%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP229-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 01:32:03 PM UTC 2026
% Result : Unsatisfiable 3.72s 11.21s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 141 ( 37 unt; 0 def)
% Number of atoms : 305 ( 282 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 262 ( 98 ~; 164 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = inverse(sk_c4)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c5)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f20]) ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f28]) ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( inverse(sk_c8) = sk_c7
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f40]) ).
fof(f46,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f52]) ).
fof(f58,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| inverse(sk_c8) != sk_c7
| sk_c8 != inverse(X2)
| multiply(X2,sk_c8) != X1
| sk_c7 != multiply(sk_c8,X1)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X2,X3,X0,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| inverse(sk_c8) != sk_c7
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 ),
inference(equality_resolution,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| inverse(sk_c8) != sk_c7
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(sk_c8,multiply(X3,sk_c8)) != sk_c7 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_269,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_270,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_271,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_444,c_83]) ).
tcf(c_478,plain,
( ~ iPr_def_10
| ( inverse(sk_c4) != sk_c8 )
| ( multiply(sk_c4,sk_c7) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_485,plain,
( ( inverse(sk_c1) = sk_c8 )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_88,c_269]) ).
tcf(c_487,plain,
( ( inverse(sk_c1) = sk_c8 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_485,c_87,c_485]) ).
tcf(c_499,plain,
( ~ iPr_def_10
| ( inverse(sk_c1) != sk_c8 )
| ( multiply(sk_c1,sk_c7) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_535,plain,
( ( inverse(sk_c8) = sk_c7 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_92,c_269]) ).
tcf(c_537,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_535,c_93,c_94,c_478,c_487,c_499]) ).
tcf(c_544,plain,
( iPr_def_11
| ( inverse(sk_c8) != sk_c7 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_271,c_537]) ).
tcf(c_697,plain,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_108,c_270]) ).
tcf(c_698,plain,
( ( inverse(sk_c1) = sk_c8 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_90,c_270]) ).
tcf(c_699,plain,
( ( inverse(sk_c5) = sk_c8 )
| ~ iPr_def_11
| ( inverse(sk_c2) != sk_c8 )
| ( multiply(sk_c8,sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_109,c_270]) ).
tcf(c_719,plain,
( ( inverse(sk_c5) = sk_c8 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_699,c_115,c_103,c_699]) ).
tcf(c_723,plain,
inverse(sk_c1) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_698,c_91,c_86,c_93,c_89,c_94,c_271,c_478,c_487,c_499,c_698]) ).
tcf(c_729,plain,
multiply(sk_c2,sk_c8) = sk_c3,
inference(global_subsumption_just,[status(thm)],[c_697,c_109,c_104,c_93,c_107,c_94,c_271,c_478,c_487,c_499,c_697]) ).
tcf(c_756,plain,
( ( inverse(sk_c2) = sk_c8 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_114,c_270]) ).
tcf(c_760,plain,
inverse(sk_c2) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_756,c_115,c_110,c_113,c_93,c_94,c_271,c_478,c_487,c_499,c_756]) ).
tcf(c_782,plain,
multiply(sk_c8,sk_c1) = identity,
inference(superposition,[status(thm)],[c_723,c_84]) ).
tcf(c_783,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_729,c_85]) ).
tcf(c_784,plain,
( ~ iPr_def_11
| ( inverse(sk_c2) != sk_c8 )
| ( multiply(sk_c8,sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_729,c_270]) ).
tcf(c_786,plain,
( ~ iPr_def_11
| ( multiply(sk_c8,sk_c3) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_784,c_115,c_110,c_113,c_93,c_94,c_271,c_478,c_487,c_499,c_756,c_784]) ).
tcf(c_792,plain,
multiply(sk_c8,sk_c2) = identity,
inference(superposition,[status(thm)],[c_760,c_84]) ).
tcf(c_820,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(inverse(sk_c8),sk_c7) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_102,c_449]) ).
tcf(c_823,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(inverse(sk_c8),sk_c7) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_98,c_449]) ).
tcf(c_824,plain,
multiply(inverse(sk_c2),sk_c3) = sk_c8,
inference(superposition,[status(thm)],[c_729,c_449]) ).
tcf(c_829,plain,
multiply(inverse(sk_c8),identity) = sk_c1,
inference(superposition,[status(thm)],[c_782,c_449]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_449,c_449]) ).
tcf(c_833,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(light_normalisation,[status(thm)],[c_824,c_760]) ).
tcf(c_1018,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(inverse(inverse(sk_c8)),sk_c3) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_820,c_449]) ).
tcf(c_1023,plain,
( ( sk_c8 = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_1018,c_830,c_833]) ).
tcf(c_1091,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(inverse(inverse(sk_c8)),sk_c3) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_823,c_449]) ).
tcf(c_1096,plain,
( ( sk_c8 = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_1091,c_830,c_833]) ).
tcf(c_1127,plain,
multiply(inverse(sk_c8),identity) = sk_c2,
inference(superposition,[status(thm)],[c_792,c_449]) ).
tcf(c_1136,plain,
( ~ iPr_def_11
| ( sk_c8 != sk_c7 ) ),
inference(superposition,[status(thm)],[c_833,c_786]) ).
tcf(c_1142,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c3,
inference(superposition,[status(thm)],[c_833,c_449]) ).
tcf(c_1144,plain,
sk_c3 = identity,
inference(demodulation,[status(thm)],[c_1142,c_84]) ).
tcf(c_1316,plain,
sk_c1 = sk_c2,
inference(demodulation,[status(thm)],[c_829,c_1127]) ).
tcf(c_1319,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_1316,c_97]) ).
tcf(c_1320,plain,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1316,c_96]) ).
tcf(c_1323,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_1316,c_92]) ).
tcf(c_1358,plain,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1320,c_270]) ).
tcf(c_1364,plain,
multiply(sk_c2,sk_c7) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_1358,c_115,c_110,c_113,c_93,c_101,c_94,c_271,c_478,c_487,c_499,c_756,c_784,c_1323,c_1319,c_1358]) ).
tcf(c_1404,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = X0,
inference(demodulation,[status(thm)],[c_783,c_83,c_1144]) ).
tcf(c_1413,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_98,c_1404]) ).
tcf(c_1416,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_792,c_1404]) ).
tcf(c_1425,plain,
( ( sk_c8 = sk_c3 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1413,c_1364]) ).
tcf(c_1426,plain,
( ( sk_c8 = identity )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_1425,c_1144]) ).
tcf(c_1633,plain,
( ( sk_c8 = sk_c7 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1023,c_270]) ).
tcf(c_1641,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_1633,c_101,c_719,c_786,c_1136,c_1633]) ).
tcf(c_1652,plain,
inverse(sk_c8) != sk_c7,
inference(backward_subsumption_resolution,[status(thm)],[c_544,c_1641]) ).
tcf(c_1657,plain,
sk_c8 = identity,
inference(backward_subsumption_resolution,[status(thm)],[c_1426,c_1652]) ).
tcf(c_1658,plain,
sk_c8 = sk_c7,
inference(backward_subsumption_resolution,[status(thm)],[c_1096,c_1652]) ).
tcf(c_1663,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_1652]) ).
tcf(c_1664,plain,
sk_c7 = identity,
inference(demodulation,[status(thm)],[c_1658,c_1657]) ).
tcf(c_1673,plain,
multiply(sk_c1,identity) = identity,
inference(demodulation,[status(thm)],[c_1663,c_1657,c_1664]) ).
tcf(c_1674,plain,
multiply(sk_c2,identity) = identity,
inference(light_normalisation,[status(thm)],[c_1673,c_1316]) ).
tcf(c_1675,plain,
sk_c2 = identity,
inference(demodulation,[status(thm)],[c_1674,c_1416]) ).
tcf(c_1676,plain,
$false,
inference(ground_joinability,[status(thm)],[c_1652,c_760,c_1657,c_1664,c_1675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP229-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n001.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Wed Sep 23 14:18:16 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.43
% 0.14/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.43
% 0.14/10.43 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 3.72/11.21 % SZS status Started for theBenchmark.p
% 3.72/11.21 % SZS status Unsatisfiable for theBenchmark.p
% 3.72/11.21
% 3.72/11.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.72/11.21
% 3.72/11.21 % ------ iProver source info
% 3.72/11.21
% 3.72/11.21 % git: date: 2026-07-19 20:42:38 +0200
% 3.72/11.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.72/11.21 % git: non_committed_changes: false
% 3.72/11.21
% 3.72/11.21 % ------ Parsing...% successful
% 3.72/11.21
% 3.72/11.21
% 3.72/11.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.72/11.21
% 3.72/11.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.72/11.21
% 3.72/11.21 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.72/11.21
% 3.72/11.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.72/11.21 % ------ Proving...
% 3.72/11.21 % ------ Problem Properties
% 3.72/11.21
% 3.72/11.21 %
% 3.72/11.21 % clauses 36
% 3.72/11.21 % conjectures 33
% 3.72/11.21 % EPR 0
% 3.72/11.21 % Horn 5
% 3.72/11.21 % unary 3
% 3.72/11.21 % binary 30
% 3.72/11.21 % lits 72
% 3.72/11.21 % lits eq 68
% 3.72/11.21 % fd_pure 0
% 3.72/11.21 % fd_pseudo 0
% 3.72/11.21 % fd_cond 0
% 3.72/11.21 % fd_pseudo_cond 0
% 3.72/11.21 % AC symbols 0
% 3.72/11.21
% 3.72/11.21 % ------ Input Options Time Limit: Unbounded
% 3.72/11.21
% 3.72/11.21
% 3.72/11.21 % ------
% 3.72/11.21 % Current options:
% 3.72/11.21 % ------
% 3.72/11.21
% 3.72/11.21
% 3.72/11.21 %
% 3.72/11.21
% 3.72/11.21 % ------ Proving...
% 3.72/11.21 %
% 3.72/11.21
% 3.72/11.21 % SZS status Unsatisfiable for theBenchmark.p
% 3.72/11.21
% 3.72/11.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/11.21
%------------------------------------------------------------------------------