%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP299-1 : 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 : n007.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 01:32:46 PM UTC 2026
% Result : Unsatisfiable 10.62s 2.31s
% Output : CNFRefutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 197 ( 92 unt; 10 def)
% Number of atoms : 541 ( 330 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 244 ( 88 ~; 156 |; 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 : 65 ( 0 sgn 65 !; 0 ?; 48 :)
% 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(f11,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f19,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c4) = 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_c3,sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c4 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c4 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c4 = inverse(sk_c3)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c7) != sk_c6
| inverse(X2) != X3
| multiply(X2,X3) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| 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_25) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c7)
| inverse(X2) != X3
| sk_c6 != multiply(X2,X3)
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c6 != multiply(sk_c5,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X2,X0,X1] :
( sk_c6 != multiply(inverse(X2),sk_c7)
| sk_c6 != multiply(X2,inverse(X2))
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c6 != multiply(sk_c5,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
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_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c4 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(inverse(X2),sk_c7) != sk_c6 )
| ( multiply(X2,inverse(X2)) != sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_345,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
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_c7 )
| ( 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
| ( multiply(inverse(X0),sk_c7) != sk_c6 )
| ( multiply(X0,inverse(X0)) != 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
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_349,definition,
iPr_def_13 = multiply(sk_c7,sk_c6),
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 = multiply(sk_c5,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_352,definition,
iPr_def_16 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_353,definition,
iPr_def_17 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_354,definition,
iPr_def_18 = multiply(sk_c3,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_355,definition,
iPr_def_19 = multiply(sk_c2,sk_c6),
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 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_358,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
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_c6 )
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_348,c_351,c_350,c_349]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c7) != sk_c6 )
| ( multiply(X0,inverse(X0)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_347]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( 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_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_345]) ).
tcf(c_364,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102,c_353]) ).
tcf(c_365,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101,c_354]) ).
tcf(c_366,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_355]) ).
tcf(c_367,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99,c_356]) ).
tcf(c_368,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_370,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_371,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_672,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_370,c_354]) ).
tcf(c_673,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_364,c_354]) ).
tcf(c_711,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_372,c_349]) ).
tcf(c_727,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_373,c_349]) ).
tcf(c_804,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_376,c_354]) ).
tcf(c_970,plain,
multiply(iPr_def_20,sk_c2) = identity,
inference(superposition,[status(thm)],[c_356,c_78]) ).
tcf(c_971,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_353,c_78]) ).
tcf(c_972,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_357,c_78]) ).
tcf(c_1214,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_13 )
| ( inverse(sk_c7) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_349,c_361]) ).
tcf(c_1215,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_355,c_361]) ).
tcf(c_1231,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1215,c_356]) ).
tcf(c_1320,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_78,c_362]) ).
tcf(c_1591,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_349,c_79]) ).
tcf(c_1592,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_1593,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_355,c_79]) ).
tcf(c_1594,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c4,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_354,c_79]) ).
tcf(c_1596,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_358,c_79]) ).
tcf(c_1597,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_351,c_79]) ).
tcf(c_1599,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_78,c_79]) ).
tcf(c_1601,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_970,c_79]) ).
tcf(c_1602,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_971,c_79]) ).
tcf(c_1603,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_972,c_79]) ).
tcf(c_1607,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1603,c_77]) ).
tcf(c_1608,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1602,c_77]) ).
tcf(c_1609,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1601,c_77]) ).
tcf(c_1832,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_358,c_1607]) ).
tcf(c_1837,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c4,
inference(superposition,[status(thm)],[c_354,c_1608]) ).
tcf(c_2215,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_355,c_1609]) ).
tcf(c_2222,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2215,c_79]) ).
tcf(c_2763,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_378,c_711]) ).
tcf(c_2774,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2763,c_1832]) ).
tcf(c_3121,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_379,c_727]) ).
tcf(c_3133,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3121,c_1832]) ).
tcf(c_4857,plain,
multiply(sk_c7,iPr_def_14) = multiply(iPr_def_13,sk_c7),
inference(superposition,[status(thm)],[c_350,c_1591]) ).
tcf(c_5721,plain,
multiply(sk_c3,iPr_def_16) = multiply(iPr_def_18,sk_c7),
inference(superposition,[status(thm)],[c_352,c_1594]) ).
tcf(c_5891,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_22,sk_c6),
inference(superposition,[status(thm)],[c_349,c_1596]) ).
tcf(c_7730,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1599,c_77]) ).
tcf(c_7734,plain,
multiply(inverse(sk_c7),iPr_def_13) = sk_c6,
inference(superposition,[status(thm)],[c_349,c_7730]) ).
tcf(c_7735,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_350,c_7730]) ).
tcf(c_7737,plain,
multiply(inverse(sk_c3),iPr_def_18) = sk_c4,
inference(superposition,[status(thm)],[c_354,c_7730]) ).
tcf(c_7738,plain,
multiply(inverse(sk_c4),iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_352,c_7730]) ).
tcf(c_7740,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_351,c_7730]) ).
tcf(c_7741,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_77,c_7730]) ).
tcf(c_7742,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_78,c_7730]) ).
tcf(c_7819,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1609,c_7730]) ).
tcf(c_7820,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1608,c_7730]) ).
tcf(c_7821,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1607,c_7730]) ).
tcf(c_7822,plain,
multiply(inverse(sk_c7),multiply(iPr_def_13,sk_c7)) = iPr_def_14,
inference(superposition,[status(thm)],[c_4857,c_7730]) ).
tcf(c_7865,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7730,c_7730]) ).
tcf(c_8679,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7742,c_7865]) ).
tcf(c_8692,plain,
multiply(sk_c5,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_8679,c_1597]) ).
tcf(c_8696,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_8679,c_2222]) ).
tcf(c_8703,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8679,c_7741]) ).
tcf(c_8707,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_8696,c_2215]) ).
tcf(c_8711,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8692,c_351]) ).
tcf(c_9954,plain,
( ( sk_c7 = iPr_def_13 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2774,c_1231]) ).
tcf(c_10094,plain,
multiply(sk_c2,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_7819,c_78]) ).
tcf(c_10097,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_7819,c_7730]) ).
tcf(c_10299,plain,
multiply(sk_c2,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_2215,c_10097]) ).
tcf(c_10435,plain,
multiply(sk_c3,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_7820,c_78]) ).
tcf(c_10438,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_7820,c_7730]) ).
tcf(c_10439,plain,
multiply(sk_c3,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_7820,c_8679]) ).
tcf(c_10450,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_804,c_10435]) ).
tcf(c_10451,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_673,c_10435]) ).
tcf(c_10452,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_672,c_10435]) ).
tcf(c_10503,plain,
( ~ iPr_def_11
| ( inverse(sk_c7) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_1214,c_1214,c_3133,c_9954]) ).
tcf(c_10721,plain,
multiply(inverse(sk_c3),identity) = iPr_def_17,
inference(superposition,[status(thm)],[c_10435,c_7730]) ).
tcf(c_10862,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10450,c_349]) ).
tcf(c_11149,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_10451,c_10450]) ).
tcf(c_11328,plain,
inverse(iPr_def_17) = sk_c3,
inference(demodulation,[status(thm)],[c_10439,c_8679]) ).
tcf(c_11342,plain,
multiply(sk_c3,sk_c4) = iPr_def_18,
inference(superposition,[status(thm)],[c_1837,c_10438]) ).
tcf(c_11480,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10452,c_358]) ).
tcf(c_11868,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10452,c_10862]) ).
tcf(c_11887,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_11868,c_1832]) ).
tcf(c_12029,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_13) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_11887,c_358]) ).
tcf(c_12049,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_12029,c_5891]) ).
tcf(c_12349,plain,
multiply(sk_c1,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_7821,c_78]) ).
tcf(c_12351,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7821,c_361]) ).
tcf(c_12352,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_7821,c_7730]) ).
tcf(c_12353,plain,
multiply(sk_c1,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_7821,c_8679]) ).
tcf(c_13660,plain,
inverse(iPr_def_21) = sk_c1,
inference(demodulation,[status(thm)],[c_12353,c_8679]) ).
tcf(c_13683,plain,
multiply(sk_c1,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_1832,c_12352]) ).
tcf(c_14158,plain,
( ( identity = iPr_def_22 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_11480,c_12349]) ).
tcf(c_14169,plain,
( ( identity = iPr_def_18 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_14158,c_8703]) ).
tcf(c_15121,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_22) = identity ) ),
inference(superposition,[status(thm)],[c_14169,c_78]) ).
tcf(c_15498,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10450,c_12049]) ).
tcf(c_19679,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_7865,c_78]) ).
tcf(c_19682,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_7865,c_7730]) ).
tcf(c_19683,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_7865,c_8679]) ).
tcf(c_19684,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_19683,c_8679]) ).
tcf(c_19700,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_360,c_19679]) ).
tcf(c_19704,plain,
( ~ iPr_def_10
| ( sk_c6 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1320,c_19684]) ).
tcf(c_19730,plain,
inverse(sk_c1) = iPr_def_21,
inference(superposition,[status(thm)],[c_13660,c_19684]) ).
tcf(c_19816,plain,
multiply(iPr_def_19,inverse(sk_c6)) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_19679,c_1593]) ).
tcf(c_19817,plain,
multiply(iPr_def_13,inverse(sk_c6)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_19679,c_1591]) ).
tcf(c_19818,plain,
multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c5,identity),
inference(superposition,[status(thm)],[c_19679,c_1597]) ).
tcf(c_19819,plain,
multiply(iPr_def_22,inverse(sk_c7)) = multiply(sk_c1,identity),
inference(superposition,[status(thm)],[c_19679,c_1596]) ).
tcf(c_19821,plain,
multiply(iPr_def_14,inverse(sk_c7)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_19679,c_1592]) ).
tcf(c_20431,plain,
multiply(sk_c7,sk_c6) = iPr_def_13,
inference(superposition,[status(thm)],[c_7734,c_19682]) ).
tcf(c_20432,plain,
multiply(sk_c6,sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_7735,c_19682]) ).
tcf(c_20434,plain,
multiply(sk_c5,sk_c7) = iPr_def_15,
inference(superposition,[status(thm)],[c_7740,c_19682]) ).
tcf(c_20687,plain,
( ~ iPr_def_12
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_78,c_19700]) ).
tcf(c_25494,plain,
multiply(iPr_def_19,inverse(sk_c6)) = sk_c2,
inference(demodulation,[status(thm)],[c_19816,c_8679]) ).
tcf(c_25580,plain,
multiply(iPr_def_13,inverse(sk_c6)) = sk_c7,
inference(demodulation,[status(thm)],[c_19817,c_8679]) ).
tcf(c_26735,plain,
multiply(iPr_def_15,inverse(sk_c7)) = sk_c5,
inference(demodulation,[status(thm)],[c_19818,c_8679]) ).
tcf(c_26753,plain,
multiply(inverse(iPr_def_15),sk_c5) = inverse(sk_c7),
inference(superposition,[status(thm)],[c_26735,c_7730]) ).
tcf(c_27446,plain,
multiply(iPr_def_22,inverse(sk_c7)) = sk_c1,
inference(demodulation,[status(thm)],[c_19819,c_8679]) ).
tcf(c_27552,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_27446,c_26753,c_26735,c_25580,c_25494,c_20687,c_20434,c_20432,c_20431,c_19821,c_19819,c_19817,c_19816,c_19730,c_19704,c_15498,c_15121,c_13683,c_13660,c_12351,c_12349,c_11342,c_11328,c_11149,c_10721,c_10503,c_10435,c_10299,c_10094,c_8711,c_8707,c_8703,c_7822,c_7740,c_7738,c_7737,c_5721,c_386,c_383,c_377,c_371,c_368,c_367,c_366,c_365,c_364,c_359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP299-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.39 % Computer : n007.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Wed Sep 23 14:22:22 UTC 2026
% 0.15/0.39 % CPUTime :
% 0.15/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 0.15/0.44
% 0.15/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.44
% 0.15/0.45 % Detected problem language: tptp
% 0.15/0.46 % Proving...
% 10.62/2.31 % SZS status Started for theBenchmark.p
% 10.62/2.31 % SZS status Unsatisfiable for theBenchmark.p
% 10.62/2.31
% 10.62/2.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.62/2.31
% 10.62/2.31 % ------ iProver source info
% 10.62/2.31
% 10.62/2.31 % git: date: 2026-07-19 20:42:38 +0200
% 10.62/2.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.62/2.31 % git: non_committed_changes: false
% 10.62/2.31
% 10.62/2.31 % ------ Parsing...% successful
% 10.62/2.31
% 10.62/2.31
% 10.62/2.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.62/2.31
% 10.62/2.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.62/2.31
% 10.62/2.31 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.62/2.31
% 10.62/2.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.62/2.31 % ------ Proving...
% 10.62/2.31 % ------ Problem Properties
% 10.62/2.31
% 10.62/2.31 %
% 10.62/2.31 % clauses 41
% 10.62/2.31 % conjectures 28
% 10.62/2.31 % EPR 25
% 10.62/2.31 % Horn 16
% 10.62/2.31 % unary 13
% 10.62/2.31 % binary 24
% 10.62/2.31 % lits 76
% 10.62/2.31 % lits eq 70
% 10.62/2.31 % fd_pure 0
% 10.62/2.31 % fd_pseudo 0
% 10.62/2.31 % fd_cond 0
% 10.62/2.31 % fd_pseudo_cond 0
% 10.62/2.31 % AC symbols 0
% 10.62/2.31
% 10.62/2.31 % ------ Schedule dynamic 5 is on
% 10.62/2.31
% 10.62/2.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.62/2.31
% 10.62/2.31
% 10.62/2.31 % ------
% 10.62/2.31 % Current options:
% 10.62/2.31 % ------
% 10.62/2.31
% 10.62/2.31
% 10.62/2.31 %
% 10.62/2.31
% 10.62/2.31 % ------ Proving...
% 10.62/2.31 %
% 10.62/2.31
% 10.62/2.31 % SZS status Unsatisfiable for theBenchmark.p
% 10.62/2.31
% 10.62/2.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.62/2.31
% 10.62/2.31
%------------------------------------------------------------------------------