%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP289-1 : 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 : n011.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 01:32:44 PM UTC 2026
% Result : Unsatisfiable 6.02s 2.29s
% Output : CNFRefutation 6.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 286 ( 93 unt; 10 def)
% Number of atoms : 936 ( 512 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 401 ( 129 ~; 272 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 57 :)
% 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_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(reorient_equations,[],[f55]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_81,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_359,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_106]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_106]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_106]) ).
tcf(c_362,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_106]) ).
tcf(c_363,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_364,definition,
iPr_def_14 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_365,definition,
iPr_def_15 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_366,definition,
iPr_def_16 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_367,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_368,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_369,definition,
iPr_def_19 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_370,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_371,definition,
iPr_def_21 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_372,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_373,definition,
iPr_def_23 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_374,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c5 )
| ( iPr_def_14 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_363,c_365,c_364]) ).
tcf(c_375,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_362]) ).
tcf(c_376,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_361]) ).
tcf(c_377,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_360]) ).
tcf(c_378,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_359]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105,c_367,c_366]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104,c_368]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_369]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102,c_370]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_371]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_372]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90,c_373]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_396,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_397,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_401,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_402,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_403,negated_conjecture,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_404,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_673,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_386,c_366]) ).
tcf(c_674,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_385,c_366]) ).
tcf(c_675,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_384,c_366]) ).
tcf(c_696,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_387,c_366]) ).
tcf(c_708,plain,
( ( sk_c5 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_388,c_366]) ).
tcf(c_722,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_389,c_364]) ).
tcf(c_742,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_390,c_364]) ).
tcf(c_762,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_391,c_364]) ).
tcf(c_795,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != X0 )
| ( sk_c5 != X0 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_808,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_393,c_366]) ).
tcf(c_841,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_394,c_369]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_878,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_392,c_373]) ).
tcf(c_879,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_391,c_373]) ).
tcf(c_883,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_381,c_373]) ).
tcf(c_906,plain,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != iPr_def_21 )
| ( sk_c5 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_795]) ).
tcf(c_911,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_370,c_79]) ).
tcf(c_912,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_368,c_79]) ).
tcf(c_913,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_372,c_79]) ).
tcf(c_914,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_367,c_79]) ).
tcf(c_921,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_395,c_371]) ).
tcf(c_966,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_396,c_373]) ).
tcf(c_1008,plain,
! [X0: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_862]) ).
tcf(c_1023,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_397,c_373]) ).
tcf(c_1205,plain,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c5 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1008]) ).
tcf(c_1206,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_404]) ).
tcf(c_1226,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_401,c_366]) ).
tcf(c_1227,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_401,c_386]) ).
tcf(c_1283,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_402,c_366]) ).
tcf(c_1323,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_403,c_366]) ).
tcf(c_1384,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_401,c_374]) ).
tcf(c_1394,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_17 )
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_383,c_374]) ).
tcf(c_1587,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_364,c_80]) ).
tcf(c_1589,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_369,c_80]) ).
tcf(c_1591,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_373,c_80]) ).
tcf(c_1592,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_371,c_80]) ).
tcf(c_1594,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1596,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_911,c_80]) ).
tcf(c_1597,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_912,c_80]) ).
tcf(c_1598,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_913,c_80]) ).
tcf(c_1599,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_914,c_80]) ).
tcf(c_1601,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1599,c_78]) ).
tcf(c_1602,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1598,c_78]) ).
tcf(c_1603,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1597,c_78]) ).
tcf(c_1604,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1596,c_78]) ).
tcf(c_2025,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_373,c_375]) ).
tcf(c_2027,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_79,c_375]) ).
tcf(c_2042,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_2025,c_372]) ).
tcf(c_2169,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_371,c_376]) ).
tcf(c_2186,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_21 )
| ( sk_c6 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2169,c_367]) ).
tcf(c_2295,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_369,c_377]) ).
tcf(c_2317,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2295,c_370]) ).
tcf(c_2434,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_366,c_378]) ).
tcf(c_2436,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c5)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_79,c_378]) ).
tcf(c_2454,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_18 )
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2434,c_368]) ).
tcf(c_2898,plain,
multiply(iPr_def_17,iPr_def_21) = sk_c6,
inference(superposition,[status(thm)],[c_371,c_1601]) ).
tcf(c_2910,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_21,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2898,c_80]) ).
tcf(c_2912,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_373,c_1602]) ).
tcf(c_2927,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_366,c_1603]) ).
tcf(c_2930,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2927,c_80]) ).
tcf(c_2932,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_369,c_1604]) ).
tcf(c_2953,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2932,c_80]) ).
tcf(c_3158,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_673,c_1603]) ).
tcf(c_3159,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3158,c_2927]) ).
tcf(c_3501,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_394,c_722]) ).
tcf(c_3507,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3501,c_2912]) ).
tcf(c_3557,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_395,c_742]) ).
tcf(c_3564,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3557,c_2912]) ).
tcf(c_3884,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_3507,c_373]) ).
tcf(c_3976,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_3564,c_373]) ).
tcf(c_3979,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_3564,c_390]) ).
tcf(c_4195,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_18,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_3979,c_365]) ).
tcf(c_4425,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_808,c_1603]) ).
tcf(c_4426,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_4425,c_2927]) ).
tcf(c_4438,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_841,c_1604]) ).
tcf(c_4439,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_4438,c_2932]) ).
tcf(c_4589,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_879,c_1602]) ).
tcf(c_4590,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4589,c_2912]) ).
tcf(c_4773,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_883,c_1602]) ).
tcf(c_4774,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4773,c_2912]) ).
tcf(c_4786,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_921,c_1601]) ).
tcf(c_4787,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4786,c_2898]) ).
tcf(c_4879,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_966,c_1602]) ).
tcf(c_4880,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4879,c_2912]) ).
tcf(c_5023,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1023,c_1602]) ).
tcf(c_5024,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5023,c_2912]) ).
tcf(c_5348,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1323,c_1603]) ).
tcf(c_5349,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c5 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5348,c_2927]) ).
tcf(c_5398,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1587]) ).
tcf(c_6070,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1589]) ).
tcf(c_6201,plain,
multiply(iPr_def_20,multiply(iPr_def_19,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_6070,c_1604]) ).
tcf(c_6226,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_23,sk_c6),
inference(superposition,[status(thm)],[c_364,c_1591]) ).
tcf(c_6483,plain,
multiply(sk_c2,iPr_def_15) = multiply(iPr_def_21,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1592]) ).
tcf(c_7678,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3884,c_6226]) ).
tcf(c_7698,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_23,iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_394,c_7678]) ).
tcf(c_8156,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1594,c_78]) ).
tcf(c_8162,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_365,c_8156]) ).
tcf(c_8164,plain,
multiply(inverse(sk_c4),iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_366,c_8156]) ).
tcf(c_8167,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_8156]) ).
tcf(c_8168,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_8156]) ).
tcf(c_8190,plain,
( ( sk_c5 = iPr_def_15 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_708,c_8156]) ).
tcf(c_8191,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_696,c_8156]) ).
tcf(c_8192,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_675,c_8156]) ).
tcf(c_8193,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_674,c_8156]) ).
tcf(c_8194,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_673,c_8156]) ).
tcf(c_8241,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1283,c_8156]) ).
tcf(c_8242,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1226,c_8156]) ).
tcf(c_8252,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1604,c_8156]) ).
tcf(c_8253,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1603,c_8156]) ).
tcf(c_8254,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1602,c_8156]) ).
tcf(c_8255,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1601,c_8156]) ).
tcf(c_8289,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_5398,c_8156]) ).
tcf(c_8294,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(inverse(iPr_def_23),iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_7698,c_8156]) ).
tcf(c_8296,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_8156,c_8156]) ).
tcf(c_8973,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_8168,c_8296]) ).
tcf(c_8983,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_8973,c_1587]) ).
tcf(c_8986,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_8973,c_2953]) ).
tcf(c_8987,plain,
multiply(sk_c5,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_8973,c_2930]) ).
tcf(c_8990,plain,
multiply(sk_c6,identity) = multiply(iPr_def_17,iPr_def_21),
inference(superposition,[status(thm)],[c_8973,c_2910]) ).
tcf(c_8995,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8973,c_8167]) ).
tcf(c_8996,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_8990,c_2898]) ).
tcf(c_8999,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_8987,c_2927]) ).
tcf(c_9003,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_8983,c_364]) ).
tcf(c_9253,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3976,c_6226]) ).
tcf(c_9274,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_23,iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_395,c_9253]) ).
tcf(c_9420,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(inverse(iPr_def_23),iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_9274,c_8156]) ).
tcf(c_9833,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_8252,c_79]) ).
tcf(c_9839,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_8252,c_8156]) ).
tcf(c_9840,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_8252,c_8973]) ).
tcf(c_9909,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(superposition,[status(thm)],[c_9833,c_1604]) ).
tcf(c_9912,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_9840,c_8973]) ).
tcf(c_9919,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_911,c_9839]) ).
tcf(c_9921,plain,
multiply(sk_c3,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_2932,c_9839]) ).
tcf(c_10369,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_391,c_2042]) ).
tcf(c_10578,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_8253,c_79]) ).
tcf(c_10581,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_8253,c_378]) ).
tcf(c_10583,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c4,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_8253,c_376]) ).
tcf(c_10584,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_8253,c_8156]) ).
tcf(c_10585,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_8253,c_8973]) ).
tcf(c_10714,plain,
( iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c5 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1384,c_374,c_906,c_1205,c_1206,c_1227,c_2186,c_3159,c_4774,c_4880,c_10369]) ).
tcf(c_11156,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_10585,c_8973]) ).
tcf(c_11160,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_4195,c_10584]) ).
tcf(c_11163,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm)],[c_912,c_10584]) ).
tcf(c_11164,plain,
multiply(sk_c4,sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_2927,c_10584]) ).
tcf(c_11221,plain,
multiply(sk_c1,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_8254,c_79]) ).
tcf(c_11225,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_8254,c_377]) ).
tcf(c_11227,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_8254,c_8156]) ).
tcf(c_11228,plain,
multiply(sk_c1,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_8254,c_8973]) ).
tcf(c_11246,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_879,c_11221]) ).
tcf(c_11247,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_878,c_11221]) ).
tcf(c_12457,plain,
inverse(iPr_def_22) = sk_c1,
inference(demodulation,[status(thm)],[c_11228,c_8973]) ).
tcf(c_12465,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_14) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_762,c_11227]) ).
tcf(c_12468,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_913,c_11227]) ).
tcf(c_12492,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c6) = sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_12465,c_6226]) ).
tcf(c_12571,plain,
( ( identity = iPr_def_23 )
| ~ iPr_def_13
| ( iPr_def_20 != iPr_def_22 )
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_11247,c_2042]) ).
tcf(c_13024,plain,
( ( sk_c6 = iPr_def_23 )
| ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(iPr_def_20)) != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_397,c_2027]) ).
tcf(c_13044,plain,
( ( sk_c6 = iPr_def_23 )
| ~ iPr_def_13
| ( sk_c6 != identity ) ),
inference(ground_joinability,[status(thm)],[c_13024,c_370,c_9912]) ).
tcf(c_13427,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_8255,c_79]) ).
tcf(c_13432,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_8255,c_376]) ).
tcf(c_13433,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_8255,c_8156]) ).
tcf(c_13434,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_8255,c_8973]) ).
tcf(c_13525,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(iPr_def_21)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_386,c_2436]) ).
tcf(c_14049,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_13434,c_8973]) ).
tcf(c_14055,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_914,c_13433]) ).
tcf(c_14056,plain,
multiply(sk_c2,sk_c6) = iPr_def_21,
inference(superposition,[status(thm)],[c_2898,c_13433]) ).
tcf(c_18728,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_14056,c_14055,c_14049,c_13525,c_13432,c_13427,c_13044,c_12571,c_12492,c_12468,c_12457,c_11247,c_11246,c_11225,c_11221,c_11164,c_11163,c_11160,c_11156,c_10714,c_10583,c_10581,c_10578,c_9921,c_9919,c_9912,c_9909,c_9833,c_9420,c_9003,c_8999,c_8996,c_8987,c_8986,c_8983,c_8995,c_8294,c_8289,c_8242,c_8241,c_8194,c_8193,c_8192,c_8191,c_8190,c_8164,c_8162,c_6483,c_6226,c_6201,c_6070,c_5349,c_5024,c_4880,c_4787,c_4590,c_4439,c_4426,c_2454,c_2436,c_2317,c_2027,c_1394,c_383,c_382,c_381,c_380,c_379,c_374,c_372,c_370,c_368,c_367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP289-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 14:22:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 6.02/2.29 % SZS status Started for theBenchmark.p
% 6.02/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 6.02/2.29
% 6.02/2.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.02/2.29
% 6.02/2.29 % ------ iProver source info
% 6.02/2.29
% 6.02/2.29 % git: date: 2026-07-19 20:42:38 +0200
% 6.02/2.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.02/2.29 % git: non_committed_changes: false
% 6.02/2.29
% 6.02/2.29 % ------ Parsing...% successful
% 6.02/2.29
% 6.02/2.29
% 6.02/2.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.02/2.29
% 6.02/2.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.02/2.29
% 6.02/2.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.02/2.29
% 6.02/2.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.02/2.29 % ------ Proving...
% 6.02/2.29 % ------ Problem Properties
% 6.02/2.29
% 6.02/2.29 %
% 6.02/2.29 % clauses 43
% 6.02/2.29 % conjectures 30
% 6.02/2.29 % EPR 26
% 6.02/2.29 % Horn 17
% 6.02/2.29 % unary 13
% 6.02/2.29 % binary 25
% 6.02/2.29 % lits 81
% 6.02/2.29 % lits eq 73
% 6.02/2.29 % fd_pure 0
% 6.02/2.29 % fd_pseudo 0
% 6.02/2.29 % fd_cond 0
% 6.02/2.29 % fd_pseudo_cond 0
% 6.02/2.29 % AC symbols 0
% 6.02/2.29
% 6.02/2.29 % ------ Schedule dynamic 5 is on
% 6.02/2.29
% 6.02/2.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.02/2.29
% 6.02/2.29
% 6.02/2.29 % ------
% 6.02/2.29 % Current options:
% 6.02/2.29 % ------
% 6.02/2.29
% 6.02/2.29
% 6.02/2.29 %
% 6.02/2.29
% 6.02/2.29 % ------ Proving...
% 6.02/2.29 %
% 6.02/2.29
% 6.02/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 6.02/2.29
% 6.02/2.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.02/2.29
% 6.02/2.29
%------------------------------------------------------------------------------