%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP214-1 : 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 : n006.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 01:31:49 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.12s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 23
% Syntax : Number of formulae : 199 ( 69 unt; 7 def)
% Number of atoms : 626 ( 345 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 364 ( 162 ~; 202 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 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_c3,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c5 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != X3
| multiply(X4,X3) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X3
| multiply(sk_c7,X1) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != X3
| sk_c6 != multiply(X4,X3)
| sk_c7 != inverse(X2)
| multiply(X2,sk_c7) != X3
| sk_c6 != multiply(sk_c7,X1)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
! [X2,X0,X1,X4] :
( multiply(X2,sk_c7) != inverse(X4)
| sk_c6 != multiply(X4,multiply(X2,sk_c7))
| sk_c7 != inverse(X2)
| sk_c6 != multiply(sk_c7,X1)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(equality_resolution,[],[f29]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_73,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_74,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_75,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_76,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_77,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_78,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_80,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X2) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,X3) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X0,sk_c7) != inverse(X1) )
| ( multiply(X1,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_213,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(sk_c7,X0) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_80]) ).
tcf(c_214,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_80]) ).
tcf(c_215,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c7) != inverse(X0) )
| ( multiply(X0,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_80]) ).
tcf(c_216,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_80]) ).
tcf(c_217,definition,
iPr_def_13 = multiply(sk_c7,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_218,definition,
iPr_def_14 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_219,definition,
iPr_def_15 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_220,definition,
iPr_def_16 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_221,definition,
iPr_def_17 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_222,definition,
iPr_def_18 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_223,definition,
iPr_def_19 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_224,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_216]) ).
tcf(c_225,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c7) != inverse(X0) )
| ( multiply(X0,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_215]) ).
tcf(c_226,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_214]) ).
tcf(c_227,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(sk_c7,X0) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_213]) ).
tcf(c_228,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_79,c_218,c_217]) ).
tcf(c_229,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_78,c_219]) ).
tcf(c_230,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_77,c_220]) ).
tcf(c_231,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_76,c_221]) ).
tcf(c_232,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_75,c_222]) ).
tcf(c_233,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_234,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_235,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_236,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_71,c_223]) ).
tcf(c_237,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_238,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_239,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_384,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_228,c_231]) ).
tcf(c_410,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_232,c_219]) ).
tcf(c_412,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_228,c_219]) ).
tcf(c_422,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_234,c_223]) ).
tcf(c_425,plain,
multiply(iPr_def_16,sk_c3) = identity,
inference(superposition,[status(thm)],[c_220,c_66]) ).
tcf(c_426,plain,
multiply(iPr_def_14,sk_c4) = identity,
inference(superposition,[status(thm)],[c_218,c_66]) ).
tcf(c_427,plain,
multiply(iPr_def_18,sk_c1) = identity,
inference(superposition,[status(thm)],[c_222,c_66]) ).
tcf(c_435,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_235,c_232]) ).
tcf(c_448,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_236,c_219]) ).
tcf(c_502,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_239,c_236]) ).
tcf(c_514,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_217,c_227]) ).
tcf(c_529,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_223,c_226]) ).
tcf(c_530,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_221,c_226]) ).
tcf(c_537,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_530,c_220]) ).
tcf(c_541,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( sk_c7 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_529,c_222]) ).
tcf(c_567,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(X0,sk_c7) != inverse(identity) ) ),
inference(superposition,[status(thm)],[c_65,c_225]) ).
tcf(c_568,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(X0) != sk_c7 )
| ( inverse(inverse(multiply(X0,sk_c7))) != multiply(X0,sk_c7) ) ),
inference(superposition,[status(thm)],[c_66,c_225]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_66,c_67]) ).
tcf(c_697,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_425,c_67]) ).
tcf(c_698,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_697,c_65]) ).
tcf(c_700,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_426,c_67]) ).
tcf(c_701,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_700,c_65]) ).
tcf(c_703,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_427,c_67]) ).
tcf(c_704,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_703,c_65]) ).
tcf(c_719,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_230,c_514]) ).
tcf(c_749,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_384,c_514]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_12
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c7) != inverse(X0) )
| ( multiply(X0,multiply(X1,iPr_def_18)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_435,c_225]) ).
tcf(c_774,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_18) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_435,c_226]) ).
tcf(c_776,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_435,c_223]) ).
tcf(c_1002,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_228,c_231]) ).
tcf(c_1032,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_223,c_704]) ).
tcf(c_1073,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_422,c_704]) ).
tcf(c_1074,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1073,c_1032]) ).
tcf(c_1671,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_774,c_435,c_502,c_541]) ).
tcf(c_1677,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_665,c_65]) ).
tcf(c_1685,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_65,c_1677]) ).
tcf(c_1686,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_66,c_1677]) ).
tcf(c_1708,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_698,c_1677]) ).
tcf(c_1709,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_701,c_1677]) ).
tcf(c_1710,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_704,c_1677]) ).
tcf(c_1716,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_1677,c_1677]) ).
tcf(c_1899,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_239,c_236]) ).
tcf(c_1907,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_1686,c_1716]) ).
tcf(c_1924,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_1907,c_1685]) ).
tcf(c_2106,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != identity )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_567,c_1924]) ).
tcf(c_2119,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_19 )
| ( inverse(sk_c1) != sk_c7 )
| ( multiply(sk_c1,sk_c7) != identity ) ),
inference(superposition,[status(thm)],[c_223,c_2106]) ).
tcf(c_2122,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 )
| ( multiply(inverse(sk_c7),sk_c7) != identity ) ),
inference(superposition,[status(thm)],[c_66,c_2106]) ).
tcf(c_2127,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_18) != sk_c6 )
| ( multiply(X0,sk_c7) != identity ) ),
inference(superposition,[status(thm)],[c_234,c_2106]) ).
tcf(c_2134,plain,
( ~ iPr_def_12
| ( identity != iPr_def_19 )
| ( sk_c6 != iPr_def_19 )
| ( sk_c7 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_2119,c_222,c_223]) ).
tcf(c_2139,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_2122,c_66]) ).
tcf(c_2510,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(X0) != sk_c7 )
| ( inverse(inverse(multiply(X0,iPr_def_18))) != multiply(X0,iPr_def_18) ) ),
inference(superposition,[status(thm)],[c_234,c_568]) ).
tcf(c_3039,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_234,c_541]) ).
tcf(c_3059,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_238,c_3039]) ).
tcf(c_3072,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_537,c_3059]) ).
tcf(c_3087,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_233,c_3072]) ).
tcf(c_3089,plain,
( ( sk_c6 = iPr_def_13 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_229,c_3072]) ).
tcf(c_3109,plain,
multiply(sk_c3,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_1708,c_66]) ).
tcf(c_3115,plain,
multiply(sk_c3,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_1708,c_1907]) ).
tcf(c_3200,plain,
inverse(iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_3115,c_1907]) ).
tcf(c_3318,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ( multiply(X0,sk_c7) != identity )
| ( multiply(X0,iPr_def_18) != sk_c6 )
| ( inverse(X0) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_2127,c_224,c_719,c_2127,c_3059]) ).
tcf(c_3319,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_18) != sk_c6 )
| ( multiply(X0,sk_c7) != identity ) ),
inference(renaming,[status(thm)],[c_3318]) ).
tcf(c_3663,plain,
multiply(sk_c4,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_1709,c_66]) ).
tcf(c_3728,plain,
( ( identity = iPr_def_15 )
| ( sk_c6 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_448,c_3663]) ).
tcf(c_3729,plain,
( ( identity = iPr_def_15 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_412,c_3663]) ).
tcf(c_3730,plain,
( ( identity = iPr_def_15 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_410,c_3663]) ).
tcf(c_4324,plain,
( ( identity = iPr_def_15 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_3729,c_514]) ).
tcf(c_4357,plain,
( ( identity = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_3730,c_541]) ).
tcf(c_4375,plain,
! [X0: $i] :
( ( identity = iPr_def_15 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_18) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_3730,c_226]) ).
tcf(c_4377,plain,
( ( identity = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_3730,c_223]) ).
tcf(c_4509,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1899,c_1002]) ).
tcf(c_4721,plain,
( ( identity = iPr_def_15 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_4375,c_3728,c_4357]) ).
tcf(c_5323,plain,
multiply(sk_c1,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_1710,c_66]) ).
tcf(c_5331,plain,
multiply(sk_c1,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_1710,c_1907]) ).
tcf(c_5412,plain,
( ( identity = iPr_def_19 )
| ( identity = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_4377,c_5323]) ).
tcf(c_5413,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_776,c_5323]) ).
tcf(c_5414,plain,
( ( identity = iPr_def_19 )
| ( sk_c7 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_422,c_5323]) ).
tcf(c_5432,plain,
iPr_def_14 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_4509,c_224,c_435,c_502,c_749,c_1671,c_2134,c_5413]) ).
tcf(c_5443,plain,
multiply(sk_c3,sk_c7) = iPr_def_14,
inference(demodulation,[status(thm)],[c_221,c_5432]) ).
tcf(c_5578,plain,
( ( sk_c7 = iPr_def_16 )
| ( sk_c6 != identity )
| ( inverse(sk_c1) != sk_c7 )
| ( multiply(sk_c1,sk_c7) != identity ) ),
inference(superposition,[status(thm)],[c_5323,c_3319]) ).
tcf(c_5594,plain,
( ( sk_c7 = iPr_def_16 )
| ( identity != iPr_def_19 )
| ( sk_c6 != identity )
| ( sk_c7 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5578,c_222,c_223]) ).
tcf(c_5607,plain,
inverse(iPr_def_18) = sk_c1,
inference(demodulation,[status(thm)],[c_5331,c_1907]) ).
tcf(c_5950,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_14 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_5443,c_226]) ).
tcf(c_5956,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_14 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5950,c_220]) ).
tcf(c_6073,plain,
( ( sk_c7 = iPr_def_16 )
| ( sk_c6 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_2510,c_1074,c_5414,c_5594]) ).
tcf(c_6087,plain,
( ( sk_c7 = iPr_def_16 )
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_238,c_6073]) ).
tcf(c_6105,plain,
sk_c7 = iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_6087,c_5414,c_6087]) ).
tcf(c_6131,plain,
( ( iPr_def_16 = iPr_def_18 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_3087,c_6105]) ).
tcf(c_6133,plain,
( ~ iPr_def_11
| ( iPr_def_16 != iPr_def_18 )
| ( sk_c6 != iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_541,c_6105]) ).
tcf(c_6166,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(iPr_def_16,X0) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_227,c_6105]) ).
tcf(c_6169,plain,
multiply(sk_c1,iPr_def_16) = iPr_def_19,
inference(demodulation,[status(thm)],[c_223,c_6105]) ).
tcf(c_6170,plain,
multiply(sk_c3,iPr_def_16) = iPr_def_17,
inference(demodulation,[status(thm)],[c_221,c_6105]) ).
tcf(c_6173,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_233,c_6105]) ).
tcf(c_6307,plain,
identity = iPr_def_17,
inference(demodulation,[status(thm)],[c_3109,c_6170]) ).
tcf(c_6311,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_4721,c_6307]) ).
tcf(c_6338,plain,
( ( iPr_def_16 = iPr_def_18 )
| ~ iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_6131,c_6311]) ).
tcf(c_6341,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6133,c_6338]) ).
tcf(c_6475,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( X0 != sk_c6 ) ),
inference(superposition,[status(thm)],[c_698,c_6166]) ).
tcf(c_6620,plain,
( ( sk_c6 = iPr_def_13 )
| ~ iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_3089,c_6311]) ).
tcf(c_6691,plain,
identity = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_5412,c_224,c_2134,c_3730,c_3728,c_4324,c_4721,c_5412]) ).
tcf(c_6693,plain,
iPr_def_15 = iPr_def_17,
inference(demodulation,[status(thm)],[c_6307,c_6691]) ).
tcf(c_6703,plain,
multiply(sk_c3,iPr_def_16) = iPr_def_15,
inference(demodulation,[status(thm)],[c_6170,c_6693]) ).
tcf(c_6787,plain,
iPr_def_14 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_773,c_224,c_435,c_502,c_749,c_1671,c_2134,c_5413]) ).
tcf(c_6789,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_6693,c_6787]) ).
tcf(c_6792,plain,
identity = iPr_def_14,
inference(demodulation,[status(thm)],[c_6691,c_6789]) ).
tcf(c_6793,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_6173,c_6789]) ).
tcf(c_6797,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_237,c_6789]) ).
tcf(c_6798,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_229,c_6789]) ).
tcf(c_6963,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_6620,c_5956,c_6105,c_6341,c_6797]) ).
tcf(c_6965,plain,
( iPr_def_12
| iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_224,c_6963]) ).
tcf(c_6990,plain,
multiply(sk_c3,iPr_def_16) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6703,c_6789]) ).
tcf(c_7057,plain,
~ iPr_def_10,
inference(equality_resolution,[status(thm)],[c_6475]) ).
tcf(c_7058,plain,
iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_6965,c_7057]) ).
tcf(c_7443,plain,
( ( inverse(inverse(sk_c7)) != sk_c7 )
| ( sk_c6 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_2139,c_2139,c_7058]) ).
tcf(c_7444,plain,
( ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(renaming,[status(thm)],[c_7443]) ).
tcf(c_7445,plain,
sk_c6 != identity,
inference(ground_joinability,[status(thm)],[c_7444,c_220,c_3200,c_6105]) ).
tcf(c_7446,plain,
sk_c6 != iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7445,c_6792]) ).
tcf(c_7447,plain,
sk_c6 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_6798,c_7446]) ).
tcf(c_7448,plain,
sk_c6 = iPr_def_19,
inference(backward_subsumption_resolution,[status(thm)],[c_6797,c_7446]) ).
tcf(c_7449,plain,
iPr_def_16 = iPr_def_18,
inference(backward_subsumption_resolution,[status(thm)],[c_6793,c_7446]) ).
tcf(c_7450,plain,
iPr_def_13 != iPr_def_14,
inference(demodulation,[status(thm)],[c_7446,c_7447]) ).
tcf(c_7459,plain,
inverse(iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_5607,c_7449]) ).
tcf(c_7462,plain,
sk_c1 = sk_c3,
inference(demodulation,[status(thm)],[c_3200,c_7459]) ).
tcf(c_7468,plain,
multiply(sk_c1,iPr_def_16) = iPr_def_14,
inference(demodulation,[status(thm)],[c_6990,c_7462]) ).
tcf(c_7475,plain,
iPr_def_14 = iPr_def_19,
inference(demodulation,[status(thm)],[c_6169,c_7468]) ).
tcf(c_7483,plain,
iPr_def_13 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7448,c_7447,c_7475]) ).
tcf(c_7564,plain,
$false,
inference(ground_joinability,[status(thm)],[c_7450,c_7483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 14:09:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 3.63/1.12 % SZS status Started for theBenchmark.p
% 3.63/1.12 % SZS status Unsatisfiable for theBenchmark.p
% 3.63/1.12
% 3.63/1.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.63/1.12
% 3.63/1.12 % ------ iProver source info
% 3.63/1.12
% 3.63/1.12 % git: date: 2026-07-19 20:42:38 +0200
% 3.63/1.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.63/1.12 % git: non_committed_changes: false
% 3.63/1.12
% 3.63/1.12 % ------ Parsing...% successful
% 3.63/1.12
% 3.63/1.12
% 3.63/1.12 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.63/1.12
% 3.63/1.12 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.63/1.12
% 3.63/1.12 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.63/1.12
% 3.63/1.12 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.63/1.12 % ------ Proving...
% 3.63/1.12 % ------ Problem Properties
% 3.63/1.12
% 3.63/1.12 %
% 3.63/1.12 % clauses 26
% 3.63/1.12 % conjectures 16
% 3.63/1.12 % EPR 13
% 3.63/1.12 % Horn 13
% 3.63/1.12 % unary 10
% 3.63/1.12 % binary 13
% 3.63/1.12 % lits 46
% 3.63/1.12 % lits eq 40
% 3.63/1.12 % fd_pure 0
% 3.63/1.12 % fd_pseudo 0
% 3.63/1.12 % fd_cond 0
% 3.63/1.12 % fd_pseudo_cond 0
% 3.63/1.12 % AC symbols 0
% 3.63/1.12
% 3.63/1.12 % ------ Schedule dynamic 5 is on
% 3.63/1.12
% 3.63/1.12 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 3.63/1.12
% 3.63/1.12 % ------
% 3.63/1.12 % Current options:
% 3.63/1.12 % ------
% 3.63/1.12
% 3.63/1.12
% 3.63/1.12 %
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% 3.63/1.12 % ------ Proving...
% 3.63/1.12 %
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% 3.63/1.12 % SZS status Unsatisfiable for theBenchmark.p
% 3.63/1.12
% 3.63/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 3.63/1.12
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