%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP361-1 : 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 01:33:24 PM UTC 2026
% Result : Unsatisfiable 10.66s 2.72s
% Output : CNFRefutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 43
% Syntax : Number of formulae : 256 ( 110 unt; 11 def)
% Number of atoms : 690 ( 435 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 327 ( 116 ~; 211 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = inverse(sk_c4)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c5 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( inverse(X3) != sk_c5
| multiply(X3,sk_c5) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( sk_c5 != inverse(X3)
| sk_c7 != multiply(X3,sk_c5)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != multiply(sk_c5,sk_c7)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| multiply(X1,sk_c7) != X0
| sk_c6 != multiply(sk_c7,X0)
| sk_c5 != inverse(sk_c7)
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1] :
( sk_c5 != inverse(X3)
| sk_c7 != multiply(X3,sk_c5)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != multiply(sk_c5,sk_c7)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c5 != inverse(sk_c7)
| multiply(sk_c6,sk_c5) != sk_c7 ),
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,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c5 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_413,definition,
iPr_def_13 = multiply(sk_c6,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c5,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = multiply(sk_c7,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c5 )
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412,c_416,c_415,c_414,c_413]) ).
tcf(c_425,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_115,c_418,c_417]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114,c_419]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_420]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112,c_421]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_109,c_422]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_103,c_423]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_895,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_421,c_84]) ).
tcf(c_896,plain,
multiply(iPr_def_17,sk_c4) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_897,plain,
multiply(iPr_def_16,sk_c7) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_898,plain,
multiply(iPr_def_18,sk_c1) = identity,
inference(superposition,[status(thm)],[c_418,c_84]) ).
tcf(c_1257,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_453,c_422]) ).
tcf(c_1938,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_13 )
| ( inverse(sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_413,c_427]) ).
tcf(c_1939,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_419,c_427]) ).
tcf(c_1954,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_19 )
| ( sk_c5 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1939,c_417]) ).
tcf(c_2065,plain,
( ~ iPr_def_12
| ( inverse(sk_c5) != sk_c7 )
| ( multiply(sk_c7,iPr_def_15) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_415,c_425]) ).
tcf(c_2994,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c5,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_413,c_85]) ).
tcf(c_2995,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2996,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2997,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_420,c_85]) ).
tcf(c_2998,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2999,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c2,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_423,c_85]) ).
tcf(c_3000,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_422,c_85]) ).
tcf(c_3002,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_3005,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_895,c_85]) ).
tcf(c_3006,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_896,c_85]) ).
tcf(c_3007,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_897,c_85]) ).
tcf(c_3008,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_898,c_85]) ).
tcf(c_3013,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3008,c_83]) ).
tcf(c_3014,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3007,c_83]) ).
tcf(c_3015,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3006,c_83]) ).
tcf(c_3016,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3005,c_83]) ).
tcf(c_3928,plain,
multiply(iPr_def_18,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_422,c_3013]) ).
tcf(c_3967,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3928,c_85]) ).
tcf(c_3969,plain,
multiply(iPr_def_16,iPr_def_23) = sk_c2,
inference(superposition,[status(thm)],[c_423,c_3014]) ).
tcf(c_4066,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_23,X0)) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3969,c_85]) ).
tcf(c_4111,plain,
multiply(iPr_def_17,iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_419,c_3015]) ).
tcf(c_4115,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_19,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4111,c_85]) ).
tcf(c_4125,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_420,c_3016]) ).
tcf(c_4630,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_20,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4125,c_85]) ).
tcf(c_9045,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_18,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1257,c_3013]) ).
tcf(c_9046,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_9045,c_3928]) ).
tcf(c_12417,plain,
multiply(sk_c6,iPr_def_15) = multiply(iPr_def_13,sk_c7),
inference(superposition,[status(thm)],[c_415,c_2994]) ).
tcf(c_12986,plain,
multiply(sk_c5,iPr_def_23) = multiply(iPr_def_15,sk_c2),
inference(superposition,[status(thm)],[c_423,c_2996]) ).
tcf(c_13190,plain,
multiply(sk_c6,multiply(iPr_def_15,sk_c2)) = multiply(iPr_def_13,iPr_def_23),
inference(superposition,[status(thm)],[c_12986,c_2994]) ).
tcf(c_13278,plain,
multiply(sk_c3,iPr_def_13) = multiply(iPr_def_20,sk_c5),
inference(superposition,[status(thm)],[c_413,c_2997]) ).
tcf(c_13279,plain,
multiply(sk_c3,iPr_def_14) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2997]) ).
tcf(c_13305,plain,
multiply(sk_c3,multiply(iPr_def_13,sk_c7)) = multiply(iPr_def_20,iPr_def_15),
inference(superposition,[status(thm)],[c_12417,c_2997]) ).
tcf(c_13720,plain,
multiply(iPr_def_21,multiply(iPr_def_20,sk_c5)) = iPr_def_13,
inference(superposition,[status(thm)],[c_13278,c_3016]) ).
tcf(c_13723,plain,
multiply(iPr_def_21,multiply(iPr_def_20,sk_c7)) = iPr_def_14,
inference(superposition,[status(thm)],[c_13279,c_3016]) ).
tcf(c_13743,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_415,c_2998]) ).
tcf(c_13984,plain,
multiply(iPr_def_17,multiply(iPr_def_19,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_13743,c_3015]) ).
tcf(c_14029,plain,
( ~ iPr_def_12
| ( inverse(sk_c2) != sk_c7 )
| ( multiply(iPr_def_23,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_2999,c_425]) ).
tcf(c_18994,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3002,c_83]) ).
tcf(c_19020,plain,
multiply(inverse(sk_c6),iPr_def_13) = sk_c5,
inference(superposition,[status(thm)],[c_413,c_18994]) ).
tcf(c_19021,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_414,c_18994]) ).
tcf(c_19022,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_415,c_18994]) ).
tcf(c_19027,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_18994]) ).
tcf(c_19028,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_18994]) ).
tcf(c_19121,plain,
multiply(inverse(iPr_def_16),identity) = sk_c7,
inference(superposition,[status(thm)],[c_897,c_18994]) ).
tcf(c_19122,plain,
multiply(inverse(iPr_def_18),identity) = sk_c1,
inference(superposition,[status(thm)],[c_898,c_18994]) ).
tcf(c_19222,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3016,c_18994]) ).
tcf(c_19223,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3015,c_18994]) ).
tcf(c_19224,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3014,c_18994]) ).
tcf(c_19242,plain,
multiply(inverse(iPr_def_18),sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_3928,c_18994]) ).
tcf(c_19282,plain,
multiply(inverse(sk_c6),multiply(iPr_def_13,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_12417,c_18994]) ).
tcf(c_19308,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_18994,c_18994]) ).
tcf(c_20842,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm)],[c_19121,c_19224]) ).
tcf(c_20875,plain,
multiply(sk_c5,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_20842,c_2996]) ).
tcf(c_20876,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_20842,c_2995]) ).
tcf(c_20881,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_20876,c_414]) ).
tcf(c_20882,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_20875,c_415]) ).
tcf(c_21792,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_19028,c_19308]) ).
tcf(c_21835,plain,
multiply(sk_c6,sk_c5) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_21792,c_2994]) ).
tcf(c_21838,plain,
multiply(sk_c6,identity) = multiply(iPr_def_21,iPr_def_20),
inference(superposition,[status(thm)],[c_21792,c_4630]) ).
tcf(c_21841,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_19),
inference(superposition,[status(thm)],[c_21792,c_4115]) ).
tcf(c_21842,plain,
multiply(sk_c2,identity) = multiply(iPr_def_16,iPr_def_23),
inference(superposition,[status(thm)],[c_21792,c_4066]) ).
tcf(c_21843,plain,
multiply(sk_c7,sk_c2) = multiply(iPr_def_23,identity),
inference(superposition,[status(thm)],[c_21792,c_2999]) ).
tcf(c_21850,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_21792,c_19027]) ).
tcf(c_21852,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_21843,c_423]) ).
tcf(c_21853,plain,
multiply(sk_c2,identity) = sk_c2,
inference(light_normalisation,[status(thm)],[c_21842,c_3969]) ).
tcf(c_21855,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_21838,c_4125]) ).
tcf(c_21856,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_21835,c_413]) ).
tcf(c_22045,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_21850,c_84]) ).
tcf(c_23043,plain,
( ( sk_c7 = iPr_def_13 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_452,c_1954]) ).
tcf(c_23092,plain,
( ( sk_c7 = iPr_def_13 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_23043,c_9046,c_23043]) ).
tcf(c_23356,plain,
( ~ iPr_def_10
| ( inverse(sk_c6) != sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_1938,c_1938,c_23092]) ).
tcf(c_23373,plain,
( ( sk_c5 = iPr_def_14 )
| ~ iPr_def_10
| ( inverse(iPr_def_23) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_445,c_23356]) ).
tcf(c_23377,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10
| ( inverse(iPr_def_23) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_441,c_23356]) ).
tcf(c_23378,plain,
( ( sk_c5 = iPr_def_17 )
| ~ iPr_def_10
| ( inverse(iPr_def_23) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_440,c_23356]) ).
tcf(c_23437,plain,
( ( inverse(iPr_def_23) != sk_c5 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_23373,c_1954,c_23377,c_23378]) ).
tcf(c_23438,plain,
( ~ iPr_def_10
| ( inverse(iPr_def_23) != sk_c5 ) ),
inference(renaming,[status(thm)],[c_23437]) ).
tcf(c_23458,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_21)) != sk_c7 )
| ( multiply(sk_c7,multiply(sk_c3,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_19222,c_425]) ).
tcf(c_23459,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_19222,c_84]) ).
tcf(c_23463,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19222,c_426]) ).
tcf(c_23464,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_19222,c_18994]) ).
tcf(c_23465,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_19222,c_21792]) ).
tcf(c_23499,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_23465,c_21792]) ).
tcf(c_23522,plain,
multiply(sk_c3,sk_c6) = iPr_def_20,
inference(superposition,[status(thm)],[c_4125,c_23464]) ).
tcf(c_32953,plain,
multiply(sk_c4,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_19223,c_84]) ).
tcf(c_32959,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c5 )
| ( multiply(sk_c4,sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19223,c_427]) ).
tcf(c_32960,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_17)) != sk_c7 )
| ( multiply(sk_c4,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19223,c_426]) ).
tcf(c_32961,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_19223,c_18994]) ).
tcf(c_32962,plain,
multiply(sk_c4,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_19223,c_21792]) ).
tcf(c_32967,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_19 )
| ( inverse(inverse(iPr_def_17)) != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_32959,c_419]) ).
tcf(c_33140,plain,
inverse(iPr_def_17) = sk_c4,
inference(demodulation,[status(thm)],[c_32962,c_21792]) ).
tcf(c_33148,plain,
multiply(sk_c4,sk_c5) = iPr_def_19,
inference(superposition,[status(thm)],[c_4111,c_32961]) ).
tcf(c_34256,plain,
multiply(sk_c7,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_19224,c_84]) ).
tcf(c_34263,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_16)) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19224,c_426]) ).
tcf(c_34264,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_19224,c_18994]) ).
tcf(c_34265,plain,
multiply(sk_c7,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_19224,c_21792]) ).
tcf(c_34456,plain,
multiply(sk_c1,identity) = multiply(iPr_def_22,iPr_def_16),
inference(superposition,[status(thm)],[c_34256,c_3000]) ).
tcf(c_34457,plain,
multiply(sk_c5,identity) = multiply(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_34256,c_2996]) ).
tcf(c_34459,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(superposition,[status(thm)],[c_34256,c_3014]) ).
tcf(c_34931,plain,
inverse(iPr_def_16) = sk_c7,
inference(demodulation,[status(thm)],[c_34265,c_21792]) ).
tcf(c_34989,plain,
multiply(sk_c7,sk_c2) = iPr_def_23,
inference(superposition,[status(thm)],[c_3969,c_34264]) ).
tcf(c_37054,plain,
multiply(iPr_def_22,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_34456,c_21792]) ).
tcf(c_37059,plain,
multiply(sk_c7,iPr_def_16) = multiply(iPr_def_18,sk_c1),
inference(superposition,[status(thm)],[c_37054,c_3967]) ).
tcf(c_37071,plain,
multiply(iPr_def_15,iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_34457,c_21792]) ).
tcf(c_37081,plain,
multiply(inverse(iPr_def_15),sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_37071,c_18994]) ).
tcf(c_37335,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_37081,c_37071,c_37059,c_37054,c_34989,c_34931,c_34459,c_34457,c_34263,c_34265,c_34256,c_33148,c_33140,c_32967,c_32960,c_32962,c_32953,c_23522,c_23499,c_23463,c_23458,c_23459,c_23438,c_21856,c_21855,c_21853,c_21852,c_21842,c_21841,c_21838,c_21835,c_21850,c_20882,c_20881,c_20876,c_20875,c_19282,c_19242,c_19122,c_19022,c_19021,c_19020,c_14029,c_13984,c_13743,c_13723,c_13720,c_13305,c_13278,c_13190,c_12986,c_12417,c_22045,c_2065,c_1954,c_897,c_457,c_456,c_455,c_454,c_453,c_452,c_451,c_450,c_449,c_448,c_447,c_446,c_445,c_444,c_443,c_442,c_441,c_440,c_439,c_438,c_435,c_434,c_433,c_432,c_431,c_430,c_429,c_428,c_424,c_421,c_417,c_416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP361-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Wed Sep 23 14:34:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40
% 0.15/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.40
% 0.15/0.40 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 10.66/2.72 % SZS status Started for theBenchmark.p
% 10.66/2.72 % SZS status Unsatisfiable for theBenchmark.p
% 10.66/2.72
% 10.66/2.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.66/2.72
% 10.66/2.72 % ------ iProver source info
% 10.66/2.72
% 10.66/2.72 % git: date: 2026-07-19 20:42:38 +0200
% 10.66/2.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.66/2.72 % git: non_committed_changes: false
% 10.66/2.72
% 10.66/2.72 % ------ Parsing...% successful
% 10.66/2.72
% 10.66/2.72
% 10.66/2.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.66/2.72
% 10.66/2.72 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.66/2.72
% 10.66/2.72 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.66/2.72
% 10.66/2.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.66/2.72 % ------ Proving...
% 10.66/2.72 % ------ Problem Properties
% 10.66/2.72
% 10.66/2.72 %
% 10.66/2.72 % clauses 48
% 10.66/2.72 % conjectures 34
% 10.66/2.72 % EPR 31
% 10.66/2.72 % Horn 17
% 10.66/2.72 % unary 14
% 10.66/2.72 % binary 30
% 10.66/2.72 % lits 90
% 10.66/2.72 % lits eq 84
% 10.66/2.72 % fd_pure 0
% 10.66/2.72 % fd_pseudo 0
% 10.66/2.72 % fd_cond 0
% 10.66/2.72 % fd_pseudo_cond 0
% 10.66/2.72 % AC symbols 0
% 10.66/2.72
% 10.66/2.72 % ------ Schedule dynamic 5 is on
% 10.66/2.72
% 10.66/2.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.66/2.72
% 10.66/2.72
% 10.66/2.72 % ------
% 10.66/2.72 % Current options:
% 10.66/2.72 % ------
% 10.66/2.72
% 10.66/2.72
% 10.66/2.72 %
% 10.66/2.72
% 10.66/2.72 % ------ Proving...
% 10.66/2.72 %
% 10.66/2.72
% 10.66/2.72 % SZS status Unsatisfiable for theBenchmark.p
% 10.66/2.72
% 10.66/2.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.66/2.73
% 10.66/2.73
%------------------------------------------------------------------------------