%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP311-1 : 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 01:32:48 PM UTC 2026
% Result : Unsatisfiable 4.74s 2.25s
% Output : CNFRefutation 10.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 45
% Syntax : Number of formulae : 379 ( 129 unt; 11 def)
% Number of atoms : 1282 ( 674 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 504 ( 163 ~; 341 |; 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 : 89 ( 0 sgn 89 !; 0 ?; 72 :)
% 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_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,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_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,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_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,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_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = 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_c3,sk_c6)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c5 = multiply(sk_c6,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,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| multiply(X1,sk_c7) != X0
| sk_c6 != multiply(sk_c7,X0)
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c5 != inverse(sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c5 != inverse(sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
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_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
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 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 )
| ( multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
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_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_413,definition,
iPr_def_13 = multiply(sk_c7,sk_c6),
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_c6),
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 = multiply(sk_c4,sk_c5),
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 = inverse(sk_c4),
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_c7 )
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c5 ) ),
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_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_418,c_417]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( 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_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110,c_422]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c2 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105,c_423]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_458,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_785,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c7,iPr_def_23) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_439,c_413]) ).
tcf(c_806,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_440,c_415]) ).
tcf(c_850,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_442,c_417]) ).
tcf(c_870,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_443,c_414]) ).
tcf(c_871,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_443,c_413]) ).
tcf(c_891,plain,
! [X0: $i] :
( ( iPr_def_13 = sk_c5 )
| ( iPr_def_13 != X0 )
| ( sk_c5 != X0 ) ),
inference(instantiation,[status(thm)],[c_459]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_459]) ).
tcf(c_937,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_437,c_423]) ).
tcf(c_938,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_436,c_423]) ).
tcf(c_939,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_435,c_423]) ).
tcf(c_940,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_434,c_423]) ).
tcf(c_941,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_433,c_423]) ).
tcf(c_970,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_421,c_84]) ).
tcf(c_971,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_972,plain,
multiply(iPr_def_16,sk_c7) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_973,plain,
multiply(iPr_def_18,sk_c1) = identity,
inference(superposition,[status(thm)],[c_418,c_84]) ).
tcf(c_988,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_444,c_420]) ).
tcf(c_995,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_444,c_414]) ).
tcf(c_996,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_444,c_413]) ).
tcf(c_1055,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_445,c_422]) ).
tcf(c_1093,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_446,c_422]) ).
tcf(c_1095,plain,
( ( sk_c7 = iPr_def_15 )
| ( inverse(iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_446,c_416]) ).
tcf(c_1118,plain,
iPr_def_13 = iPr_def_13,
inference(instantiation,[status(thm)],[c_458]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_459]) ).
tcf(c_1125,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_447,c_417]) ).
tcf(c_1140,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_448,c_417]) ).
tcf(c_1174,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_449,c_417]) ).
tcf(c_1203,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_450,c_417]) ).
tcf(c_1204,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_450,c_415]) ).
tcf(c_1238,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_451,c_417]) ).
tcf(c_1273,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_452,c_417]) ).
tcf(c_1274,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_452,c_415]) ).
tcf(c_1359,plain,
( ( iPr_def_13 = iPr_def_16 )
| ( sk_c5 = iPr_def_14 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_454,c_452]) ).
tcf(c_1436,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_13) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_455,c_417]) ).
tcf(c_1491,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_13) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_456,c_417]) ).
tcf(c_1547,plain,
( ( sk_c5 = iPr_def_13 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_457,c_417]) ).
tcf(c_1910,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_417,c_426]) ).
tcf(c_1911,plain,
( ~ iPr_def_11
| ( sk_c6 != sk_c5 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_426]) ).
tcf(c_1929,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( sk_c6 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1910,c_419]) ).
tcf(c_2049,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_420,c_427]) ).
tcf(c_2050,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_15 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_427]) ).
tcf(c_2067,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_21 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2049,c_421]) ).
tcf(c_2169,plain,
( ~ iPr_def_12
| ( inverse(sk_c1) != sk_c7 )
| ( multiply(sk_c7,iPr_def_22) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_422,c_425]) ).
tcf(c_2170,plain,
( ~ iPr_def_12
| ( inverse(identity) != sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_425]) ).
tcf(c_2187,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_18 )
| ( multiply(sk_c7,iPr_def_22) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2169,c_418]) ).
tcf(c_2292,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c5 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_14 )
| ( sk_c5 != iPr_def_16 )
| ( sk_c5 != iPr_def_14 )
| ( sk_c7 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_457,c_424]) ).
tcf(c_2633,plain,
! [X0: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != sk_c5 )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1119]) ).
tcf(c_2751,plain,
! [X0: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_925]) ).
tcf(c_2765,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_413,c_85]) ).
tcf(c_2766,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_2767,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_2768,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_417,c_85]) ).
tcf(c_2769,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2771,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_2773,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2776,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_970,c_85]) ).
tcf(c_2777,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_971,c_85]) ).
tcf(c_2778,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_972,c_85]) ).
tcf(c_2779,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_973,c_85]) ).
tcf(c_2784,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2779,c_83]) ).
tcf(c_2785,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2778,c_83]) ).
tcf(c_2786,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2777,c_83]) ).
tcf(c_2787,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2776,c_83]) ).
tcf(c_2823,plain,
( ( iPr_def_13 = sk_c5 )
| ( iPr_def_13 != iPr_def_13 )
| ( sk_c5 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_891]) ).
tcf(c_2911,plain,
multiply(iPr_def_18,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_422,c_2784]) ).
tcf(c_2923,plain,
multiply(iPr_def_16,iPr_def_13) = sk_c6,
inference(superposition,[status(thm)],[c_413,c_2785]) ).
tcf(c_2924,plain,
multiply(iPr_def_16,iPr_def_23) = sk_c2,
inference(superposition,[status(thm)],[c_423,c_2785]) ).
tcf(c_3037,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_13,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2923,c_85]) ).
tcf(c_3286,plain,
multiply(iPr_def_19,iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_417,c_2786]) ).
tcf(c_3293,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_17,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3286,c_85]) ).
tcf(c_3307,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_420,c_2787]) ).
tcf(c_3323,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_20,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3307,c_85]) ).
tcf(c_4257,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_13) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_785,c_2785]) ).
tcf(c_4259,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4257,c_2923]) ).
tcf(c_4290,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_13,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_806]) ).
tcf(c_4295,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_450,c_806]) ).
tcf(c_4302,plain,
( ( sk_c2 = iPr_def_15 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4295,c_2924]) ).
tcf(c_4578,plain,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_16 != iPr_def_16 )
| ( sk_c5 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_2751]) ).
tcf(c_4579,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_458]) ).
tcf(c_4620,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_15) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_4302,c_423]) ).
tcf(c_4623,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_4302,c_435]) ).
tcf(c_5221,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_446,c_870]) ).
tcf(c_5275,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_445,c_871]) ).
tcf(c_5278,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_13) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_871,c_2785]) ).
tcf(c_5280,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5278,c_2923]) ).
tcf(c_6066,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_988,c_2787]) ).
tcf(c_6067,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6066,c_3307]) ).
tcf(c_6132,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_445,c_995]) ).
tcf(c_6239,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_18,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1055,c_2784]) ).
tcf(c_6240,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6239,c_2911]) ).
tcf(c_6411,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_18,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1093,c_2784]) ).
tcf(c_6412,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6411,c_2911]) ).
tcf(c_6569,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1140,c_2786]) ).
tcf(c_6570,plain,
( ( sk_c5 = iPr_def_16 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6569,c_3286]) ).
tcf(c_6613,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1174,c_2786]) ).
tcf(c_6614,plain,
( ( sk_c5 = iPr_def_16 )
| ( sk_c6 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_6613,c_3286]) ).
tcf(c_6857,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1203,c_2786]) ).
tcf(c_6858,plain,
( ( sk_c5 = iPr_def_16 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6857,c_3286]) ).
tcf(c_6902,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1238,c_2786]) ).
tcf(c_6903,plain,
( ( sk_c5 = iPr_def_16 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_6902,c_3286]) ).
tcf(c_6947,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1273,c_2786]) ).
tcf(c_6948,plain,
( ( sk_c5 = iPr_def_16 )
| ( sk_c5 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6947,c_3286]) ).
tcf(c_7152,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1436,c_2786]) ).
tcf(c_7153,plain,
( ( sk_c5 = iPr_def_13 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_7152,c_3286]) ).
tcf(c_7357,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1491,c_2786]) ).
tcf(c_7358,plain,
( ( sk_c5 = iPr_def_13 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_7357,c_3286]) ).
tcf(c_7402,plain,
( ( sk_c5 = iPr_def_13 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1547,c_2786]) ).
tcf(c_7403,plain,
( ( sk_c5 = iPr_def_14 )
| ( sk_c5 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_7402,c_3286]) ).
tcf(c_9167,plain,
multiply(sk_c7,iPr_def_14) = multiply(iPr_def_13,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2765]) ).
tcf(c_9296,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_13,iPr_def_21) = multiply(iPr_def_21,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_446,c_9167]) ).
tcf(c_9300,plain,
multiply(iPr_def_16,multiply(iPr_def_13,sk_c7)) = iPr_def_14,
inference(superposition,[status(thm)],[c_9167,c_2785]) ).
tcf(c_9331,plain,
( ( iPr_def_13 = iPr_def_16 )
| ( iPr_def_16 != sk_c5 )
| ( iPr_def_13 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_2633]) ).
tcf(c_9381,plain,
multiply(sk_c6,iPr_def_13) = multiply(iPr_def_14,sk_c6),
inference(superposition,[status(thm)],[c_413,c_2766]) ).
tcf(c_9382,plain,
multiply(sk_c6,iPr_def_23) = multiply(iPr_def_14,sk_c2),
inference(superposition,[status(thm)],[c_423,c_2766]) ).
tcf(c_9384,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c6,iPr_def_13) = multiply(iPr_def_14,iPr_def_19) ) ),
inference(superposition,[status(thm)],[c_996,c_2766]) ).
tcf(c_9395,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c6,iPr_def_23) = multiply(iPr_def_14,iPr_def_22) ) ),
inference(superposition,[status(thm)],[c_939,c_2766]) ).
tcf(c_9397,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(sk_c6,iPr_def_23) = multiply(iPr_def_14,iPr_def_22) ) ),
inference(superposition,[status(thm)],[c_937,c_2766]) ).
tcf(c_9552,plain,
( ( iPr_def_13 = iPr_def_16 )
| ( sk_c5 = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_1359,c_1118,c_2823,c_4578,c_4579,c_6948,c_7403,c_9331]) ).
tcf(c_9606,plain,
( ( iPr_def_13 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_9552,c_417]) ).
tcf(c_9714,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_14,iPr_def_19) = multiply(iPr_def_19,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_444,c_9381]) ).
tcf(c_9723,plain,
multiply(sk_c7,multiply(iPr_def_14,sk_c6)) = multiply(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_9381,c_2765]) ).
tcf(c_9852,plain,
multiply(sk_c3,iPr_def_14) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2767]) ).
tcf(c_9864,plain,
multiply(sk_c3,multiply(iPr_def_14,sk_c6)) = multiply(iPr_def_20,iPr_def_13),
inference(superposition,[status(thm)],[c_9381,c_2767]) ).
tcf(c_9985,plain,
multiply(iPr_def_21,multiply(iPr_def_20,sk_c7)) = iPr_def_14,
inference(superposition,[status(thm)],[c_9852,c_2787]) ).
tcf(c_9998,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_17,sk_c6),
inference(superposition,[status(thm)],[c_415,c_2768]) ).
tcf(c_10093,plain,
multiply(iPr_def_19,multiply(iPr_def_17,sk_c6)) = iPr_def_15,
inference(superposition,[status(thm)],[c_9998,c_2786]) ).
tcf(c_10126,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2769]) ).
tcf(c_10139,plain,
multiply(sk_c5,multiply(iPr_def_14,sk_c2)) = multiply(iPr_def_15,iPr_def_23),
inference(superposition,[status(thm)],[c_9382,c_2769]) ).
tcf(c_10241,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(iPr_def_15,sk_c7) = multiply(iPr_def_16,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_452,c_10126]) ).
tcf(c_10625,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c6,iPr_def_23) = multiply(iPr_def_16,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_4290,c_3037]) ).
tcf(c_10635,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c2) = multiply(iPr_def_16,iPr_def_15) ) ),
inference(light_normalisation,[status(thm)],[c_10625,c_9382]) ).
tcf(c_10694,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_21) = multiply(iPr_def_19,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_5221,c_3293]) ).
tcf(c_10809,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c6,iPr_def_17) = multiply(iPr_def_21,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_5275,c_3323]) ).
tcf(c_12052,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2773,c_83]) ).
tcf(c_12070,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_414,c_12052]) ).
tcf(c_12072,plain,
multiply(inverse(sk_c4),iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_417,c_12052]) ).
tcf(c_12073,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c6,
inference(superposition,[status(thm)],[c_415,c_12052]) ).
tcf(c_12075,plain,
multiply(inverse(sk_c1),iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_422,c_12052]) ).
tcf(c_12076,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_12052]) ).
tcf(c_12077,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_12052]) ).
tcf(c_12078,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_85,c_12052]) ).
tcf(c_12124,plain,
( ( iPr_def_13 = iPr_def_16 )
| ( multiply(inverse(sk_c4),iPr_def_17) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9606,c_12052]) ).
tcf(c_12126,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(sk_c4),iPr_def_17) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1125,c_12052]) ).
tcf(c_12127,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(inverse(sk_c4),iPr_def_17) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_850,c_12052]) ).
tcf(c_12176,plain,
multiply(inverse(iPr_def_16),identity) = sk_c7,
inference(superposition,[status(thm)],[c_972,c_12052]) ).
tcf(c_12177,plain,
multiply(inverse(iPr_def_18),identity) = sk_c1,
inference(superposition,[status(thm)],[c_973,c_12052]) ).
tcf(c_12241,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2787,c_12052]) ).
tcf(c_12242,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2786,c_12052]) ).
tcf(c_12243,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2785,c_12052]) ).
tcf(c_12245,plain,
multiply(inverse(iPr_def_18),sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_2911,c_12052]) ).
tcf(c_12303,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_12052,c_12052]) ).
tcf(c_13381,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm)],[c_12176,c_12243]) ).
tcf(c_13399,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_13381,c_2766]) ).
tcf(c_13404,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_13399,c_414]) ).
tcf(c_13672,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_12077,c_12303]) ).
tcf(c_13690,plain,
multiply(sk_c6,identity) = multiply(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_13672,c_3037]) ).
tcf(c_13691,plain,
multiply(sk_c5,sk_c6) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_13672,c_2769]) ).
tcf(c_13696,plain,
multiply(sk_c6,identity) = multiply(iPr_def_21,iPr_def_20),
inference(superposition,[status(thm)],[c_13672,c_3323]) ).
tcf(c_13697,plain,
multiply(sk_c5,identity) = multiply(iPr_def_19,iPr_def_17),
inference(superposition,[status(thm)],[c_13672,c_3293]) ).
tcf(c_13707,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_13672,c_12076]) ).
tcf(c_13712,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_13697,c_3286]) ).
tcf(c_13716,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_13691,c_415]) ).
tcf(c_13794,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_13707,c_84]) ).
tcf(c_13936,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_445,c_2067]) ).
tcf(c_14017,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_13936,c_6412,c_13936]) ).
tcf(c_14781,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_12241,c_425]) ).
tcf(c_14782,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_12241,c_84]) ).
tcf(c_14785,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c6 )
| ( multiply(sk_c3,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_12241,c_426]) ).
tcf(c_14787,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_12241,c_12052]) ).
tcf(c_14788,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_12241,c_13672]) ).
tcf(c_14834,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(superposition,[status(thm)],[c_14782,c_2787]) ).
tcf(c_14841,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_14788,c_13672]) ).
tcf(c_14845,plain,
( ( sk_c3 = iPr_def_16 )
| ( sk_c7 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1095,c_14841]) ).
tcf(c_14882,plain,
multiply(sk_c3,sk_c6) = iPr_def_20,
inference(superposition,[status(thm)],[c_3307,c_14787]) ).
tcf(c_15266,plain,
( ~ iPr_def_11
| ( sk_c6 != identity )
| ( sk_c6 != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_1911,c_13707]) ).
tcf(c_15406,plain,
( ~ iPr_def_10
| ( inverse(sk_c5) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_2050,c_2050,c_14017]) ).
tcf(c_15431,plain,
( ( sk_c5 = iPr_def_14 )
| ~ iPr_def_10
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_452,c_15406]) ).
tcf(c_15432,plain,
( ( sk_c7 = iPr_def_21 )
| ~ iPr_def_10
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_451,c_15406]) ).
tcf(c_15433,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_10
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_450,c_15406]) ).
tcf(c_15788,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_14) = multiply(iPr_def_20,sk_c7) ) ),
inference(superposition,[status(thm)],[c_14845,c_9852]) ).
tcf(c_15901,plain,
( ( inverse(iPr_def_16) != sk_c7 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_15431,c_2067,c_15433,c_15432]) ).
tcf(c_15902,plain,
( ~ iPr_def_10
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(renaming,[status(thm)],[c_15901]) ).
tcf(c_16076,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_12242,c_84]) ).
tcf(c_16079,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_19)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_12242,c_426]) ).
tcf(c_16081,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_12242,c_12052]) ).
tcf(c_16082,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_12242,c_13672]) ).
tcf(c_16090,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(inverse(iPr_def_19)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_16079,c_417]) ).
tcf(c_16115,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_16076,c_2786]) ).
tcf(c_16122,plain,
inverse(iPr_def_19) = sk_c4,
inference(demodulation,[status(thm)],[c_16082,c_13672]) ).
tcf(c_16623,plain,
multiply(sk_c4,sk_c5) = iPr_def_17,
inference(superposition,[status(thm)],[c_3286,c_16081]) ).
tcf(c_16733,plain,
multiply(sk_c7,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_12243,c_84]) ).
tcf(c_16738,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_12243,c_12052]) ).
tcf(c_16739,plain,
multiply(sk_c7,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_12243,c_13672]) ).
tcf(c_16802,plain,
multiply(sk_c1,identity) = multiply(iPr_def_22,iPr_def_16),
inference(superposition,[status(thm)],[c_16733,c_2771]) ).
tcf(c_16803,plain,
multiply(sk_c6,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_16733,c_2766]) ).
tcf(c_17482,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_14)) = sk_c7,
inference(superposition,[status(thm)],[c_414,c_12078]) ).
tcf(c_17485,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),multiply(X0,iPr_def_17)) = sk_c5,
inference(superposition,[status(thm)],[c_16623,c_12078]) ).
tcf(c_17487,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),multiply(X0,iPr_def_15)) = sk_c6,
inference(superposition,[status(thm)],[c_415,c_12078]) ).
tcf(c_17539,plain,
! [X0: $i] :
( ( sk_c5 = iPr_def_13 )
| ( multiply(inverse(multiply(X0,sk_c4)),multiply(X0,iPr_def_17)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1547,c_12078]) ).
tcf(c_17585,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_23)) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_939,c_12078]) ).
tcf(c_17640,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,identity)) = iPr_def_16,
inference(superposition,[status(thm)],[c_16733,c_12078]) ).
tcf(c_17642,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_23)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_4620,c_12078]) ).
tcf(c_17694,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,iPr_def_19)),multiply(X0,iPr_def_14)) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_6132,c_12078]) ).
tcf(c_17702,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_19)),multiply(X0,sk_c5)) = iPr_def_17,
inference(superposition,[status(thm)],[c_3286,c_12078]) ).
tcf(c_17715,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(multiply(X0,iPr_def_13)),multiply(X0,iPr_def_15)) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_4290,c_12078]) ).
tcf(c_17784,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),X0) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_17640,c_13672]) ).
tcf(c_21462,plain,
inverse(iPr_def_16) = sk_c7,
inference(demodulation,[status(thm)],[c_16739,c_13672]) ).
tcf(c_21468,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_15902,c_21462]) ).
tcf(c_21469,plain,
~ iPr_def_10,
inference(equality_resolution_simp,[status(thm)],[c_21468]) ).
tcf(c_21470,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c5 != iPr_def_16 )
| ( sk_c5 != iPr_def_14 )
| ( sk_c5 != iPr_def_13 )
| ( sk_c7 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_424,c_21469]) ).
tcf(c_21517,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_15) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1274,c_16738]) ).
tcf(c_21519,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_15) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1204,c_16738]) ).
tcf(c_21526,plain,
multiply(sk_c7,sk_c6) = iPr_def_13,
inference(superposition,[status(thm)],[c_2923,c_16738]) ).
tcf(c_21551,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c6 )
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_16738,c_425]) ).
tcf(c_21612,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c6 ) ),
inference(ground_joinability,[status(thm)],[c_21551,c_21462]) ).
tcf(c_21939,plain,
multiply(inverse(multiply(inverse(iPr_def_14),sk_c6)),identity) = sk_c7,
inference(superposition,[status(thm)],[c_84,c_17482]) ).
tcf(c_22233,plain,
( ( sk_c6 = iPr_def_19 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_439,c_21612]) ).
tcf(c_22234,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_438,c_21612]) ).
tcf(c_22273,plain,
multiply(iPr_def_22,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_16802,c_13672]) ).
tcf(c_22827,plain,
inverse(multiply(inverse(iPr_def_14),sk_c6)) = sk_c7,
inference(demodulation,[status(thm)],[c_21939,c_13672]) ).
tcf(c_22849,plain,
multiply(sk_c7,multiply(inverse(iPr_def_14),sk_c6)) = identity,
inference(superposition,[status(thm)],[c_22827,c_84]) ).
tcf(c_22918,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c7,multiply(inverse(iPr_def_14),iPr_def_23)) = identity ) ),
inference(superposition,[status(thm)],[c_438,c_22849]) ).
tcf(c_22922,plain,
multiply(iPr_def_14,multiply(inverse(iPr_def_14),sk_c6)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_22849,c_2766]) ).
tcf(c_22923,plain,
multiply(inverse(iPr_def_14),sk_c6) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_22849,c_2785]) ).
tcf(c_22927,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,identity)) = multiply(inverse(iPr_def_14),sk_c6),
inference(superposition,[status(thm)],[c_22849,c_12078]) ).
tcf(c_22930,plain,
multiply(iPr_def_14,multiply(inverse(iPr_def_14),sk_c6)) = multiply(iPr_def_14,iPr_def_16),
inference(light_normalisation,[status(thm)],[c_22922,c_16803]) ).
tcf(c_22980,plain,
multiply(inverse(iPr_def_14),sk_c6) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_22927,c_13672,c_17784]) ).
tcf(c_26008,plain,
multiply(inverse(iPr_def_17),multiply(sk_c4,iPr_def_15)) = sk_c6,
inference(superposition,[status(thm)],[c_16623,c_17487]) ).
tcf(c_26041,plain,
multiply(inverse(multiply(inverse(iPr_def_15),sk_c5)),identity) = sk_c6,
inference(superposition,[status(thm)],[c_84,c_17487]) ).
tcf(c_26062,plain,
multiply(inverse(iPr_def_17),multiply(iPr_def_17,sk_c6)) = sk_c6,
inference(light_normalisation,[status(thm)],[c_26008,c_9998]) ).
tcf(c_26250,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(inverse(iPr_def_14),iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_438,c_22980]) ).
tcf(c_26308,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_16803,c_13672]) ).
tcf(c_26537,plain,
inverse(multiply(inverse(iPr_def_15),sk_c5)) = sk_c6,
inference(demodulation,[status(thm)],[c_26041,c_13672]) ).
tcf(c_26568,plain,
multiply(sk_c6,multiply(inverse(iPr_def_15),sk_c5)) = identity,
inference(superposition,[status(thm)],[c_26537,c_84]) ).
tcf(c_26647,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_26568,c_26537,c_26308,c_26250,c_26062,c_22980,c_22930,c_22923,c_22922,c_22918,c_22273,c_22234,c_22233,c_21526,c_21519,c_21517,c_21470,c_21469,c_21462,c_17715,c_17702,c_17694,c_17642,c_17585,c_17539,c_17487,c_17485,c_16739,c_16733,c_16623,c_16122,c_16115,c_16090,c_16079,c_15788,c_15266,c_14882,c_14841,c_14834,c_14785,c_14781,c_14782,c_13716,c_13712,c_13697,c_13696,c_13691,c_13690,c_13707,c_13404,c_12245,c_12177,c_12127,c_12126,c_12124,c_12075,c_12073,c_12072,c_12070,c_10809,c_10694,c_10635,c_10241,c_10139,c_10126,c_10093,c_9998,c_9985,c_9864,c_9852,c_9723,c_9714,c_9397,c_9395,c_9384,c_9382,c_9381,c_9300,c_9296,c_9167,c_7358,c_7153,c_6903,c_6858,c_6614,c_6570,c_6240,c_6067,c_5280,c_4623,c_4259,c_2292,c_2187,c_2170,c_1929,c_13794,c_972,c_941,c_940,c_939,c_938,c_937,c_432,c_431,c_430,c_429,c_428,c_424,c_421,c_419,c_418,c_416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP311-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 14:28:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 4.74/2.25 % SZS status Started for theBenchmark.p
% 4.74/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 4.74/2.25
% 4.74/2.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.74/2.25
% 4.74/2.25 % ------ iProver source info
% 4.74/2.25
% 4.74/2.25 % git: date: 2026-07-19 20:42:38 +0200
% 4.74/2.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.74/2.25 % git: non_committed_changes: false
% 4.74/2.25
% 4.74/2.25 % ------ Parsing...% successful
% 4.74/2.25
% 4.74/2.25
% 4.74/2.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.74/2.25
% 4.74/2.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.74/2.25
% 4.74/2.25 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.74/2.25
% 4.74/2.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.74/2.25 % ------ Proving...
% 4.74/2.25 % ------ Problem Properties
% 4.74/2.25
% 4.74/2.25 %
% 4.74/2.25 % clauses 48
% 4.74/2.25 % conjectures 34
% 4.74/2.25 % EPR 31
% 4.74/2.25 % Horn 17
% 4.74/2.25 % unary 14
% 4.74/2.25 % binary 30
% 4.74/2.25 % lits 90
% 4.74/2.25 % lits eq 84
% 4.74/2.25 % fd_pure 0
% 4.74/2.25 % fd_pseudo 0
% 4.74/2.25 % fd_cond 0
% 4.74/2.25 % fd_pseudo_cond 0
% 4.74/2.25 % AC symbols 0
% 4.74/2.25
% 4.74/2.25 % ------ Schedule dynamic 5 is on
% 4.74/2.25
% 4.74/2.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.74/2.25
% 4.74/2.25
% 4.74/2.25 % ------
% 4.74/2.25 % Current options:
% 4.74/2.25 % ------
% 4.74/2.25
% 4.74/2.25
% 4.74/2.25 %
% 4.74/2.25
% 4.74/2.25 % ------ Proving...
% 4.74/2.25 %
% 4.74/2.25
% 4.74/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 4.74/2.25
% 4.74/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.26/2.26
% 10.26/2.26
%------------------------------------------------------------------------------