%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP222-1 : 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 : n026.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 01:31:51 PM UTC 2026
% Result : Unsatisfiable 0.80s 1.21s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 165 ( 31 unt; 0 def)
% Number of atoms : 361 ( 309 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 317 ( 121 ~; 196 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 49 :)
% 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_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c4)
| inverse(sk_c1) = sk_c7 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = inverse(sk_c5)
| inverse(sk_c1) = sk_c7 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| inverse(sk_c1) = sk_c7 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c7 = inverse(sk_c5)
| sk_c6 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = inverse(sk_c5)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f34]) ).
fof(f38,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f44,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != X2
| multiply(X1,X2) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c6 != multiply(X2,sk_c7)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c6
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,plain,
! [X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c6 != multiply(inverse(X1),sk_c7)
| sk_c6 != multiply(X1,inverse(X1))
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 ),
inference(equality_resolution,[],[f45]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_77,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_84,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 )
| ( multiply(inverse(X3),sk_c7) != sk_c6 )
| ( multiply(X3,inverse(X3)) != sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_98,plain,
multiply(inverse(sk_c7),sk_c7) = identity,
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_181,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_96]) ).
tcf(c_182,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_96]) ).
tcf(c_183,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_96]) ).
tcf(c_184,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_315,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c5) = identity ) ),
inference(superposition,[status(thm)],[c_90,c_74]) ).
tcf(c_325,plain,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = identity ) ),
inference(superposition,[status(thm)],[c_78,c_74]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_74,c_75]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_376,c_73]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c7) = sk_c6 )
| ( sk_c6 != X1 )
| ( multiply(inverse(X0),sk_c7) != X1 ) ),
inference(instantiation,[status(thm)],[c_214]) ).
tcf(c_458,plain,
! [X0: $i] :
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(sk_c5,multiply(sk_c6,X0)) = multiply(sk_c7,X0) ) ),
inference(superposition,[status(thm)],[c_87,c_75]) ).
tcf(c_470,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c5,multiply(sk_c6,X0)) = multiply(sk_c7,X0) ) ),
inference(superposition,[status(thm)],[c_83,c_75]) ).
tcf(c_483,plain,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_80,c_182]) ).
tcf(c_484,plain,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_182]) ).
tcf(c_486,plain,
( ( inverse(sk_c1) = sk_c7 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_76,c_182]) ).
tcf(c_487,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_88,c_182]) ).
tcf(c_492,plain,
( ~ iPr_def_11
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_182]) ).
tcf(c_493,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ( inverse(multiply(X0,X1)) != sk_c7 )
| ( multiply(X0,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_75,c_182]) ).
tcf(c_518,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_487,c_89]) ).
tcf(c_529,plain,
( ( inverse(sk_c1) = sk_c7 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_486,c_77]) ).
tcf(c_563,plain,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_484,c_85]) ).
tcf(c_574,plain,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_483,c_81]) ).
tcf(c_599,plain,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ~ iPr_def_10
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_181]) ).
tcf(c_600,plain,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ~ iPr_def_10
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_87,c_181]) ).
tcf(c_601,plain,
( ( inverse(sk_c1) = sk_c7 )
| ~ iPr_def_10
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_79,c_181]) ).
tcf(c_602,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_10
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_91,c_181]) ).
tcf(c_603,plain,
( ( inverse(sk_c4) = sk_c7 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_81,c_181]) ).
tcf(c_604,plain,
( ( inverse(sk_c5) = sk_c7 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_181]) ).
tcf(c_620,plain,
( ( inverse(sk_c5) = sk_c7 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_604,c_78]) ).
tcf(c_631,plain,
( ( inverse(sk_c4) = sk_c7 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_603,c_77]) ).
tcf(c_639,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_602,c_620]) ).
tcf(c_645,plain,
( ( inverse(sk_c1) = sk_c7 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_601,c_620]) ).
tcf(c_657,plain,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_600,c_620]) ).
tcf(c_663,plain,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_599,c_620]) ).
tcf(c_678,plain,
( ( inverse(sk_c1) = sk_c7 )
| ~ iPr_def_12
| ( multiply(sk_c4,sk_c7) != sk_c6 )
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_77,c_183]) ).
tcf(c_679,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_12
| ( multiply(sk_c4,sk_c7) != sk_c6 )
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_89,c_183]) ).
tcf(c_712,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_12
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_679,c_88]) ).
tcf(c_727,plain,
( ( inverse(sk_c1) = sk_c7 )
| ~ iPr_def_12
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_678,c_76]) ).
tcf(c_753,plain,
! [X0: $i] :
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,multiply(sk_c5,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_315,c_75]) ).
tcf(c_756,plain,
! [X0: $i] :
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,multiply(sk_c5,X0)) = X0 ) ),
inference(demodulation,[status(thm)],[c_753,c_73]) ).
tcf(c_771,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,multiply(sk_c5,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_325,c_75]) ).
tcf(c_774,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,multiply(sk_c5,X0)) = X0 ) ),
inference(demodulation,[status(thm)],[c_771,c_73]) ).
tcf(c_798,plain,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(inverse(sk_c5),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_379]) ).
tcf(c_799,plain,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(inverse(sk_c5),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_87,c_379]) ).
tcf(c_803,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(inverse(sk_c1),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_82,c_379]) ).
tcf(c_804,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(inverse(sk_c2),sk_c6) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_85,c_379]) ).
tcf(c_805,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(inverse(sk_c2),sk_c6) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_86,c_379]) ).
tcf(c_810,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_74,c_379]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_379,c_379]) ).
tcf(c_969,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c3,multiply(sk_c7,X0)) = multiply(sk_c6,X0) ) ),
inference(superposition,[status(thm)],[c_93,c_75]) ).
tcf(c_1272,plain,
( ( multiply(inverse(sk_c7),sk_c7) = sk_c6 )
| ( sk_c6 != identity )
| ( multiply(inverse(sk_c7),sk_c7) != identity ) ),
inference(instantiation,[status(thm)],[c_442]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(sk_c5,multiply(multiply(sk_c6,X0),X1)) = multiply(multiply(sk_c7,X0),X1) ) ),
inference(superposition,[status(thm)],[c_458,c_75]) ).
tcf(c_1356,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(sk_c5,multiply(sk_c6,multiply(X0,X1))) = multiply(sk_c7,multiply(X0,X1)) ) ),
inference(demodulation,[status(thm)],[c_1347,c_75]) ).
tcf(c_1439,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c5,multiply(multiply(sk_c6,X0),X1)) = multiply(multiply(sk_c7,X0),X1) ) ),
inference(superposition,[status(thm)],[c_470,c_75]) ).
tcf(c_1448,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c5,multiply(sk_c6,multiply(X0,X1))) = multiply(sk_c7,multiply(X0,X1)) ) ),
inference(demodulation,[status(thm)],[c_1439,c_75]) ).
tcf(c_1518,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( sk_c6 != identity )
| ( inverse(multiply(inverse(multiply(X0,sk_c7)),X0)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_493]) ).
tcf(c_1790,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c1) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_184,c_645]) ).
tcf(c_1794,plain,
( iPr_def_12
| ( inverse(sk_c1) = sk_c7 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1790,c_529]) ).
tcf(c_1804,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c2) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_184,c_639]) ).
tcf(c_1808,plain,
( iPr_def_12
| ( inverse(sk_c2) = sk_c3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1804,c_518]) ).
tcf(c_1827,plain,
( iPr_def_12
| iPr_def_11
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_184,c_663]) ).
tcf(c_1831,plain,
( iPr_def_12
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1827,c_574]) ).
tcf(c_1841,plain,
( iPr_def_12
| iPr_def_11
| ( multiply(sk_c2,sk_c3) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_184,c_657]) ).
tcf(c_1845,plain,
( iPr_def_12
| ( multiply(sk_c2,sk_c3) = sk_c6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1841,c_563]) ).
tcf(c_2048,plain,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_727,c_727,c_1794]) ).
tcf(c_2052,plain,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_77,c_2048]) ).
tcf(c_2058,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_712,c_712,c_1808]) ).
tcf(c_2063,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_89,c_2058]) ).
tcf(c_3129,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_91,c_756]) ).
tcf(c_3152,plain,
inverse(sk_c2) = sk_c3,
inference(forward_subsumption_resolution,[status(thm)],[c_3129,c_2063]) ).
tcf(c_3165,plain,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_79,c_774]) ).
tcf(c_3189,plain,
inverse(sk_c1) = sk_c7,
inference(forward_subsumption_resolution,[status(thm)],[c_3165,c_2052]) ).
tcf(c_3294,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_810,c_816]) ).
tcf(c_3419,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_816,c_74]) ).
tcf(c_3422,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(inverse(inverse(X0))),sk_c7) != sk_c6 )
| ( multiply(X0,inverse(inverse(inverse(X0)))) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_816,c_183]) ).
tcf(c_3428,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_816,c_3294]) ).
tcf(c_3429,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_3428,c_3294]) ).
tcf(c_3456,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_3422,c_816,c_3419,c_3429]) ).
tcf(c_3481,plain,
inverse(inverse(sk_c7)) = sk_c7,
inference(instantiation,[status(thm)],[c_3429]) ).
tcf(c_3484,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( multiply(inverse(sk_c7),sk_c7) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_3456]) ).
tcf(c_3546,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c3 ) ),
inference(demodulation,[status(thm)],[c_805,c_3152]) ).
tcf(c_3551,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(inverse(sk_c3),sk_c3) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_3546,c_379]) ).
tcf(c_3560,plain,
( ( sk_c6 = identity )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_3551,c_74]) ).
tcf(c_3588,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c3 ) ),
inference(demodulation,[status(thm)],[c_804,c_3152]) ).
tcf(c_3593,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(inverse(sk_c3),sk_c3) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_3588,c_379]) ).
tcf(c_3602,plain,
( ( sk_c6 = identity )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_3593,c_74]) ).
tcf(c_3622,plain,
inverse(sk_c4) = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_969,c_98,c_184,c_492,c_631,c_1272,c_3481,c_3484,c_3602]) ).
tcf(c_3674,plain,
( ~ iPr_def_12
| ( multiply(sk_c4,sk_c7) != sk_c6 )
| ( multiply(inverse(sk_c4),sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_3622,c_183]) ).
tcf(c_3676,plain,
( ~ iPr_def_12
| ( multiply(sk_c4,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_3674,c_3622]) ).
tcf(c_3681,plain,
inverse(sk_c5) = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_803,c_98,c_184,c_492,c_620,c_1272,c_3481,c_3484,c_3560]) ).
tcf(c_3713,plain,
( ( multiply(sk_c7,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_798,c_3681]) ).
tcf(c_3714,plain,
( ( multiply(sk_c2,sk_c3) = sk_c6 )
| ( multiply(sk_c7,sk_c7) = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_799,c_3681]) ).
tcf(c_3851,plain,
( ~ iPr_def_10
| ( inverse(sk_c1) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_181]) ).
tcf(c_4421,plain,
multiply(sk_c2,sk_c3) = sk_c6,
inference(global_subsumption_just,[status(thm)],[c_1356,c_84,c_1845,c_3676,c_3714]) ).
tcf(c_4454,plain,
multiply(inverse(sk_c2),sk_c6) = sk_c3,
inference(superposition,[status(thm)],[c_4421,c_379]) ).
tcf(c_4456,plain,
multiply(sk_c3,sk_c6) = sk_c3,
inference(demodulation,[status(thm)],[c_4454,c_3152]) ).
tcf(c_4495,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_1448,c_80,c_1831,c_3676,c_3713]) ).
tcf(c_4560,plain,
sk_c6 != identity,
inference(global_subsumption_just,[status(thm)],[c_1518,c_98,c_184,c_492,c_1272,c_3189,c_3481,c_3484,c_3851,c_4495]) ).
tcf(c_5103,plain,
! [X0: $i] : multiply(inverse(sk_c3),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3152,c_816]) ).
tcf(c_5280,plain,
multiply(sk_c2,sk_c3) = identity,
inference(superposition,[status(thm)],[c_3152,c_3419]) ).
tcf(c_5388,plain,
multiply(inverse(sk_c3),sk_c3) = sk_c6,
inference(superposition,[status(thm)],[c_4456,c_379]) ).
tcf(c_5391,plain,
sk_c6 = identity,
inference(demodulation,[status(thm)],[c_5388,c_5103,c_5280]) ).
tcf(c_5395,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5391,c_4560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 14:13:53 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.80/1.21 % SZS status Started for theBenchmark.p
% 0.80/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.80/1.21
% 0.80/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.80/1.21
% 0.80/1.21 % ------ iProver source info
% 0.80/1.21
% 0.80/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.80/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.80/1.21 % git: non_committed_changes: false
% 0.80/1.21
% 0.80/1.21 % ------ Parsing...% successful
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.80/1.21
% 0.80/1.21 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 0.80/1.21
% 0.80/1.21 % ------ Preprocessing... gs_s sp: 4 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 0.80/1.21
% 0.80/1.21 % ------ Preprocessing...
% 0.80/1.21 % ------ Proving...
% 0.80/1.21 % ------ Problem Properties
% 0.80/1.21
% 0.80/1.21 %
% 0.80/1.21 % clauses 27
% 0.80/1.21 % conjectures 24
% 0.80/1.21 % EPR 1
% 0.80/1.21 % Horn 6
% 0.80/1.21 % unary 3
% 0.80/1.21 % binary 20
% 0.80/1.21 % lits 55
% 0.80/1.21 % lits eq 49
% 0.80/1.21 % fd_pure 0
% 0.80/1.21 % fd_pseudo 0
% 0.80/1.21 % fd_cond 0
% 0.80/1.21 % fd_pseudo_cond 0
% 0.80/1.21 % AC symbols 0
% 0.80/1.21
% 0.80/1.21 % ------ Input Options Time Limit: Unbounded
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21 % ------
% 0.80/1.21 % Current options:
% 0.80/1.21 % ------
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21 %
% 0.80/1.21
% 0.80/1.21 % ------ Proving...
% 0.80/1.21 %
% 0.80/1.21
% 0.80/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.80/1.21
% 0.80/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.22
% 0.80/1.22
%------------------------------------------------------------------------------