%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP336-1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:03 PM UTC 2026
% Result : Unsatisfiable 42.83s 7.44s
% Output : CNFRefutation 42.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 31
% Syntax : Number of formulae : 217 ( 47 unt; 0 def)
% Number of atoms : 489 ( 437 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 442 ( 170 ~; 272 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 95 !; 0 ?; 64 :)
% 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_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c10 = inverse(sk_c5)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c10 = inverse(sk_c5)
| sk_c10 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c10 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c6)
| sk_c10 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f63,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f69,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c5)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f77]) ).
fof(f81,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c7 = inverse(sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f81]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X6,sk_c8)
| inverse(X5) != X6
| sk_c9 != multiply(X5,X6)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c9 != multiply(X2,sk_c10)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X6,sk_c8)
| inverse(X5) != X6
| sk_c9 != multiply(X5,X6)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(equality_resolution,[],[f102]) ).
fof(f104,plain,
! [X3,X0,X1,X4,X5] :
( sk_c9 != multiply(inverse(X5),sk_c8)
| sk_c9 != multiply(X5,inverse(X5))
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(equality_resolution,[],[f103]) ).
tcf(c_101,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_102,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c9 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_124,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c10 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_133,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_140,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_142,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_152,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c10 )
| ( inverse(X3) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c10) != sk_c8 )
| ( multiply(X4,sk_c9) != sk_c10 )
| ( multiply(X3,sk_c10) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c10 )
| ( multiply(inverse(X2),sk_c10) != sk_c9 )
| ( multiply(inverse(X1),sk_c8) != sk_c9 )
| ( multiply(X2,inverse(X2)) != sk_c9 )
| ( multiply(X1,inverse(X1)) != sk_c9 ) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_597,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_152]) ).
tcf(c_598,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_152]) ).
tcf(c_599,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c10) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_152]) ).
tcf(c_600,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_152]) ).
tcf(c_601,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_152]) ).
tcf(c_602,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_865,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( sk_c8 != X0 )
| ( multiply(sk_c9,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_603]) ).
tcf(c_866,plain,
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( sk_c8 != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_865]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_603]) ).
tcf(c_869,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_868]) ).
tcf(c_870,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_871,plain,
( ( sk_c8 = sk_c10 )
| ( sk_c8 != sk_c8 )
| ( sk_c10 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_869]) ).
tcf(c_875,plain,
( ( sk_c8 = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_869]) ).
tcf(c_876,plain,
multiply(identity,sk_c8) = sk_c8,
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_881,plain,
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(sk_c9,sk_c10) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_865]) ).
tcf(c_892,plain,
( ( multiply(sk_c9,sk_c10) = multiply(identity,sk_c8) )
| ( sk_c10 != sk_c8 )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_604]) ).
tcf(c_1075,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_102,c_103]) ).
tcf(c_1433,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1075,c_101]) ).
tcf(c_1448,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(inverse(sk_c4),sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_112,c_1433]) ).
tcf(c_1449,plain,
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( multiply(inverse(sk_c10),sk_c9) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_106,c_1433]) ).
tcf(c_1451,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(inverse(sk_c10),sk_c9) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_114,c_1433]) ).
tcf(c_1456,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(inverse(sk_c5),sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_140,c_1433]) ).
tcf(c_1457,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(inverse(sk_c5),sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_116,c_1433]) ).
tcf(c_1463,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(inverse(sk_c6),sk_c9) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_117,c_1433]) ).
tcf(c_1483,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_102,c_1433]) ).
tcf(c_1491,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_1433,c_1433]) ).
tcf(c_1791,plain,
( ( inverse(sk_c1) = sk_c10 )
| ~ iPr_def_10
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_597,c_116]) ).
tcf(c_1795,plain,
( ( inverse(sk_c5) = sk_c10 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_597,c_123]) ).
tcf(c_1799,plain,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_597,c_124]) ).
tcf(c_1957,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = X0 )
| ( X0 != sk_c9 ) ),
inference(resolution,[status(thm)],[c_603,c_114]) ).
tcf(c_2032,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_603,c_602]) ).
tcf(c_2033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_603,c_605]) ).
tcf(c_2123,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_1483,c_1491]) ).
tcf(c_2132,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_1491,c_102]) ).
tcf(c_2389,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c10,sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_113,c_1448]) ).
tcf(c_2412,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_139,c_1456]) ).
tcf(c_2482,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_115,c_1457]) ).
tcf(c_2517,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c7,sk_c9) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_118,c_1463]) ).
tcf(c_2565,plain,
( ( inverse(sk_c6) = sk_c7 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_126,c_597]) ).
tcf(c_2708,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_137,c_2132]) ).
tcf(c_2709,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_113,c_2132]) ).
tcf(c_3234,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c9 != identity )
| ( multiply(inverse(X0),sk_c10) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_599,c_2132]) ).
tcf(c_3241,plain,
( ~ iPr_def_12
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_102,c_3234]) ).
tcf(c_3253,plain,
! [X0: $i] :
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(inverse(X0),sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_600,c_2132]) ).
tcf(c_3260,plain,
( ~ iPr_def_13
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_102,c_3253]) ).
tcf(c_3400,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_2708,c_136]) ).
tcf(c_3455,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_2709,c_112]) ).
tcf(c_4194,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_601,c_114]) ).
tcf(c_4195,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_601,c_138]) ).
tcf(c_4704,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c7,multiply(sk_c9,X0)) = multiply(sk_c7,X0) ) ),
inference(superposition,[status(thm)],[c_2517,c_103]) ).
tcf(c_4818,plain,
( ( inverse(sk_c1) = sk_c10 )
| ~ iPr_def_10
| ( inverse(sk_c10) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_2389,c_597]) ).
tcf(c_4830,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_136,c_598]) ).
tcf(c_4831,plain,
( ( inverse(sk_c1) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_112,c_598]) ).
tcf(c_4837,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_102,c_598]) ).
tcf(c_4862,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c6,sk_c7) = identity ) ),
inference(superposition,[status(thm)],[c_142,c_2132]) ).
tcf(c_4871,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_1483,c_2123]) ).
tcf(c_4872,plain,
( ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4837,c_4871]) ).
tcf(c_4889,plain,
( ( inverse(sk_c1) = sk_c10 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_4818,c_115,c_1791]) ).
tcf(c_4893,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_4830,c_3400,c_4872]) ).
tcf(c_4897,plain,
( ( inverse(sk_c1) = sk_c10 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_4831,c_3455,c_4872]) ).
tcf(c_4937,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1075,c_101]) ).
tcf(c_4997,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(inverse(sk_c10),sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_2482,c_4937]) ).
tcf(c_5012,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(inverse(sk_c7),multiply(sk_c7,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_4704,c_4937]) ).
tcf(c_5015,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_5012,c_4937]) ).
tcf(c_5017,plain,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c10 ) ),
inference(instantiation,[status(thm)],[c_5015]) ).
tcf(c_5027,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(inverse(sk_c10),sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_2412,c_4937]) ).
tcf(c_5115,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(inverse(sk_c6),identity) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_4862,c_4937]) ).
tcf(c_5977,plain,
( ( sk_c10 = sk_c8 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_1451,c_4997]) ).
tcf(c_6009,plain,
inverse(sk_c1) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_1457,c_866,c_871,c_870,c_3241,c_3260,c_3455,c_4194,c_4889,c_4897,c_5017,c_5977]) ).
tcf(c_6045,plain,
inverse(sk_c10) = sk_c1,
inference(superposition,[status(thm)],[c_6009,c_4871]) ).
tcf(c_6233,plain,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c1,sk_c9) = sk_c10 ) ),
inference(light_normalisation,[status(thm)],[c_5027,c_6045]) ).
tcf(c_6238,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_6233,c_597]) ).
tcf(c_6242,plain,
( ( inverse(sk_c2) = sk_c3 )
| ~ iPr_def_10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_6238,c_6009]) ).
tcf(c_6376,plain,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1449,c_6045]) ).
tcf(c_6387,plain,
( ( sk_c10 = sk_c8 )
| ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_6376,c_6233]) ).
tcf(c_6495,plain,
inverse(sk_c2) = sk_c3,
inference(global_subsumption_just,[status(thm)],[c_5115,c_870,c_875,c_876,c_881,c_892,c_3241,c_3260,c_3400,c_4195,c_4893,c_6242,c_6387]) ).
tcf(c_7477,plain,
inverse(sk_c1) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_1957,c_866,c_871,c_870,c_3241,c_3260,c_3455,c_4194,c_4889,c_4897,c_5017,c_5977]) ).
tcf(c_7484,plain,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ~ iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_1799,c_7477]) ).
tcf(c_7491,plain,
sk_c10 = inverse(sk_c1),
inference(resolution,[status(thm)],[c_7477,c_2032]) ).
tcf(c_10607,plain,
multiply(sk_c1,sk_c10) = identity,
inference(superposition,[status(thm)],[c_6009,c_2132]) ).
tcf(c_10608,plain,
multiply(sk_c2,sk_c3) = identity,
inference(superposition,[status(thm)],[c_6495,c_2132]) ).
tcf(c_10623,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_133,c_10608]) ).
tcf(c_10627,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_134,c_10608]) ).
tcf(c_10633,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_10607,c_598]) ).
tcf(c_10635,plain,
( ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10633,c_6009]) ).
tcf(c_10642,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c6,sk_c7) = identity ) ),
inference(superposition,[status(thm)],[c_10627,c_2132]) ).
tcf(c_10696,plain,
sk_c9 = identity,
inference(superposition,[status(thm)],[c_10642,c_10623]) ).
tcf(c_10701,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_10635,c_10696]) ).
tcf(c_12940,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c10 )
| ( X0 != sk_c1 ) ),
inference(resolution,[status(thm)],[c_7491,c_2033]) ).
tcf(c_12941,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_12940]) ).
tcf(c_13307,plain,
( ~ iPr_def_10
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_7484,c_597]) ).
tcf(c_13310,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_13307,c_866,c_871,c_870,c_1795,c_3241,c_3260,c_3455,c_4194,c_4889,c_4897,c_5017,c_5977,c_13307]) ).
tcf(c_22228,plain,
! [X0: $i] : multiply(sk_c9,X0) = X0,
inference(light_normalisation,[status(thm)],[c_101,c_10696]) ).
tcf(c_22230,plain,
( ( sk_c10 = sk_c8 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_107,c_22228]) ).
tcf(c_22231,plain,
( ( sk_c10 = sk_c8 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_105,c_22228]) ).
tcf(c_22232,plain,
! [X0: $i] : multiply(inverse(X0),X0) = sk_c9,
inference(light_normalisation,[status(thm)],[c_102,c_10696]) ).
tcf(c_22237,plain,
~ iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_3260,c_10696]) ).
tcf(c_22238,plain,
~ iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_3241,c_10696]) ).
tcf(c_22239,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_601,c_22237]) ).
tcf(c_22240,plain,
( iPr_def_11
| iPr_def_10
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22239,c_22238]) ).
tcf(c_22241,plain,
! [X0: $i] : multiply(X0,sk_c9) = X0,
inference(light_normalisation,[status(thm)],[c_2123,c_10696]) ).
tcf(c_22243,plain,
( ( sk_c10 = sk_c1 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_123,c_22241]) ).
tcf(c_22251,plain,
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_104,c_22228]) ).
tcf(c_22256,plain,
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_106,c_22228]) ).
tcf(c_22261,plain,
( ( sk_c10 = sk_c5 )
| ( sk_c10 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108,c_22228,c_22241]) ).
tcf(c_22283,plain,
! [X0: $i] :
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c4,multiply(sk_c10,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_22251,c_103]) ).
tcf(c_22294,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(sk_c9,X1),
inference(superposition,[status(thm)],[c_22232,c_103]) ).
tcf(c_22309,plain,
( ( sk_c10 = sk_c1 )
| ( sk_c10 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_124,c_22241]) ).
tcf(c_22325,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = sk_c9,
inference(superposition,[status(thm)],[c_1491,c_22232]) ).
tcf(c_22331,plain,
( ( inverse(sk_c6) = sk_c7 )
| ~ iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_2565,c_6009]) ).
tcf(c_22334,plain,
! [X0: $i] : multiply(inverse(sk_c10),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_6009,c_1491]) ).
tcf(c_22384,plain,
multiply(sk_c1,sk_c9) = inverse(sk_c10),
inference(superposition,[status(thm)],[c_22334,c_22241]) ).
tcf(c_22388,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_22331,c_13310]) ).
tcf(c_22390,plain,
( iPr_def_11
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_22240,c_22388]) ).
tcf(c_22391,negated_conjecture,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_598,c_10701]) ).
tcf(c_22393,plain,
( ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_22390,c_22391]) ).
tcf(c_22402,plain,
( ( sk_c10 = sk_c8 )
| ( inverse(sk_c10) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_22261,c_22230]) ).
tcf(c_22409,plain,
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_22231,c_22232]) ).
tcf(c_22430,plain,
( ( sk_c10 = sk_c1 )
| ( inverse(sk_c10) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_22309,c_22243]) ).
tcf(c_22488,plain,
! [X0: $i] :
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c4,multiply(sk_c10,X0)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_22283,c_22228]) ).
tcf(c_22494,plain,
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_22256,c_22488]) ).
tcf(c_22549,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_22294,c_22228]) ).
tcf(c_22600,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c10,X0)) = X0,
inference(superposition,[status(thm)],[c_22549,c_22334]) ).
tcf(c_23429,plain,
( ( sk_c10 != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_22393,c_22228]) ).
tcf(c_29638,plain,
inverse(sk_c10) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_22402,c_12941,c_22430]) ).
tcf(c_29649,plain,
multiply(sk_c10,sk_c10) = sk_c9,
inference(superposition,[status(thm)],[c_29638,c_22325]) ).
tcf(c_29738,plain,
( ( sk_c10 = sk_c8 )
| ( multiply(sk_c1,sk_c9) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_22409,c_22600]) ).
tcf(c_29840,plain,
( ( sk_c10 = sk_c4 )
| ( sk_c10 = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_29738,c_22384,c_29638]) ).
tcf(c_29880,plain,
( ( sk_c8 = sk_c4 )
| ( sk_c10 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_22494,c_22241]) ).
tcf(c_29885,plain,
sk_c10 = sk_c8,
inference(superposition,[status(thm)],[c_29840,c_29880]) ).
tcf(c_29900,plain,
multiply(sk_c10,sk_c8) != sk_c9,
inference(backward_subsumption_resolution,[status(thm)],[c_23429,c_29885]) ).
tcf(c_32332,plain,
sk_c9 != sk_c9,
inference(light_normalisation,[status(thm)],[c_29900,c_29649,c_29885]) ).
tcf(c_32333,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_32332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP336-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.37 % Computer : n003.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Sep 23 14:32:04 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.43 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 42.83/7.44 % SZS status Started for theBenchmark.p
% 42.83/7.44 % SZS status Unsatisfiable for theBenchmark.p
% 42.83/7.44
% 42.83/7.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 42.83/7.44
% 42.83/7.44 % ------ iProver source info
% 42.83/7.44
% 42.83/7.44 % git: date: 2026-07-19 20:42:38 +0200
% 42.83/7.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 42.83/7.44 % git: non_committed_changes: false
% 42.83/7.44
% 42.83/7.44 % ------ Parsing...% successful
% 42.83/7.44
% 42.83/7.44
% 42.83/7.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 42.83/7.44
% 42.83/7.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 42.83/7.44
% 42.83/7.44 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 42.83/7.44
% 42.83/7.44 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 42.83/7.44 % ------ Proving...
% 42.83/7.44 % ------ Problem Properties
% 42.83/7.44
% 42.83/7.44 %
% 42.83/7.44 % clauses 56
% 42.83/7.44 % conjectures 53
% 42.83/7.44 % EPR 0
% 42.83/7.44 % Horn 7
% 42.83/7.44 % unary 3
% 42.83/7.44 % binary 48
% 42.83/7.44 % lits 117
% 42.83/7.44 % lits eq 109
% 42.83/7.44 % fd_pure 0
% 42.83/7.44 % fd_pseudo 0
% 42.83/7.44 % fd_cond 0
% 42.83/7.44 % fd_pseudo_cond 0
% 42.83/7.44 % AC symbols 0
% 42.83/7.44
% 42.83/7.44 % ------ Input Options Time Limit: Unbounded
% 42.83/7.44
% 42.83/7.44
% 42.83/7.44 % ------
% 42.83/7.44 % Current options:
% 42.83/7.44 % ------
% 42.83/7.44
% 42.83/7.44
% 42.83/7.44 %
% 42.83/7.44
% 42.83/7.44 % ------ Proving...
% 42.83/7.44 %
% 42.83/7.44
% 42.83/7.44 % SZS status Unsatisfiable for theBenchmark.p
% 42.83/7.44
% 42.83/7.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 42.83/7.44
% 42.83/7.44
%------------------------------------------------------------------------------