%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP316-1 : 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 : n017.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 01:32:49 PM UTC 2026
% Result : Unsatisfiable 5.94s 2.29s
% Output : CNFRefutation 10.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 296 ( 89 unt; 11 def)
% Number of atoms : 950 ( 537 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 424 ( 140 ~; 284 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 70 !; 0 ?; 50 :)
% 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_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f45,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != inverse(X4)
| sk_c8 != multiply(X4,sk_c6)
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2
| sk_c7 != multiply(sk_c8,X2)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X3,X0,X1,X4] :
( sk_c6 != inverse(X4)
| sk_c8 != multiply(X4,sk_c6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(sk_c8,multiply(X3,sk_c8))
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c7,sk_c8) != sk_c6 ),
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_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c8,sk_c4) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c4 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c4 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c4 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c6) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
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_c8 )
| ( multiply(X0,sk_c8) != 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_c6 )
| ( multiply(X0,sk_c6) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c8,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c4 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109,c_422]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_423]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97,c_424]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_20 = sk_c4 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_751,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_430,c_418]) ).
tcf(c_819,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_442,c_418]) ).
tcf(c_875,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_439,c_421]) ).
tcf(c_887,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_435,c_422]) ).
tcf(c_889,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_432,c_422]) ).
tcf(c_890,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_431,c_422]) ).
tcf(c_903,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_444,c_424]) ).
tcf(c_904,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_443,c_424]) ).
tcf(c_913,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_914,plain,
multiply(iPr_def_16,sk_c5) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_915,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_916,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_963,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( sk_c8 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_447,c_446]) ).
tcf(c_964,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_447,c_422]) ).
tcf(c_1002,plain,
( ( sk_c7 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_448,c_418]) ).
tcf(c_1059,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_449,c_431]) ).
tcf(c_1102,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_450,c_422]) ).
tcf(c_1106,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_450,c_432]) ).
tcf(c_1196,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_453,c_422]) ).
tcf(c_1198,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_453,c_435]) ).
tcf(c_1299,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_455,c_437]) ).
tcf(c_1526,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_963,c_424]) ).
tcf(c_1589,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_17 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1106,c_1059]) ).
tcf(c_1595,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1106,c_420]) ).
tcf(c_1676,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1198,c_434]) ).
tcf(c_2014,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_15 )
| ( inverse(sk_c6) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_415,c_428]) ).
tcf(c_2015,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_420,c_428]) ).
tcf(c_2016,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_424,c_428]) ).
tcf(c_2027,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_23 )
| ( sk_c7 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2016,c_423]) ).
tcf(c_2031,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2015,c_419]) ).
tcf(c_2108,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_429]) ).
tcf(c_2240,plain,
( ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c8,iPr_def_20) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_420,c_426]) ).
tcf(c_2241,plain,
( ~ iPr_def_13
| ( inverse(sk_c1) != sk_c8 )
| ( multiply(sk_c8,iPr_def_24) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_424,c_426]) ).
tcf(c_2252,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_23 )
| ( multiply(sk_c8,iPr_def_24) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2241,c_423]) ).
tcf(c_2256,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_19 )
| ( multiply(sk_c8,iPr_def_20) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2240,c_419]) ).
tcf(c_2602,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2603,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2604,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c4,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_2606,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2608,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_422,c_85]) ).
tcf(c_2610,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2612,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_913,c_85]) ).
tcf(c_2613,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_914,c_85]) ).
tcf(c_2614,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_915,c_85]) ).
tcf(c_2615,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_916,c_85]) ).
tcf(c_2621,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2615,c_83]) ).
tcf(c_2622,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2614,c_83]) ).
tcf(c_2623,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2613,c_83]) ).
tcf(c_2624,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2612,c_83]) ).
tcf(c_2725,plain,
multiply(iPr_def_17,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_422,c_2621]) ).
tcf(c_2761,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_424,c_2622]) ).
tcf(c_2765,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2761,c_85]) ).
tcf(c_3221,plain,
multiply(iPr_def_16,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_418,c_2623]) ).
tcf(c_3234,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_18,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3221,c_85]) ).
tcf(c_3242,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_420,c_2624]) ).
tcf(c_3245,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3242,c_85]) ).
tcf(c_4072,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_22 )
| ( multiply(iPr_def_18,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1299,c_875]) ).
tcf(c_4444,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_964,c_2621]) ).
tcf(c_4445,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4444,c_2725]) ).
tcf(c_4660,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1102,c_2621]) ).
tcf(c_4661,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c7 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_4660,c_2725]) ).
tcf(c_4949,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1196,c_2621]) ).
tcf(c_4950,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4949,c_2725]) ).
tcf(c_7018,plain,
multiply(sk_c5,iPr_def_15) = multiply(iPr_def_18,sk_c8),
inference(superposition,[status(thm)],[c_415,c_2606]) ).
tcf(c_7191,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_22,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2608]) ).
tcf(c_7618,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2610,c_83]) ).
tcf(c_7623,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_7618]) ).
tcf(c_7624,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_7618]) ).
tcf(c_7630,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_7618]) ).
tcf(c_7631,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_7618]) ).
tcf(c_7737,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2624,c_7618]) ).
tcf(c_7738,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2623,c_7618]) ).
tcf(c_7739,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2622,c_7618]) ).
tcf(c_7740,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2621,c_7618]) ).
tcf(c_7764,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7618,c_7618]) ).
tcf(c_8323,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_21 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1676,c_452]) ).
tcf(c_8452,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7631,c_7764]) ).
tcf(c_8462,plain,
multiply(sk_c6,sk_c8) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_8452,c_2603]) ).
tcf(c_8463,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_8452,c_2602]) ).
tcf(c_8464,plain,
multiply(sk_c8,sk_c4) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_8452,c_2604]) ).
tcf(c_8465,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_8452,c_3245]) ).
tcf(c_8466,plain,
multiply(sk_c6,identity) = multiply(iPr_def_16,iPr_def_18),
inference(superposition,[status(thm)],[c_8452,c_3234]) ).
tcf(c_8468,plain,
multiply(sk_c8,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_8452,c_2765]) ).
tcf(c_8475,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8452,c_7630]) ).
tcf(c_8478,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_8468,c_2761]) ).
tcf(c_8480,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_8466,c_3221]) ).
tcf(c_8482,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_8464,c_421]) ).
tcf(c_8483,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_8463,c_414]) ).
tcf(c_8484,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8462,c_415]) ).
tcf(c_8584,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_8475,c_84]) ).
tcf(c_8741,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_444,c_2027]) ).
tcf(c_8774,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_8741,c_4661,c_8741]) ).
tcf(c_8804,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_2031,c_2031,c_8774]) ).
tcf(c_8825,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_11
| ( iPr_def_20 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_453,c_8804]) ).
tcf(c_8969,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_8825,c_2027,c_4445,c_4950]) ).
tcf(c_9410,plain,
multiply(sk_c3,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_7737,c_84]) ).
tcf(c_9415,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_7737,c_7618]) ).
tcf(c_9429,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1595,c_9410]) ).
tcf(c_9695,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8323,c_1198]) ).
tcf(c_9856,plain,
multiply(sk_c3,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_3242,c_9415]) ).
tcf(c_10453,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_16)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c5,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7738,c_426]) ).
tcf(c_10455,plain,
multiply(sk_c5,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_7738,c_84]) ).
tcf(c_10458,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7738,c_429]) ).
tcf(c_10459,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_7738,c_427]) ).
tcf(c_10460,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_7738,c_7618]) ).
tcf(c_10461,plain,
multiply(sk_c5,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_7738,c_8452]) ).
tcf(c_10462,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_18 )
| ( inverse(inverse(iPr_def_16)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_10459,c_418]) ).
tcf(c_10476,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1002,c_10455]) ).
tcf(c_10477,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_819,c_10455]) ).
tcf(c_10478,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_751,c_10455]) ).
tcf(c_10495,plain,
inverse(iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_10461,c_8452]) ).
tcf(c_10503,plain,
multiply(sk_c5,identity) = sk_c5,
inference(superposition,[status(thm)],[c_914,c_10460]) ).
tcf(c_10504,plain,
multiply(sk_c5,sk_c6) = iPr_def_18,
inference(superposition,[status(thm)],[c_3221,c_10460]) ).
tcf(c_10577,plain,
( ~ iPr_def_11
| ( inverse(sk_c6) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_2014,c_2014,c_8969]) ).
tcf(c_10806,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2108,c_8475]) ).
tcf(c_11562,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_10477,c_424]) ).
tcf(c_11762,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_10478,c_10476]) ).
tcf(c_11801,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10478,c_422]) ).
tcf(c_12041,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_11762,c_9429]) ).
tcf(c_12132,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_23)) != sk_c8 )
| ( multiply(sk_c1,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7739,c_428]) ).
tcf(c_12133,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_7739,c_84]) ).
tcf(c_12138,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_7739,c_7618]) ).
tcf(c_12139,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_7739,c_8452]) ).
tcf(c_12146,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( inverse(inverse(iPr_def_23)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_12132,c_424]) ).
tcf(c_12154,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( identity = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1526,c_12133]) ).
tcf(c_12155,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_904,c_12133]) ).
tcf(c_12156,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_903,c_12133]) ).
tcf(c_12711,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_12156,c_12155]) ).
tcf(c_12766,plain,
( ( identity = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_12156,c_420]) ).
tcf(c_12775,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_12766,c_9410]) ).
tcf(c_12963,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_12139,c_8452]) ).
tcf(c_12971,plain,
multiply(sk_c1,sk_c8) = iPr_def_24,
inference(superposition,[status(thm)],[c_2761,c_12138]) ).
tcf(c_13371,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_7740,c_84]) ).
tcf(c_13374,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c7 )
| ( multiply(sk_c2,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7740,c_429]) ).
tcf(c_13375,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_7740,c_427]) ).
tcf(c_13376,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_7740,c_7618]) ).
tcf(c_13377,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_7740,c_8452]) ).
tcf(c_13381,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_22 )
| ( inverse(inverse(iPr_def_17)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_13374,c_422]) ).
tcf(c_13391,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_890,c_13371]) ).
tcf(c_13392,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_889,c_13371]) ).
tcf(c_13393,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_887,c_13371]) ).
tcf(c_13784,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_13392,c_13391]) ).
tcf(c_13842,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_13392,c_420]) ).
tcf(c_13851,plain,
( ( identity = iPr_def_22 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_13842,c_9410]) ).
tcf(c_14178,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_13393,c_434]) ).
tcf(c_14427,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_13851,c_12775]) ).
tcf(c_14466,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_13377,c_8452]) ).
tcf(c_14474,plain,
multiply(sk_c2,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_2725,c_13376]) ).
tcf(c_14644,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_13784,c_12711]) ).
tcf(c_14920,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( identity = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_14178,c_422]) ).
tcf(c_14929,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_14920,c_13371]) ).
tcf(c_14973,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_14929,c_12154]) ).
tcf(c_15036,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_11562,c_12133]) ).
tcf(c_15240,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_17 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_14644,c_1589]) ).
tcf(c_15345,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_14973,c_9695]) ).
tcf(c_15868,plain,
( ( identity = iPr_def_22 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_11801,c_13371]) ).
tcf(c_15885,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_15868,c_15036]) ).
tcf(c_16249,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_15885,c_14427]) ).
tcf(c_17068,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_16249,c_12041]) ).
tcf(c_18569,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_17068,c_15345,c_15240,c_14474,c_14466,c_13381,c_13375,c_13371,c_12971,c_12963,c_12146,c_12133,c_10806,c_10577,c_10504,c_10503,c_10495,c_10462,c_10458,c_10453,c_10455,c_9856,c_9410,c_8484,c_8483,c_8482,c_8480,c_8478,c_8466,c_8465,c_8464,c_8463,c_8462,c_7624,c_7623,c_7191,c_7018,c_4072,c_2256,c_2252,c_2031,c_8584,c_459,c_458,c_457,c_456,c_455,c_454,c_453,c_448,c_447,c_442,c_441,c_437,c_436,c_435,c_434,c_433,c_432,c_431,c_430,c_425,c_423,c_417,c_416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP316-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 14:22:15 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 5.94/2.29 % SZS status Started for theBenchmark.p
% 5.94/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 5.94/2.29
% 5.94/2.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.94/2.29
% 5.94/2.29 % ------ iProver source info
% 5.94/2.29
% 5.94/2.29 % git: date: 2026-07-19 20:42:38 +0200
% 5.94/2.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.94/2.29 % git: non_committed_changes: false
% 5.94/2.29
% 5.94/2.29 % ------ Parsing...% successful
% 5.94/2.29
% 5.94/2.29
% 5.94/2.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.94/2.29
% 5.94/2.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.94/2.29
% 5.94/2.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.94/2.29
% 5.94/2.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 5.94/2.29 % ------ Proving...
% 5.94/2.29 % ------ Problem Properties
% 5.94/2.29
% 5.94/2.29 %
% 5.94/2.29 % clauses 49
% 5.94/2.29 % conjectures 35
% 5.94/2.29 % EPR 31
% 5.94/2.29 % Horn 18
% 5.94/2.29 % unary 14
% 5.94/2.29 % binary 30
% 5.94/2.29 % lits 92
% 5.94/2.29 % lits eq 84
% 5.94/2.29 % fd_pure 0
% 5.94/2.29 % fd_pseudo 0
% 5.94/2.29 % fd_cond 0
% 5.94/2.29 % fd_pseudo_cond 0
% 5.94/2.29 % AC symbols 0
% 5.94/2.29
% 5.94/2.29 % ------ Schedule dynamic 5 is on
% 5.94/2.29
% 5.94/2.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.94/2.29
% 5.94/2.29
% 5.94/2.29 % ------
% 5.94/2.29 % Current options:
% 5.94/2.29 % ------
% 5.94/2.29
% 5.94/2.29
% 5.94/2.29 %
% 5.94/2.29
% 5.94/2.29 % ------ Proving...
% 5.94/2.29 %
% 5.94/2.29
% 5.94/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 5.94/2.29
% 5.94/2.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.58/2.30
% 10.58/2.30
%------------------------------------------------------------------------------