.04
% 35.20/7.04 % ------ Proving...
% 35.20/7.04 %
% 35.20/7.04
% 35.20/7.04 % SZS status Unsatisfiable for theBenchmark.p
% 35.20/7.04
% 35.20/7.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.20/7.05
% 35.20/7.05
%------------------------------------------------------------------------------