%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP372-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:26 PM UTC 2026
% Result : Unsatisfiable 29.37s 4.82s
% Output : CNFRefutation 29.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 45
% Syntax : Number of formulae : 461 ( 117 unt; 12 def)
% Number of atoms : 1783 ( 901 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 754 ( 254 ~; 500 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 105 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = inverse(sk_c3)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c4)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f14]) ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f26]) ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f34]) ).
fof(f38,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f64,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != multiply(sk_c8,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != multiply(sk_c8,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f77]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_474,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_476,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_477,definition,
iPr_def_13 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_478,definition,
iPr_def_14 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,definition,
iPr_def_15 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_483,definition,
iPr_def_19 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_484,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c7 )
| ( iPr_def_13 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_476,c_479,c_478,c_477]) ).
tcf(c_490,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_491,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_474]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_494,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_127,c_481,c_480]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_126,c_482]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_125,c_483]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124,c_484]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_123,c_485]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_505,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_508,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_487]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_488]) ).
tcf(c_520,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_521,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_522,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_524,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_527,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_528,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_530,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_531,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_794,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_498,c_496]) ).
tcf(c_821,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_498,c_477]) ).
tcf(c_834,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c8,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_499,c_478]) ).
tcf(c_880,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c8,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_505,c_478]) ).
tcf(c_899,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_506,c_494]) ).
tcf(c_926,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c8,iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_508,c_477]) ).
tcf(c_951,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_14) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_509,c_477]) ).
tcf(c_953,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_509,c_497]) ).
tcf(c_981,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_498,c_486]) ).
tcf(c_999,plain,
multiply(iPr_def_15,sk_c8) = identity,
inference(superposition,[status(thm)],[c_479,c_90]) ).
tcf(c_1000,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_484,c_90]) ).
tcf(c_1001,plain,
multiply(iPr_def_16,sk_c4) = identity,
inference(superposition,[status(thm)],[c_480,c_90]) ).
tcf(c_1002,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_487,c_90]) ).
tcf(c_1003,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_481,c_90]) ).
tcf(c_1007,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1020,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_510,c_508]) ).
tcf(c_1044,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1007]) ).
tcf(c_1045,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_530]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1103,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_512,c_477]) ).
tcf(c_1122,plain,
( ( sk_c7 = iPr_def_15 )
| ( iPr_def_15 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1044]) ).
tcf(c_1180,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1053]) ).
tcf(c_1181,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1007]) ).
tcf(c_1189,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_515,c_488]) ).
tcf(c_1195,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_515,c_477]) ).
tcf(c_1213,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1053]) ).
tcf(c_1214,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1007]) ).
tcf(c_1218,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_24 )
| ( X0 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1053]) ).
tcf(c_1233,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c8 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_516,c_514]) ).
tcf(c_1234,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_516,c_486]) ).
tcf(c_1238,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_516,c_477]) ).
tcf(c_1386,plain,
iPr_def_17 = iPr_def_17,
inference(instantiation,[status(thm)],[c_530]) ).
tcf(c_1418,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_520,c_477]) ).
tcf(c_1465,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1483,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_21 )
| ( X0 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_1053]) ).
tcf(c_1484,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_21 )
| ( X0 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_1007]) ).
tcf(c_1504,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_521,c_486]) ).
tcf(c_1576,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_522,c_486]) ).
tcf(c_1580,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c8,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_522,c_477]) ).
tcf(c_1644,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1709,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c8,iPr_def_15) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_524,c_477]) ).
tcf(c_1713,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_524,c_494]) ).
tcf(c_1776,plain,
iPr_def_21 = iPr_def_21,
inference(instantiation,[status(thm)],[c_530]) ).
tcf(c_1963,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_15) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_527,c_477]) ).
tcf(c_2076,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_528,c_526]) ).
tcf(c_2128,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_2162,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c8,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_529,c_478]) ).
tcf(c_2202,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_477,c_491]) ).
tcf(c_2203,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_22 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_486,c_491]) ).
tcf(c_2227,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_22 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2203,c_481]) ).
tcf(c_2231,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( sk_c7 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2202,c_479]) ).
tcf(c_2401,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_2409,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_21 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_485,c_493]) ).
tcf(c_2411,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_488,c_493]) ).
tcf(c_2423,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2411,c_487]) ).
tcf(c_2431,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_21 )
| ( sk_c8 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2409,c_484]) ).
tcf(c_2482,plain,
( ~ iPr_def_12
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c8,iPr_def_21) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_485,c_490]) ).
tcf(c_2504,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_20 )
| ( multiply(sk_c8,iPr_def_21) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2482,c_484]) ).
tcf(c_2568,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_22 )
| ( sk_c7 != iPr_def_15 )
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_505,c_489]) ).
tcf(c_2698,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_477,c_91]) ).
tcf(c_2699,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_485,c_91]) ).
tcf(c_2701,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_482,c_91]) ).
tcf(c_2702,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_488,c_91]) ).
tcf(c_2706,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2708,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_999,c_91]) ).
tcf(c_2709,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1000,c_91]) ).
tcf(c_2710,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1001,c_91]) ).
tcf(c_2711,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1002,c_91]) ).
tcf(c_2712,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1003,c_91]) ).
tcf(c_2717,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2712,c_89]) ).
tcf(c_2718,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2711,c_89]) ).
tcf(c_2719,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2710,c_89]) ).
tcf(c_2720,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2709,c_89]) ).
tcf(c_2721,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2708,c_89]) ).
tcf(c_2797,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_530]) ).
tcf(c_2946,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_899,c_479]) ).
tcf(c_2947,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_899,c_477]) ).
tcf(c_3226,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_15,iPr_def_23) = identity ) ),
inference(superposition,[status(thm)],[c_1233,c_999]) ).
tcf(c_3271,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_21 = X0 )
| ( iPr_def_21 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_3824,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_2128]) ).
tcf(c_3858,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( inverse(iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1713,c_479]) ).
tcf(c_3859,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1713,c_477]) ).
tcf(c_4407,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(sk_c8,iPr_def_15) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2076,c_477]) ).
tcf(c_4527,plain,
multiply(iPr_def_17,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_486,c_2717]) ).
tcf(c_4545,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_488,c_2718]) ).
tcf(c_4556,plain,
multiply(iPr_def_16,iPr_def_18) = sk_c8,
inference(superposition,[status(thm)],[c_482,c_2719]) ).
tcf(c_4561,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_485,c_2720]) ).
tcf(c_5134,plain,
multiply(iPr_def_15,iPr_def_13) = sk_c7,
inference(superposition,[status(thm)],[c_477,c_2721]) ).
tcf(c_5135,plain,
multiply(iPr_def_15,iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_483,c_2721]) ).
tcf(c_5136,plain,
multiply(iPr_def_15,iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_478,c_2721]) ).
tcf(c_5156,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_15,multiply(iPr_def_23,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_515,c_2721]) ).
tcf(c_5157,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_15,multiply(iPr_def_23,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_512,c_2721]) ).
tcf(c_5308,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_19,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_5135,c_91]) ).
tcf(c_5310,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_14,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_5136,c_91]) ).
tcf(c_5645,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_15,iPr_def_14) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_880,c_2721]) ).
tcf(c_5646,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5645,c_5136]) ).
tcf(c_5994,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_15,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_951,c_2721]) ).
tcf(c_5995,plain,
( ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5994,c_5134]) ).
tcf(c_6515,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_981,c_2717]) ).
tcf(c_6516,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6515,c_4527]) ).
tcf(c_7193,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_518,c_1103]) ).
tcf(c_7206,plain,
( ( sk_c8 = iPr_def_16 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_7193,c_4545]) ).
tcf(c_7420,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1189,c_2718]) ).
tcf(c_7421,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_7420,c_4545]) ).
tcf(c_7797,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_521,c_1195]) ).
tcf(c_7812,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_7797,c_4545]) ).
tcf(c_7917,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1234,c_2717]) ).
tcf(c_7918,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c8 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_7917,c_4527]) ).
tcf(c_8133,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_7812,c_1238]) ).
tcf(c_8134,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_7812,c_7206]) ).
tcf(c_8155,plain,
( ( sk_c7 = iPr_def_17 )
| ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_7812,c_821]) ).
tcf(c_8173,plain,
( ( sk_c8 = iPr_def_13 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_7812,c_479]) ).
tcf(c_8198,plain,
( ( sk_c7 = iPr_def_17 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_8155,c_4561]) ).
tcf(c_8228,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_8133,c_4561]) ).
tcf(c_8988,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1504,c_2717]) ).
tcf(c_8989,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_8988,c_4527]) ).
tcf(c_9045,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1576,c_2717]) ).
tcf(c_9046,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_9045,c_4527]) ).
tcf(c_9994,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_15,iPr_def_14) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2162,c_2721]) ).
tcf(c_9995,plain,
( ( sk_c6 = iPr_def_13 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9994,c_5136]) ).
tcf(c_10525,plain,
! [X0: $i] :
( ( iPr_def_21 = X0 )
| ( iPr_def_21 != iPr_def_21 )
| ( X0 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_3271]) ).
tcf(c_11484,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_15,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_8134,c_999]) ).
tcf(c_11508,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_11484,c_5134]) ).
tcf(c_12001,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_24,sk_c7),
inference(superposition,[status(thm)],[c_477,c_2702]) ).
tcf(c_12440,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8228,c_1580]) ).
tcf(c_12442,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8228,c_1418]) ).
tcf(c_12445,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8228,c_7812]) ).
tcf(c_12448,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8228,c_7206]) ).
tcf(c_12559,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_12442,c_4545]) ).
tcf(c_12562,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_12440,c_4545]) ).
tcf(c_13927,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_2947,c_491]) ).
tcf(c_14029,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_15 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_11508,c_527]) ).
tcf(c_14031,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_15 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_11508,c_524]) ).
tcf(c_14040,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_14 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_11508,c_509]) ).
tcf(c_14042,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_14 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_11508,c_506]) ).
tcf(c_14149,plain,
( ( sk_c7 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_21 )
| ( sk_c7 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_1484]) ).
tcf(c_14183,plain,
( ( iPr_def_17 = iPr_def_14 )
| ( iPr_def_17 != iPr_def_17 )
| ( iPr_def_14 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_3824]) ).
tcf(c_14187,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1465]) ).
tcf(c_14192,plain,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_15 != iPr_def_17 )
| ( sk_c7 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1180]) ).
tcf(c_14458,plain,
( ( sk_c7 = iPr_def_21 )
| ( iPr_def_21 != iPr_def_17 )
| ( sk_c7 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1181]) ).
tcf(c_14716,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( multiply(iPr_def_15,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_12445,c_999]) ).
tcf(c_14741,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_14716,c_5134]) ).
tcf(c_15155,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( multiply(iPr_def_15,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_12448,c_999]) ).
tcf(c_15180,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_15155,c_5134]) ).
tcf(c_15633,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_1007]) ).
tcf(c_15816,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_12562,c_12559]) ).
tcf(c_15828,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_12562,c_8198]) ).
tcf(c_17184,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_14741,c_522]) ).
tcf(c_17186,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_14741,c_520]) ).
tcf(c_17568,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( identity = iPr_def_14 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_15180,c_509]) ).
tcf(c_18106,plain,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_17 != iPr_def_14 )
| ( sk_c7 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1213]) ).
tcf(c_18124,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_2401]) ).
tcf(c_18134,plain,
( ( sk_c7 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_14 )
| ( sk_c7 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1214]) ).
tcf(c_19019,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != iPr_def_21 )
| ( X0 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_2401]) ).
tcf(c_19678,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_15,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_15816,c_999]) ).
tcf(c_19705,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_19678,c_5134]) ).
tcf(c_20227,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1644]) ).
tcf(c_21588,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( multiply(iPr_def_15,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_15828,c_999]) ).
tcf(c_21613,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_21588,c_5134]) ).
tcf(c_24009,plain,
( ( identity = sk_c7 )
| ( identity != iPr_def_21 )
| ( sk_c7 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_1483]) ).
tcf(c_24467,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_19705,c_2076]) ).
tcf(c_24469,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_19705,c_794]) ).
tcf(c_24477,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_19705,c_520]) ).
tcf(c_25519,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_21613,c_522]) ).
tcf(c_25923,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_15,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_24467,c_89]) ).
tcf(c_25945,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_17,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_24469,c_89]) ).
tcf(c_26008,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2706,c_89]) ).
tcf(c_26052,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_26008]) ).
tcf(c_26053,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_26008]) ).
tcf(c_26075,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(inverse(sk_c8),iPr_def_14) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_834,c_26008]) ).
tcf(c_26144,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2721,c_26008]) ).
tcf(c_26145,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2720,c_26008]) ).
tcf(c_26146,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2719,c_26008]) ).
tcf(c_26202,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_26008,c_26008]) ).
tcf(c_26352,plain,
( ( sk_c6 = iPr_def_13 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_26075,c_479,c_5136]) ).
tcf(c_26658,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_26053,c_26202]) ).
tcf(c_26670,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_26658,c_2698]) ).
tcf(c_26681,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_26658,c_26052]) ).
tcf(c_26687,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_26670,c_477]) ).
tcf(c_27986,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_528,c_526]) ).
tcf(c_28157,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_477,c_491]) ).
tcf(c_28189,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( sk_c7 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_28157,c_479]) ).
tcf(c_28280,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_488,c_493]) ).
tcf(c_28288,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_28280,c_487]) ).
tcf(c_28354,plain,
( iPr_def_12
| ( iPr_def_13 != sk_c6 )
| ( iPr_def_14 != sk_c7 )
| ( iPr_def_15 != sk_c7 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_489,c_489,c_1045,c_1122,c_2231,c_2227,c_5646,c_26352]) ).
tcf(c_28355,negated_conjecture,
( iPr_def_12
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c7 )
| ( iPr_def_13 != sk_c6 ) ),
inference(renaming,[status(thm)],[c_28354]) ).
tcf(c_30070,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_26681,c_90]) ).
tcf(c_30129,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_15,sk_c8) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_4545,c_5156]) ).
tcf(c_30142,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_30129,c_999]) ).
tcf(c_30178,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_15,sk_c8) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_4545,c_5157]) ).
tcf(c_30191,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_30178,c_999]) ).
tcf(c_32362,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14031,c_14029]) ).
tcf(c_33028,plain,
( ( sk_c7 = identity )
| ( identity != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1044]) ).
tcf(c_35800,plain,
( ( iPr_def_21 = iPr_def_17 )
| ( iPr_def_21 != iPr_def_21 )
| ( iPr_def_17 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_10525]) ).
tcf(c_36039,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_30191,c_30142]) ).
tcf(c_36670,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_14042,c_14040]) ).
tcf(c_39278,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_15,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_32362,c_89]) ).
tcf(c_41940,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_36039,c_89]) ).
tcf(c_42541,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_3859,c_491]) ).
tcf(c_44408,plain,
( ( sk_c7 = iPr_def_21 )
| ( identity = iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_17184,c_1776,c_6516,c_14458,c_25519,c_35800]) ).
tcf(c_44409,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_44408]) ).
tcf(c_44761,plain,
( ( sk_c7 = iPr_def_19 )
| ( identity = iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_17186,c_14149,c_24477,c_44409]) ).
tcf(c_44762,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(renaming,[status(thm)],[c_44761]) ).
tcf(c_44824,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_44762,c_44409]) ).
tcf(c_49815,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_15)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_26144,c_490]) ).
tcf(c_49817,plain,
multiply(sk_c8,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_26144,c_90]) ).
tcf(c_49821,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_26144,c_26008]) ).
tcf(c_49822,plain,
multiply(sk_c8,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_26144,c_26658]) ).
tcf(c_49833,plain,
( ( identity = iPr_def_13 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1963,c_49817]) ).
tcf(c_49834,plain,
( ( identity = iPr_def_13 )
| ( sk_c8 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1709,c_49817]) ).
tcf(c_49943,plain,
multiply(sk_c4,identity) = multiply(iPr_def_18,iPr_def_15),
inference(superposition,[status(thm)],[c_49817,c_2701]) ).
tcf(c_49944,plain,
multiply(sk_c3,identity) = multiply(iPr_def_21,iPr_def_15),
inference(superposition,[status(thm)],[c_49817,c_2699]) ).
tcf(c_49945,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(superposition,[status(thm)],[c_49817,c_2721]) ).
tcf(c_52360,plain,
( ( identity = iPr_def_13 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_49833,c_479]) ).
tcf(c_52631,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_49834,c_49833]) ).
tcf(c_53209,plain,
inverse(iPr_def_15) = sk_c8,
inference(demodulation,[status(thm)],[c_49822,c_26658]) ).
tcf(c_53290,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(iPr_def_15) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_49821,c_490]) ).
tcf(c_53393,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_53290,c_53209]) ).
tcf(c_54408,plain,
( ( identity = iPr_def_17 )
| ( iPr_def_17 != sk_c7 )
| ( identity != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_18124]) ).
tcf(c_54411,plain,
( ( identity = iPr_def_14 )
| ( iPr_def_14 != iPr_def_17 )
| ( identity != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_14187]) ).
tcf(c_54417,plain,
( ( identity = sk_c7 )
| ( identity != iPr_def_17 )
| ( sk_c7 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1180]) ).
tcf(c_54421,plain,
( ( identity = sk_c7 )
| ( identity != iPr_def_24 )
| ( sk_c7 != iPr_def_24 ) ),
inference(instantiation,[status(thm)],[c_1218]) ).
tcf(c_58927,plain,
multiply(iPr_def_18,iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_49943,c_26658]) ).
tcf(c_58933,plain,
multiply(iPr_def_21,iPr_def_15) = sk_c3,
inference(demodulation,[status(thm)],[c_49944,c_26658]) ).
tcf(c_64666,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_4407,c_49817]) ).
tcf(c_64972,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( iPr_def_13 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_52631,c_36670]) ).
tcf(c_66776,plain,
multiply(sk_c6,identity) = multiply(iPr_def_15,iPr_def_14),
inference(superposition,[status(thm)],[c_26658,c_5310]) ).
tcf(c_66780,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_66776,c_5136]) ).
tcf(c_67248,plain,
( ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != identity )
| ( sk_c7 != identity ) ),
inference(instantiation,[status(thm)],[c_15633]) ).
tcf(c_67453,plain,
( ( sk_c8 = iPr_def_20 )
| ( identity = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_17568,c_953,c_1386,c_5995,c_8989,c_14183,c_18106,c_30142,c_54408,c_54411,c_54421]) ).
tcf(c_67454,plain,
( ( identity = iPr_def_14 )
| ( sk_c8 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_67453]) ).
tcf(c_67617,plain,
( ( identity = iPr_def_14 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_67454,c_479]) ).
tcf(c_70188,plain,
( ( identity = iPr_def_17 )
| ( iPr_def_17 != iPr_def_21 )
| ( identity != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_19019]) ).
tcf(c_71429,plain,
( ( iPr_def_14 = identity )
| ( iPr_def_14 != iPr_def_14 )
| ( identity != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_20227]) ).
tcf(c_76640,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_26145,c_26658]) ).
tcf(c_76799,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_76640,c_26658]) ).
tcf(c_76802,plain,
( ( identity = iPr_def_14 )
| ( sk_c3 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_67617,c_76799]) ).
tcf(c_76803,plain,
( ( identity = iPr_def_13 )
| ( sk_c3 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_52360,c_76799]) ).
tcf(c_76805,plain,
( ( sk_c3 = iPr_def_15 )
| ( sk_c8 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_8173,c_76799]) ).
tcf(c_78490,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_28189,c_2231,c_2227,c_5646,c_26352]) ).
tcf(c_78501,plain,
( ( iPr_def_19 = iPr_def_21 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_27986,c_78490]) ).
tcf(c_79826,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_28288,c_2431,c_2423,c_7421,c_7918]) ).
tcf(c_79828,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_79826,c_2431,c_8989,c_9046,c_79826]) ).
tcf(c_79830,plain,
( iPr_def_12
| ( sk_c6 != iPr_def_13 )
| ( sk_c7 != iPr_def_15 )
| ( sk_c7 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_28355,c_79828]) ).
tcf(c_81862,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_15,sk_c8) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_76805,c_485]) ).
tcf(c_81865,plain,
( ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_81862,c_999]) ).
tcf(c_82237,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_15,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_81865,c_999]) ).
tcf(c_82262,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_82237,c_5134]) ).
tcf(c_82929,plain,
sk_c7 = identity,
inference(global_subsumption_just,[status(thm)],[c_82262,c_1045,c_6516,c_21613,c_24009,c_33028,c_54417,c_70188,c_82262]) ).
tcf(c_82943,plain,
( ~ iPr_def_12
| ( sk_c8 != identity ) ),
inference(demodulation,[status(thm)],[c_53393,c_82929]) ).
tcf(c_82980,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_24,identity),
inference(demodulation,[status(thm)],[c_12001,c_82929]) ).
tcf(c_82991,plain,
! [X0: $i] : multiply(sk_c8,multiply(identity,X0)) = multiply(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_2698,c_82929]) ).
tcf(c_83027,plain,
( ( identity = iPr_def_14 )
| ( multiply(sk_c8,iPr_def_19) = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_926,c_82929]) ).
tcf(c_83030,plain,
multiply(iPr_def_15,iPr_def_13) = identity,
inference(demodulation,[status(thm)],[c_5134,c_82929]) ).
tcf(c_83034,plain,
multiply(iPr_def_17,iPr_def_22) = identity,
inference(demodulation,[status(thm)],[c_4527,c_82929]) ).
tcf(c_83038,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( identity != iPr_def_15 )
| ( identity != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_489,c_82929]) ).
tcf(c_83044,plain,
( ( identity = iPr_def_15 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_527,c_82929]) ).
tcf(c_83046,plain,
( ( identity = iPr_def_15 )
| ( sk_c5 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_525,c_82929]) ).
tcf(c_83056,plain,
( ( identity = iPr_def_14 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_511,c_82929]) ).
tcf(c_83061,plain,
( ( identity = iPr_def_14 )
| ( sk_c5 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_507,c_82929]) ).
tcf(c_83176,plain,
! [X0: $i] : multiply(sk_c8,X0) = multiply(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_82991,c_89]) ).
tcf(c_83223,plain,
multiply(iPr_def_13,sk_c6) = iPr_def_14,
inference(demodulation,[status(thm)],[c_478,c_83176]) ).
tcf(c_83225,plain,
multiply(iPr_def_13,sk_c5) = iPr_def_19,
inference(demodulation,[status(thm)],[c_483,c_83176]) ).
tcf(c_83237,plain,
multiply(iPr_def_13,iPr_def_15) = identity,
inference(demodulation,[status(thm)],[c_49817,c_83176]) ).
tcf(c_83245,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_13,iPr_def_22) = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_880,c_83176]) ).
tcf(c_83341,plain,
multiply(inverse(iPr_def_17),identity) = iPr_def_22,
inference(superposition,[status(thm)],[c_83034,c_26008]) ).
tcf(c_83574,plain,
( ( identity = iPr_def_15 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_83044,c_479]) ).
tcf(c_83575,plain,
( ( identity = iPr_def_15 )
| ( sk_c3 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_83574,c_76799]) ).
tcf(c_84324,plain,
multiply(inverse(iPr_def_13),identity) = iPr_def_15,
inference(superposition,[status(thm)],[c_83237,c_26008]) ).
tcf(c_84746,plain,
( ( identity = iPr_def_14 )
| ( multiply(iPr_def_13,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_83056,c_83223]) ).
tcf(c_84883,plain,
( ( identity = iPr_def_14 )
| ( multiply(iPr_def_13,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_83061,c_83225]) ).
tcf(c_85725,plain,
inverse(iPr_def_13) = iPr_def_15,
inference(demodulation,[status(thm)],[c_84324,c_26658]) ).
tcf(c_86032,plain,
multiply(sk_c1,iPr_def_13) = iPr_def_24,
inference(demodulation,[status(thm)],[c_82980,c_26658]) ).
tcf(c_86033,plain,
multiply(inverse(sk_c1),iPr_def_24) = iPr_def_13,
inference(superposition,[status(thm)],[c_86032,c_26008]) ).
tcf(c_86036,plain,
sk_c8 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_86033,c_487,c_4545]) ).
tcf(c_86040,plain,
( ~ iPr_def_12
| ( identity != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_82943,c_86036]) ).
tcf(c_86080,plain,
inverse(iPr_def_15) = iPr_def_13,
inference(demodulation,[status(thm)],[c_53209,c_86036]) ).
tcf(c_86122,plain,
multiply(iPr_def_16,iPr_def_18) = iPr_def_13,
inference(demodulation,[status(thm)],[c_4556,c_86036]) ).
tcf(c_86142,plain,
multiply(sk_c3,iPr_def_13) = iPr_def_21,
inference(demodulation,[status(thm)],[c_485,c_86036]) ).
tcf(c_86144,plain,
multiply(sk_c4,iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_482,c_86036]) ).
tcf(c_86672,plain,
( ( iPr_def_16 = iPr_def_20 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_52631,c_86040]) ).
tcf(c_86673,plain,
( ( iPr_def_19 = iPr_def_21 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_64666,c_86040]) ).
tcf(c_89801,plain,
multiply(sk_c4,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_26146,c_90]) ).
tcf(c_89805,plain,
multiply(sk_c4,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_26146,c_26658]) ).
tcf(c_89874,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(superposition,[status(thm)],[c_89801,c_2719]) ).
tcf(c_90625,plain,
inverse(iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_89805,c_26658]) ).
tcf(c_90632,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c4 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_3858,c_90625]) ).
tcf(c_90637,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c4 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_2946,c_90625]) ).
tcf(c_95020,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_25923,c_3226]) ).
tcf(c_95083,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_25945,c_83034]) ).
tcf(c_96935,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_19 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_95020,c_44824]) ).
tcf(c_98081,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_13 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_95083,c_64666]) ).
tcf(c_98384,plain,
iPr_def_19 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_96935,c_1020,c_2076,c_2568,c_78501,c_79828,c_79830,c_86673,c_98081]) ).
tcf(c_98416,plain,
multiply(sk_c3,iPr_def_13) = iPr_def_19,
inference(demodulation,[status(thm)],[c_86142,c_98384]) ).
tcf(c_98438,plain,
multiply(iPr_def_19,iPr_def_15) = sk_c3,
inference(demodulation,[status(thm)],[c_58933,c_98384]) ).
tcf(c_98526,plain,
( ( identity = iPr_def_15 )
| ( multiply(iPr_def_15,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_83575,c_98416]) ).
tcf(c_98534,plain,
( ( identity = iPr_def_13 )
| ( multiply(iPr_def_15,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_76803,c_98416]) ).
tcf(c_98535,plain,
( ( identity = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_76802,c_98416]) ).
tcf(c_98604,plain,
multiply(sk_c5,iPr_def_15) = multiply(iPr_def_15,sk_c3),
inference(superposition,[status(thm)],[c_98438,c_5308]) ).
tcf(c_99270,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_11
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_13927,c_9995,c_13927,c_78490]) ).
tcf(c_99272,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c4 != identity ) ),
inference(light_normalisation,[status(thm)],[c_99270,c_82929,c_90625]) ).
tcf(c_99289,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_11
| ( identity != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_90637,c_99272]) ).
tcf(c_100043,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_42541,c_9995,c_42541,c_78490]) ).
tcf(c_100045,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c4 != identity ) ),
inference(light_normalisation,[status(thm)],[c_100043,c_82929,c_90625]) ).
tcf(c_100067,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11
| ( identity != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_90632,c_100045]) ).
tcf(c_100240,plain,
( iPr_def_12
| ( identity != iPr_def_15 )
| ( identity != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(global_subsumption_just,[status(thm)],[c_83038,c_1045,c_1122,c_1386,c_2431,c_2797,c_6516,c_8989,c_9046,c_14183,c_14192,c_18134,c_21613,c_24009,c_33028,c_54417,c_67248,c_70188,c_71429,c_79826,c_79830,c_82262,c_83038,c_99289,c_100067]) ).
tcf(c_100258,plain,
( iPr_def_12
| ( sk_c6 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_22 )
| ( identity != iPr_def_15 )
| ( identity != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5646,c_100240]) ).
tcf(c_103621,plain,
( ( identity = iPr_def_15 )
| ( multiply(iPr_def_15,sk_c3) = multiply(iPr_def_18,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_83046,c_98604]) ).
tcf(c_103624,plain,
multiply(inverse(sk_c5),multiply(iPr_def_15,sk_c3)) = iPr_def_15,
inference(superposition,[status(thm)],[c_98604,c_26008]) ).
tcf(c_103629,plain,
( ( identity = iPr_def_15 )
| ( multiply(iPr_def_15,sk_c3) = sk_c4 ) ),
inference(light_normalisation,[status(thm)],[c_103621,c_58927]) ).
tcf(c_105304,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_39278,c_5136]) ).
tcf(c_105395,plain,
( iPr_def_12
| ( iPr_def_16 = iPr_def_20 )
| ( iPr_def_13 != iPr_def_14 )
| ( identity != iPr_def_15 )
| ( identity != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_105304,c_100240]) ).
tcf(c_105935,plain,
iPr_def_16 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_41940,c_32362,c_36670,c_64972,c_86672,c_105395]) ).
tcf(c_105972,plain,
inverse(iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_76799,c_105935]) ).
tcf(c_106031,plain,
sk_c3 = sk_c4,
inference(demodulation,[status(thm)],[c_90625,c_105972]) ).
tcf(c_106053,plain,
multiply(sk_c3,iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_86144,c_106031]) ).
tcf(c_106063,plain,
iPr_def_18 = iPr_def_19,
inference(demodulation,[status(thm)],[c_98416,c_106053]) ).
tcf(c_106078,plain,
iPr_def_18 = iPr_def_21,
inference(demodulation,[status(thm)],[c_98384,c_106063]) ).
tcf(c_106091,plain,
multiply(iPr_def_13,sk_c5) = iPr_def_18,
inference(demodulation,[status(thm)],[c_83225,c_106063]) ).
tcf(c_106105,plain,
multiply(iPr_def_15,iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_5135,c_106063]) ).
tcf(c_106427,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_106105,c_106091,c_106078,c_106063,c_106053,c_106031,c_105972,c_103629,c_103624,c_100258,c_100240,c_98535,c_98534,c_98526,c_89874,c_86122,c_86080,c_86040,c_86036,c_85725,c_84883,c_84746,c_83341,c_83245,c_83223,c_83030,c_83027,c_82929,c_66780,c_66776,c_49945,c_49815,c_26687,c_26681,c_9995,c_2504,c_30070,c_499,c_498,c_497,c_495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP372-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 14:35:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 29.37/4.82 % SZS status Started for theBenchmark.p
% 29.37/4.82 % SZS status Unsatisfiable for theBenchmark.p
% 29.37/4.82
% 29.37/4.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.37/4.82
% 29.37/4.82 % ------ iProver source info
% 29.37/4.82
% 29.37/4.82 % git: date: 2026-07-19 20:42:38 +0200
% 29.37/4.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.37/4.82 % git: non_committed_changes: false
% 29.37/4.82
% 29.37/4.82 % ------ Parsing...% successful
% 29.37/4.82
% 29.37/4.82
% 29.37/4.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.37/4.82
% 29.37/4.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 29.37/4.82
% 29.37/4.82 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 29.37/4.82
% 29.37/4.82 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 29.37/4.82 % ------ Proving...
% 29.37/4.82 % ------ Problem Properties
% 29.37/4.82
% 29.37/4.82 %
% 29.37/4.82 % clauses 55
% 29.37/4.82 % conjectures 40
% 29.37/4.82 % EPR 37
% 29.37/4.82 % Horn 18
% 29.37/4.82 % unary 15
% 29.37/4.82 % binary 36
% 29.37/4.82 % lits 102
% 29.37/4.82 % lits eq 96
% 29.37/4.82 % fd_pure 0
% 29.37/4.82 % fd_pseudo 0
% 29.37/4.82 % fd_cond 0
% 29.37/4.82 % fd_pseudo_cond 0
% 29.37/4.82 % AC symbols 0
% 29.37/4.82
% 29.37/4.82 % ------ Schedule dynamic 5 is on
% 29.37/4.82
% 29.37/4.82 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 29.37/4.82
% 29.37/4.82
% 29.37/4.82 % ------
% 29.37/4.82 % Current options:
% 29.37/4.82 % ------
% 29.37/4.82
% 29.37/4.82
% 29.37/4.82 %
% 29.37/4.82
% 29.37/4.82 % ------ Proving...
% 29.37/4.82 %
% 29.37/4.82
% 29.37/4.82 % SZS status Unsatisfiable for theBenchmark.p
% 29.37/4.82
% 29.37/4.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.37/4.83
% 29.37/4.83
%------------------------------------------------------------------------------