%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP348-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 01:33:18 PM UTC 2026
% Result : Unsatisfiable 6.40s 1.78s
% Output : CNFRefutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 33
% Syntax : Number of formulae : 195 ( 79 unt; 9 def)
% Number of atoms : 546 ( 328 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 250 ( 89 ~; 161 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = inverse(sk_c3)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = inverse(sk_c3)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c3)
| sk_c5 = multiply(sk_c2,sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X0,X1] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(X1,sk_c4) != sk_c5
| inverse(X1) != sk_c5
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X0,X1] :
( sk_c6 != multiply(X2,sk_c5)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(sk_c4,sk_c5)
| sk_c5 != inverse(sk_c4)
| sk_c5 != multiply(X1,sk_c4)
| sk_c5 != inverse(X1)
| sk_c6 != multiply(X0,sk_c5)
| inverse(X0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(reorient_equations,[],[f45]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_79,negated_conjecture,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c1,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c1,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c1,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c2,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c2,sk_c4) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c2,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c2,sk_c4) = sk_c5 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c4) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c5 )
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c4) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_305,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c4) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_96]) ).
tcf(c_306,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_96]) ).
tcf(c_307,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( inverse(sk_c4) != sk_c5 )
| ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_308,definition,
iPr_def_12 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_309,definition,
iPr_def_13 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_310,definition,
iPr_def_14 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_311,definition,
iPr_def_15 = multiply(sk_c3,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_312,definition,
iPr_def_16 = multiply(sk_c2,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_313,definition,
iPr_def_17 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_314,definition,
iPr_def_18 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_315,definition,
iPr_def_19 = multiply(sk_c1,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_316,definition,
iPr_def_20 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_317,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c6 )
| ( iPr_def_12 != sk_c4 ) ),
inference(demodulation,[status(thm)],[c_307,c_310,c_309,c_308]) ).
tcf(c_319,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_306]) ).
tcf(c_320,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c4) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_305]) ).
tcf(c_321,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_312,c_311]) ).
tcf(c_322,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_94,c_313]) ).
tcf(c_323,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_324,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_325,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91,c_314]) ).
tcf(c_326,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_327,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_328,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_329,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87,c_315]) ).
tcf(c_330,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_331,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_332,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_333,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_83,c_316]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_335,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_336,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_337,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_12 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_338,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_12 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_339,negated_conjecture,
( ( iPr_def_13 = sk_c6 )
| ( iPr_def_12 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_340,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_12 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_569,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c5 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_324,c_328]) ).
tcf(c_575,plain,
( ( sk_c5 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_13) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_327,c_308]) ).
tcf(c_577,plain,
( ( sk_c5 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_325,c_308]) ).
tcf(c_922,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_335,c_331]) ).
tcf(c_980,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c5 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_336,c_332]) ).
tcf(c_1047,plain,
multiply(iPr_def_14,sk_c4) = identity,
inference(superposition,[status(thm)],[c_310,c_74]) ).
tcf(c_1048,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_313,c_74]) ).
tcf(c_1049,plain,
multiply(iPr_def_20,sk_c1) = identity,
inference(superposition,[status(thm)],[c_316,c_74]) ).
tcf(c_1050,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_314,c_74]) ).
tcf(c_1163,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c3) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_311,c_319]) ).
tcf(c_1164,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( inverse(sk_c1) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_315,c_319]) ).
tcf(c_1172,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_20 )
| ( sk_c6 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1164,c_316]) ).
tcf(c_1176,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( sk_c6 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1163,c_313]) ).
tcf(c_1240,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_16 )
| ( inverse(sk_c2) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_312,c_320]) ).
tcf(c_1241,plain,
( ~ iPr_def_10
| ( sk_c5 != sk_c4 )
| ( inverse(identity) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_73,c_320]) ).
tcf(c_1254,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_18 )
| ( sk_c5 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1240,c_314]) ).
tcf(c_1552,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_308,c_75]) ).
tcf(c_1553,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_309,c_75]) ).
tcf(c_1556,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c4,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_312,c_75]) ).
tcf(c_1558,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_74,c_75]) ).
tcf(c_1560,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1047,c_75]) ).
tcf(c_1561,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1048,c_75]) ).
tcf(c_1562,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1049,c_75]) ).
tcf(c_1563,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1050,c_75]) ).
tcf(c_1567,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1563,c_73]) ).
tcf(c_1568,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1562,c_73]) ).
tcf(c_1569,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1561,c_73]) ).
tcf(c_1570,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1560,c_73]) ).
tcf(c_2032,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_13) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_922,c_308]) ).
tcf(c_2327,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c5 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_13) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_569,c_575]) ).
tcf(c_2379,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c4,
inference(superposition,[status(thm)],[c_312,c_1567]) ).
tcf(c_2382,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2379,c_75]) ).
tcf(c_2421,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_315,c_1568]) ).
tcf(c_2424,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2421,c_75]) ).
tcf(c_2459,plain,
multiply(iPr_def_17,iPr_def_15) = sk_c5,
inference(superposition,[status(thm)],[c_311,c_1569]) ).
tcf(c_2462,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_15,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2459,c_75]) ).
tcf(c_2471,plain,
multiply(iPr_def_14,iPr_def_13) = sk_c5,
inference(superposition,[status(thm)],[c_309,c_1570]) ).
tcf(c_2692,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_13,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2471,c_75]) ).
tcf(c_5063,plain,
( ( sk_c5 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_12) = multiply(iPr_def_13,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_577,c_1553]) ).
tcf(c_5624,plain,
multiply(sk_c2,iPr_def_13) = multiply(iPr_def_16,sk_c5),
inference(superposition,[status(thm)],[c_309,c_1556]) ).
tcf(c_7626,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_13) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_980,c_2032]) ).
tcf(c_8560,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1558,c_73]) ).
tcf(c_8569,plain,
multiply(inverse(sk_c5),iPr_def_12) = sk_c6,
inference(superposition,[status(thm)],[c_308,c_8560]) ).
tcf(c_8574,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_73,c_8560]) ).
tcf(c_8575,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_74,c_8560]) ).
tcf(c_8648,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1570,c_8560]) ).
tcf(c_8651,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1567,c_8560]) ).
tcf(c_8677,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_8560,c_8560]) ).
tcf(c_9053,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_8575,c_8677]) ).
tcf(c_9061,plain,
multiply(sk_c5,sk_c6) = multiply(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_9053,c_1552]) ).
tcf(c_9064,plain,
multiply(sk_c4,sk_c5) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_9053,c_1553]) ).
tcf(c_9065,plain,
multiply(sk_c5,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_9053,c_2424]) ).
tcf(c_9066,plain,
multiply(sk_c4,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_9053,c_2382]) ).
tcf(c_9072,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_9053,c_8574]) ).
tcf(c_9076,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_9064,c_309]) ).
tcf(c_9079,plain,
multiply(iPr_def_12,identity) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_9061,c_308]) ).
tcf(c_9099,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_15),
inference(superposition,[status(thm)],[c_9053,c_2462]) ).
tcf(c_9106,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_9072,c_74]) ).
tcf(c_9124,plain,
multiply(sk_c5,identity) = multiply(iPr_def_14,iPr_def_13),
inference(superposition,[status(thm)],[c_9053,c_2692]) ).
tcf(c_10547,plain,
( ( sk_c5 = iPr_def_14 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_332,c_1172]) ).
tcf(c_10549,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_330,c_1172]) ).
tcf(c_10550,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_329,c_1172]) ).
tcf(c_10626,plain,
multiply(sk_c4,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_8648,c_74]) ).
tcf(c_10630,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_8648,c_8560]) ).
tcf(c_10631,plain,
multiply(sk_c4,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_8648,c_9053]) ).
tcf(c_10685,plain,
( ( sk_c6 != iPr_def_20 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_10547,c_1176,c_10550,c_10549]) ).
tcf(c_10686,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_10685]) ).
tcf(c_10730,plain,
( ( sk_c5 = iPr_def_14 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_336,c_10686]) ).
tcf(c_10732,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_334,c_10686]) ).
tcf(c_10733,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_333,c_10686]) ).
tcf(c_10838,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_10730,c_1176,c_10733,c_10732]) ).
tcf(c_10857,plain,
multiply(sk_c2,identity) = multiply(iPr_def_16,iPr_def_14),
inference(superposition,[status(thm)],[c_10626,c_1556]) ).
tcf(c_10911,plain,
inverse(iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_10631,c_9053]) ).
tcf(c_10930,plain,
multiply(sk_c4,sk_c5) = iPr_def_13,
inference(superposition,[status(thm)],[c_2471,c_10630]) ).
tcf(c_10997,plain,
multiply(iPr_def_16,iPr_def_14) = sk_c2,
inference(demodulation,[status(thm)],[c_10857,c_9053]) ).
tcf(c_10998,plain,
multiply(inverse(iPr_def_16),sk_c2) = iPr_def_14,
inference(superposition,[status(thm)],[c_10997,c_8560]) ).
tcf(c_11000,plain,
multiply(sk_c4,iPr_def_14) = multiply(iPr_def_18,sk_c2),
inference(superposition,[status(thm)],[c_10997,c_2382]) ).
tcf(c_11189,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),multiply(sk_c2,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_10998,c_75]) ).
tcf(c_11368,plain,
multiply(inverse(iPr_def_16),iPr_def_16) = multiply(iPr_def_14,sk_c4),
inference(superposition,[status(thm)],[c_312,c_11189]) ).
tcf(c_11374,plain,
multiply(inverse(iPr_def_16),multiply(iPr_def_16,sk_c5)) = multiply(iPr_def_14,iPr_def_13),
inference(superposition,[status(thm)],[c_5624,c_11189]) ).
tcf(c_11379,plain,
multiply(inverse(iPr_def_16),iPr_def_16) = identity,
inference(light_normalisation,[status(thm)],[c_11368,c_1047]) ).
tcf(c_11380,plain,
multiply(inverse(iPr_def_16),multiply(iPr_def_16,sk_c5)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_11374,c_2471]) ).
tcf(c_12268,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_8651,c_74]) ).
tcf(c_12271,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_18)) != sk_c5 )
| ( multiply(sk_c2,sk_c4) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_8651,c_320]) ).
tcf(c_12273,plain,
multiply(sk_c2,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_8651,c_9053]) ).
tcf(c_12280,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_16 )
| ( inverse(inverse(iPr_def_18)) != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_12271,c_312]) ).
tcf(c_12583,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(superposition,[status(thm)],[c_12268,c_1567]) ).
tcf(c_12635,plain,
inverse(iPr_def_18) = sk_c2,
inference(demodulation,[status(thm)],[c_12273,c_9053]) ).
tcf(c_12846,plain,
( ~ iPr_def_10
| ( sk_c5 != identity )
| ( sk_c5 != sk_c4 ) ),
inference(light_normalisation,[status(thm)],[c_1241,c_9072]) ).
tcf(c_15202,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_12846,c_12635,c_12583,c_12280,c_11380,c_11379,c_11374,c_11000,c_10997,c_10930,c_10911,c_10838,c_10631,c_10626,c_9124,c_9099,c_9079,c_9076,c_9066,c_9065,c_9061,c_9072,c_8569,c_7626,c_5063,c_2327,c_1254,c_9106,c_340,c_339,c_338,c_337,c_334,c_333,c_328,c_327,c_326,c_325,c_324,c_323,c_322,c_321,c_317,c_314,c_310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP348-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n017.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 14:27:48 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 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...
% 6.40/1.78 % SZS status Started for theBenchmark.p
% 6.40/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 6.40/1.78
% 6.40/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.40/1.78
% 6.40/1.78 % ------ iProver source info
% 6.40/1.78
% 6.40/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 6.40/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.40/1.78 % git: non_committed_changes: false
% 6.40/1.78
% 6.40/1.78 % ------ Parsing...% successful
% 6.40/1.78
% 6.40/1.78
% 6.40/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.40/1.78
% 6.40/1.78 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.40/1.78
% 6.40/1.78 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.40/1.78
% 6.40/1.78 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.40/1.78 % ------ Proving...
% 6.40/1.78 % ------ Problem Properties
% 6.40/1.78
% 6.40/1.78 %
% 6.40/1.78 % clauses 35
% 6.40/1.78 % conjectures 23
% 6.40/1.78 % EPR 21
% 6.40/1.78 % Horn 14
% 6.40/1.78 % unary 12
% 6.40/1.78 % binary 20
% 6.40/1.78 % lits 63
% 6.40/1.78 % lits eq 59
% 6.40/1.78 % fd_pure 0
% 6.40/1.78 % fd_pseudo 0
% 6.40/1.78 % fd_cond 0
% 6.40/1.78 % fd_pseudo_cond 0
% 6.40/1.78 % AC symbols 0
% 6.40/1.78
% 6.40/1.78 % ------ Schedule dynamic 5 is on
% 6.40/1.78
% 6.40/1.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.40/1.78
% 6.40/1.78
% 6.40/1.78 % ------
% 6.40/1.78 % Current options:
% 6.40/1.78 % ------
% 6.40/1.78
% 6.40/1.78
% 6.40/1.78 %
% 6.40/1.78
% 6.40/1.78 % ------ Proving...
% 6.40/1.78 %
% 6.40/1.78
% 6.40/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 6.40/1.78
% 6.40/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.40/1.78
% 6.40/1.78
%------------------------------------------------------------------------------