%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP363-1 : 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 : n015.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 01:33:24 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.77s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 189 ( 88 unt; 10 def)
% Number of atoms : 491 ( 320 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 257 ( 100 ~; 157 |; 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 45 :)
% 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_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2
| sk_c6 != multiply(sk_c7,X2)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c5 != multiply(sk_c6,sk_c7)
| inverse(X0) != sk_c6
| sk_c5 != multiply(X0,sk_c6)
| sk_c5 != inverse(sk_c6)
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X3,X0,X1] :
( sk_c7 != inverse(X3)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c5 != multiply(sk_c6,sk_c7)
| inverse(X0) != sk_c6
| sk_c5 != multiply(X0,sk_c6)
| sk_c5 != inverse(sk_c6)
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(equality_resolution,[],[f54]) ).
tcf(c_77,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c5 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c6) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c5 )
| ( multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_345,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_104]) ).
tcf(c_346,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_104]) ).
tcf(c_347,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_348,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_349,definition,
iPr_def_13 = multiply(sk_c6,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_350,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_351,definition,
iPr_def_15 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_352,definition,
iPr_def_16 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_353,definition,
iPr_def_17 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_354,definition,
iPr_def_18 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_355,definition,
iPr_def_19 = multiply(sk_c7,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_356,definition,
iPr_def_20 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_357,definition,
iPr_def_21 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_358,definition,
iPr_def_22 = multiply(sk_c1,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_359,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c5 )
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_348,c_351,c_350,c_349]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_347]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_346]) ).
tcf(c_362,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_345]) ).
tcf(c_363,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103,c_353,c_352]) ).
tcf(c_364,negated_conjecture,
( ( iPr_def_18 = sk_c4 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102,c_354]) ).
tcf(c_365,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101,c_355]) ).
tcf(c_366,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_356]) ).
tcf(c_367,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99,c_357]) ).
tcf(c_368,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_369,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97,c_358]) ).
tcf(c_370,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_18 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_371,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_20 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_375,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_18 = sk_c4 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_833,plain,
multiply(iPr_def_20,sk_c2) = identity,
inference(superposition,[status(thm)],[c_356,c_78]) ).
tcf(c_834,plain,
multiply(iPr_def_16,sk_c3) = identity,
inference(superposition,[status(thm)],[c_352,c_78]) ).
tcf(c_835,plain,
multiply(iPr_def_15,sk_c6) = identity,
inference(superposition,[status(thm)],[c_351,c_78]) ).
tcf(c_836,plain,
multiply(iPr_def_17,sk_c1) = identity,
inference(superposition,[status(thm)],[c_353,c_78]) ).
tcf(c_1139,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(iPr_def_15) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_835,c_361]) ).
tcf(c_1180,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_357,c_362]) ).
tcf(c_1197,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_21 )
| ( sk_c6 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1180,c_356]) ).
tcf(c_1286,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_350,c_79]) ).
tcf(c_1288,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c4,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_355,c_79]) ).
tcf(c_1290,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c6,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_358,c_79]) ).
tcf(c_1292,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_78,c_79]) ).
tcf(c_1294,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_833,c_79]) ).
tcf(c_1295,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_834,c_79]) ).
tcf(c_1296,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_835,c_79]) ).
tcf(c_1297,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_836,c_79]) ).
tcf(c_1301,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1297,c_77]) ).
tcf(c_1302,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1296,c_77]) ).
tcf(c_1303,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1295,c_77]) ).
tcf(c_1304,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1294,c_77]) ).
tcf(c_1861,plain,
( ~ iPr_def_12
| ( inverse(sk_c3) != sk_c7 )
| ( multiply(sk_c7,iPr_def_18) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_354,c_360]) ).
tcf(c_1877,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_16 )
| ( multiply(sk_c7,iPr_def_18) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1861,c_352]) ).
tcf(c_2387,plain,
multiply(iPr_def_17,iPr_def_22) = sk_c6,
inference(superposition,[status(thm)],[c_358,c_1301]) ).
tcf(c_2392,plain,
multiply(iPr_def_15,iPr_def_13) = sk_c5,
inference(superposition,[status(thm)],[c_349,c_1302]) ).
tcf(c_2393,plain,
multiply(iPr_def_15,iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_350,c_1302]) ).
tcf(c_2486,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_14,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2393,c_79]) ).
tcf(c_2488,plain,
multiply(iPr_def_16,iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_354,c_1303]) ).
tcf(c_2504,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_18,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2488,c_79]) ).
tcf(c_2506,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c6,
inference(superposition,[status(thm)],[c_357,c_1304]) ).
tcf(c_2901,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2506,c_79]) ).
tcf(c_5876,plain,
multiply(sk_c6,iPr_def_19) = multiply(iPr_def_14,sk_c4),
inference(superposition,[status(thm)],[c_355,c_1286]) ).
tcf(c_6032,plain,
multiply(iPr_def_15,multiply(iPr_def_14,sk_c4)) = iPr_def_19,
inference(superposition,[status(thm)],[c_5876,c_1302]) ).
tcf(c_6583,plain,
multiply(sk_c1,multiply(iPr_def_14,sk_c4)) = multiply(iPr_def_22,iPr_def_19),
inference(superposition,[status(thm)],[c_5876,c_1290]) ).
tcf(c_7027,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1292,c_77]) ).
tcf(c_7044,plain,
multiply(inverse(sk_c7),iPr_def_19) = sk_c4,
inference(superposition,[status(thm)],[c_355,c_7027]) ).
tcf(c_7047,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_77,c_7027]) ).
tcf(c_7048,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_78,c_7027]) ).
tcf(c_7124,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1304,c_7027]) ).
tcf(c_7125,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1303,c_7027]) ).
tcf(c_7126,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1302,c_7027]) ).
tcf(c_7127,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1301,c_7027]) ).
tcf(c_7145,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7027,c_7027]) ).
tcf(c_7457,plain,
( ~ iPr_def_12
| ( inverse(inverse(identity)) != sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7047,c_360]) ).
tcf(c_7469,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7048,c_7145]) ).
tcf(c_7483,plain,
multiply(sk_c7,sk_c4) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_7469,c_1288]) ).
tcf(c_7487,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_7469,c_7047]) ).
tcf(c_7488,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_7483,c_355]) ).
tcf(c_7516,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_7487,c_78]) ).
tcf(c_8033,plain,
multiply(sk_c7,identity) = multiply(iPr_def_15,iPr_def_14),
inference(superposition,[status(thm)],[c_7469,c_2486]) ).
tcf(c_8036,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_8033,c_2393]) ).
tcf(c_8563,plain,
multiply(sk_c7,identity) = multiply(iPr_def_16,iPr_def_18),
inference(superposition,[status(thm)],[c_7469,c_2504]) ).
tcf(c_8574,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_7469,c_2901]) ).
tcf(c_9324,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_20)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7124,c_361]) ).
tcf(c_9325,plain,
multiply(sk_c2,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_7124,c_78]) ).
tcf(c_9329,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_7124,c_7027]) ).
tcf(c_9330,plain,
multiply(sk_c2,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_7124,c_7469]) ).
tcf(c_9333,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_9324,c_357]) ).
tcf(c_9374,plain,
inverse(iPr_def_20) = sk_c2,
inference(demodulation,[status(thm)],[c_9330,c_7469]) ).
tcf(c_9504,plain,
multiply(sk_c2,sk_c6) = iPr_def_21,
inference(superposition,[status(thm)],[c_2506,c_9329]) ).
tcf(c_9844,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c3,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_7125,c_362]) ).
tcf(c_9846,plain,
multiply(sk_c3,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_7125,c_78]) ).
tcf(c_9850,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_7125,c_7027]) ).
tcf(c_9851,plain,
multiply(sk_c3,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_7125,c_7469]) ).
tcf(c_9960,plain,
inverse(iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_9851,c_7469]) ).
tcf(c_9967,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_834,c_9850]) ).
tcf(c_9968,plain,
multiply(sk_c3,sk_c7) = iPr_def_18,
inference(superposition,[status(thm)],[c_2488,c_9850]) ).
tcf(c_10559,plain,
multiply(sk_c6,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_7126,c_78]) ).
tcf(c_10563,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_7126,c_7027]) ).
tcf(c_10564,plain,
multiply(sk_c6,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_7126,c_7469]) ).
tcf(c_10853,plain,
multiply(sk_c1,identity) = multiply(iPr_def_22,iPr_def_15),
inference(superposition,[status(thm)],[c_10559,c_1290]) ).
tcf(c_10855,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(superposition,[status(thm)],[c_10559,c_1302]) ).
tcf(c_11487,plain,
inverse(iPr_def_15) = sk_c6,
inference(demodulation,[status(thm)],[c_10564,c_7469]) ).
tcf(c_11492,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c6 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_1139,c_11487]) ).
tcf(c_11493,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(equality_resolution_simp,[status(thm)],[c_11492]) ).
tcf(c_12533,plain,
multiply(sk_c6,sk_c5) = iPr_def_13,
inference(superposition,[status(thm)],[c_2392,c_10563]) ).
tcf(c_12534,plain,
multiply(sk_c6,sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_2393,c_10563]) ).
tcf(c_12849,plain,
multiply(iPr_def_22,iPr_def_15) = sk_c1,
inference(demodulation,[status(thm)],[c_10853,c_7469]) ).
tcf(c_14365,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c1,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_7127,c_362]) ).
tcf(c_14367,plain,
multiply(sk_c1,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_7127,c_78]) ).
tcf(c_14371,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_7127,c_7027]) ).
tcf(c_14372,plain,
multiply(sk_c1,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_7127,c_7469]) ).
tcf(c_14391,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_22 )
| ( inverse(inverse(iPr_def_17)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_14365,c_358]) ).
tcf(c_14498,plain,
inverse(iPr_def_17) = sk_c1,
inference(demodulation,[status(thm)],[c_14372,c_7469]) ).
tcf(c_15154,plain,
multiply(sk_c1,sk_c6) = iPr_def_22,
inference(superposition,[status(thm)],[c_2387,c_14371]) ).
tcf(c_18416,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_15154,c_14498,c_14391,c_14367,c_12849,c_12534,c_12533,c_11493,c_11487,c_10855,c_10564,c_10559,c_9968,c_9967,c_9960,c_9844,c_9846,c_9504,c_9374,c_9333,c_9325,c_8574,c_8563,c_8036,c_8033,c_7488,c_7483,c_7487,c_7457,c_7044,c_6583,c_6032,c_5876,c_1877,c_7516,c_1197,c_835,c_386,c_380,c_379,c_378,c_377,c_376,c_375,c_374,c_373,c_372,c_371,c_370,c_369,c_368,c_367,c_366,c_365,c_364,c_363,c_359,c_356,c_353,c_352,c_351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP363-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 14:38:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 1.31/1.77 % SZS status Started for theBenchmark.p
% 1.31/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.77
% 1.31/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.31/1.77
% 1.31/1.77 % ------ iProver source info
% 1.31/1.77
% 1.31/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 1.31/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.31/1.77 % git: non_committed_changes: false
% 1.31/1.77
% 1.31/1.77 % ------ Parsing...% successful
% 1.31/1.77
% 1.31/1.77
% 1.31/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.31/1.77
% 1.31/1.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.31/1.77
% 1.31/1.77 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.31/1.77
% 1.31/1.77 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.31/1.77 % ------ Proving...
% 1.31/1.77 % ------ Problem Properties
% 1.31/1.77
% 1.31/1.77 %
% 1.31/1.77 % clauses 41
% 1.31/1.77 % conjectures 28
% 1.31/1.77 % EPR 25
% 1.31/1.77 % Horn 16
% 1.31/1.77 % unary 13
% 1.31/1.77 % binary 24
% 1.31/1.77 % lits 76
% 1.31/1.77 % lits eq 70
% 1.31/1.77 % fd_pure 0
% 1.31/1.77 % fd_pseudo 0
% 1.31/1.77 % fd_cond 0
% 1.31/1.77 % fd_pseudo_cond 0
% 1.31/1.77 % AC symbols 0
% 1.31/1.77
% 1.31/1.77 % ------ Schedule dynamic 5 is on
% 1.31/1.77
% 1.31/1.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.31/1.77
% 1.31/1.77
% 1.31/1.77 % ------
% 1.31/1.77 % Current options:
% 1.31/1.77 % ------
% 1.31/1.77
% 1.31/1.77
% 1.31/1.77 %
% 1.31/1.77
% 1.31/1.77 % ------ Proving...
% 1.31/1.77 %
% 1.31/1.77
% 1.31/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.77
% 1.31/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.31/1.77
% 1.31/1.77
%------------------------------------------------------------------------------