%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP359-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : 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 01:33:23 PM UTC 2026
% Result : Unsatisfiable 18.38s 3.19s
% Output : CNFRefutation 18.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 48
% Syntax : Number of formulae : 406 ( 138 unt; 11 def)
% Number of atoms : 1398 ( 749 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 584 ( 203 ~; 381 |; 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 126 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = inverse(sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = inverse(sk_c4)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0
| sk_c7 != multiply(sk_c8,X0)
| sk_c6 != inverse(sk_c8)
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c6 != inverse(sk_c8)
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X1,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c6 != inverse(sk_c8)
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(equality_resolution,[],[f67]) ).
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_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_117,plain,
multiply(identity,sk_c8) = sk_c8,
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_405,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_406,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_407,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_408,definition,
iPr_def_12 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_409,definition,
iPr_def_13 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_410,definition,
iPr_def_14 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_411,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_412,definition,
iPr_def_16 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_413,definition,
iPr_def_17 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_414,definition,
iPr_def_18 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_415,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_416,definition,
iPr_def_20 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_417,definition,
iPr_def_21 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_418,definition,
iPr_def_22 = multiply(sk_c8,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_419,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c6 )
| ( iPr_def_13 != sk_c6 )
| ( iPr_def_12 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_407,c_410,c_409,c_408]) ).
tcf(c_421,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_406]) ).
tcf(c_422,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_405]) ).
tcf(c_423,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_412,c_411]) ).
tcf(c_424,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_413]) ).
tcf(c_425,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_414]) ).
tcf(c_426,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_415]) ).
tcf(c_427,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_416]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_417]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_418]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_12 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_12 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_12 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_12 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_12 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_13 = sk_c6 )
| ( iPr_def_12 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_453,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_459,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_704,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_426,c_409]) ).
tcf(c_757,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_435,c_408]) ).
tcf(c_830,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c2) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_423,c_418]) ).
tcf(c_831,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_434,c_418]) ).
tcf(c_833,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_432,c_418]) ).
tcf(c_834,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_431,c_418]) ).
tcf(c_850,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_415,c_84]) ).
tcf(c_851,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_411,c_84]) ).
tcf(c_852,plain,
multiply(iPr_def_14,sk_c8) = identity,
inference(superposition,[status(thm)],[c_410,c_84]) ).
tcf(c_853,plain,
multiply(iPr_def_16,sk_c1) = identity,
inference(superposition,[status(thm)],[c_412,c_84]) ).
tcf(c_866,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_439,c_408]) ).
tcf(c_886,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_12 )
| ( iPr_def_12 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_887,plain,
( ( sk_c8 = iPr_def_12 )
| ( iPr_def_12 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_886]) ).
tcf(c_888,plain,
! [X0: $i] :
( ( sk_c8 = multiply(sk_c7,sk_c6) )
| ( sk_c8 != X0 )
| ( multiply(sk_c7,sk_c6) != X0 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_923,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c8,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_442,c_414]) ).
tcf(c_928,plain,
( ( sk_c8 = iPr_def_12 )
| ( iPr_def_12 != multiply(sk_c7,sk_c6) )
| ( sk_c8 != multiply(sk_c7,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_886]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(sk_c7,sk_c6) )
| ( sk_c8 != multiply(X0,X1) )
| ( multiply(sk_c7,sk_c6) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_888]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c7,sk_c6) = multiply(X0,X1) )
| ( sk_c6 != X1 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_455]) ).
tcf(c_951,plain,
( ( sk_c8 = multiply(sk_c7,sk_c6) )
| ( sk_c8 != multiply(sk_c8,sk_c8) )
| ( multiply(sk_c7,sk_c6) != multiply(sk_c8,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_949]) ).
tcf(c_952,plain,
( ( multiply(sk_c7,sk_c6) = multiply(sk_c8,sk_c8) )
| ( sk_c6 != sk_c8 )
| ( sk_c7 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_950]) ).
tcf(c_1002,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c6 = iPr_def_13 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_446,c_440]) ).
tcf(c_1023,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_15,sk_c5) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_447,c_414]) ).
tcf(c_1084,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(sk_c8,iPr_def_18) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_449,c_409]) ).
tcf(c_1123,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_450,c_409]) ).
tcf(c_1147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_1150,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_1228,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c8 = iPr_def_12 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_452,c_446]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_1415,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_1503,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_416,c_421]) ).
tcf(c_1530,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1503,c_415]) ).
tcf(c_1620,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_1635,plain,
! [X0: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_1147]) ).
tcf(c_1636,plain,
( ( sk_c8 = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1635]) ).
tcf(c_1643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_1147]) ).
tcf(c_1741,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c8,iPr_def_20) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_416,c_422]) ).
tcf(c_1744,plain,
( ~ iPr_def_10
| ( inverse(identity) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_422]) ).
tcf(c_1746,plain,
( ~ iPr_def_10
| ( inverse(iPr_def_14) != sk_c8 )
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_852,c_422]) ).
tcf(c_1768,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( multiply(sk_c8,iPr_def_20) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1741,c_415]) ).
tcf(c_1907,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1308]) ).
tcf(c_1965,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_408,c_85]) ).
tcf(c_1966,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_409,c_85]) ).
tcf(c_1967,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_416,c_85]) ).
tcf(c_1968,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_1969,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_413,c_85]) ).
tcf(c_1970,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c2,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_1971,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_417,c_85]) ).
tcf(c_1973,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_1976,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_850,c_85]) ).
tcf(c_1977,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_851,c_85]) ).
tcf(c_1978,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_852,c_85]) ).
tcf(c_1979,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_853,c_85]) ).
tcf(c_1983,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1979,c_83]) ).
tcf(c_1984,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1978,c_83]) ).
tcf(c_1985,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1977,c_83]) ).
tcf(c_1986,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1976,c_83]) ).
tcf(c_2076,plain,
multiply(iPr_def_16,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_417,c_1983]) ).
tcf(c_2079,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2076,c_85]) ).
tcf(c_2081,plain,
multiply(iPr_def_14,iPr_def_13) = sk_c7,
inference(superposition,[status(thm)],[c_409,c_1984]) ).
tcf(c_2082,plain,
multiply(iPr_def_14,iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_414,c_1984]) ).
tcf(c_2083,plain,
multiply(iPr_def_14,iPr_def_22) = sk_c2,
inference(superposition,[status(thm)],[c_418,c_1984]) ).
tcf(c_2090,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_14,multiply(iPr_def_19,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_426,c_1984]) ).
tcf(c_2171,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_13,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2081,c_85]) ).
tcf(c_2173,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_18,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2082,c_85]) ).
tcf(c_2175,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_22,X0)) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2083,c_85]) ).
tcf(c_2209,plain,
multiply(iPr_def_15,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_413,c_1985]) ).
tcf(c_2334,plain,
( ( sk_c8 = iPr_def_16 )
| ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_451,c_704]) ).
tcf(c_2574,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2209,c_85]) ).
tcf(c_2576,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_416,c_1986]) ).
tcf(c_2580,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2576,c_85]) ).
tcf(c_2610,plain,
( ( sk_c7 = iPr_def_22 )
| ( iPr_def_22 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1620]) ).
tcf(c_2801,plain,
! [X0: $i] :
( ( sk_c8 = identity )
| ( identity != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_2898,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_1643]) ).
tcf(c_2899,plain,
( ( sk_c8 = multiply(sk_c8,sk_c8) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(sk_c8,sk_c8) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_2898]) ).
tcf(c_2935,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_22,iPr_def_14) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_441,c_757]) ).
tcf(c_3360,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_429,c_830]) ).
tcf(c_3362,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3360,c_2076]) ).
tcf(c_3417,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_831,c_1984]) ).
tcf(c_3419,plain,
( ( sk_c2 = iPr_def_21 )
| ( sk_c6 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3417,c_2083]) ).
tcf(c_3843,plain,
( ( sk_c6 = iPr_def_13 )
| ( iPr_def_13 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1907]) ).
tcf(c_4095,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_834,c_1984]) ).
tcf(c_4097,plain,
( ( sk_c2 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4095,c_2083]) ).
tcf(c_4335,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_14) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_445,c_866]) ).
tcf(c_4974,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_448,c_1023]) ).
tcf(c_4980,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_4974,c_2209]) ).
tcf(c_5191,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = multiply(identity,X2) )
| ( X1 != X2 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_455]) ).
tcf(c_5192,plain,
( ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c8) )
| ( sk_c8 != identity )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_5191]) ).
tcf(c_5474,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1167]) ).
tcf(c_5475,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1152]) ).
tcf(c_5476,plain,
( ( sk_c7 = sk_c8 )
| ( sk_c8 != iPr_def_18 )
| ( sk_c7 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_5475]) ).
tcf(c_5477,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c8 != iPr_def_18 )
| ( sk_c7 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_5474]) ).
tcf(c_5694,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != iPr_def_13 )
| ( X0 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_1308]) ).
tcf(c_5695,plain,
( ( sk_c6 = sk_c8 )
| ( sk_c8 != iPr_def_13 )
| ( sk_c6 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_5694]) ).
tcf(c_6336,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_14,iPr_def_13) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1084,c_1984]) ).
tcf(c_6338,plain,
( ( sk_c8 = iPr_def_12 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6336,c_2081]) ).
tcf(c_6584,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_451,c_1123]) ).
tcf(c_6593,plain,
( ( sk_c8 = iPr_def_13 )
| ( sk_c8 = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6584,c_2576]) ).
tcf(c_6743,plain,
( ( sk_c8 = iPr_def_12 )
| ( multiply(iPr_def_14,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_6593,c_852]) ).
tcf(c_6773,plain,
( ( sk_c8 = iPr_def_12 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_6743,c_2081]) ).
tcf(c_8077,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6773,c_449]) ).
tcf(c_9774,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c6 = iPr_def_13 ) ),
inference(global_subsumption_just,[status(thm)],[c_1002,c_440,c_1150,c_1415,c_2610,c_3843]) ).
tcf(c_9775,plain,
( ( sk_c6 = iPr_def_13 )
| ( sk_c7 = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_9774]) ).
tcf(c_10091,plain,
multiply(sk_c8,iPr_def_12) = multiply(iPr_def_13,sk_c6),
inference(superposition,[status(thm)],[c_408,c_1966]) ).
tcf(c_10412,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_22) = multiply(iPr_def_20,iPr_def_21) ) ),
inference(superposition,[status(thm)],[c_833,c_1967]) ).
tcf(c_10682,plain,
( ( sk_c6 = iPr_def_13 )
| ( sk_c8 = iPr_def_12 ) ),
inference(global_subsumption_just,[status(thm)],[c_1228,c_459,c_452,c_887,c_1415,c_3843]) ).
tcf(c_10683,plain,
( ( sk_c8 = iPr_def_12 )
| ( sk_c6 = iPr_def_13 ) ),
inference(renaming,[status(thm)],[c_10682]) ).
tcf(c_12508,plain,
multiply(sk_c1,multiply(iPr_def_13,sk_c6)) = multiply(iPr_def_21,iPr_def_12),
inference(superposition,[status(thm)],[c_10091,c_1971]) ).
tcf(c_12901,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2576,c_2090]) ).
tcf(c_12907,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_12901,c_852]) ).
tcf(c_13381,plain,
( iPr_def_11
| iPr_def_10
| ( identity = iPr_def_20 )
| ( iPr_def_12 != iPr_def_16 )
| ( sk_c6 != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_12907,c_419]) ).
tcf(c_14930,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_14) = multiply(iPr_def_14,iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_4335,c_2175]) ).
tcf(c_21901,plain,
( ( identity = sk_c7 )
| ( identity != iPr_def_18 )
| ( sk_c7 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_5474]) ).
tcf(c_21903,plain,
( ( sk_c8 = identity )
| ( identity != sk_c7 )
| ( sk_c8 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_2801]) ).
tcf(c_21917,plain,
sk_c8 = iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_2334,c_117,c_459,c_408,c_928,c_951,c_952,c_1636,c_2899,c_4980,c_5192,c_5476,c_5477,c_5695,c_6338,c_6593,c_8077,c_10683,c_21901,c_21903]) ).
tcf(c_21963,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_2580,c_21917]) ).
tcf(c_21965,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_17,X0)) = multiply(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_2574,c_21917]) ).
tcf(c_21971,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_21,X0)) = multiply(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_2079,c_21917]) ).
tcf(c_21977,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_12,X0)) = multiply(iPr_def_21,X0),
inference(demodulation,[status(thm)],[c_1971,c_21917]) ).
tcf(c_21978,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(sk_c2,X0)) = multiply(iPr_def_22,X0),
inference(demodulation,[status(thm)],[c_1970,c_21917]) ).
tcf(c_21980,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_12,X0)) = multiply(iPr_def_17,X0),
inference(demodulation,[status(thm)],[c_1969,c_21917]) ).
tcf(c_21981,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(sk_c5,X0)) = multiply(iPr_def_18,X0),
inference(demodulation,[status(thm)],[c_1968,c_21917]) ).
tcf(c_21983,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_12,X0)) = multiply(iPr_def_20,X0),
inference(demodulation,[status(thm)],[c_1967,c_21917]) ).
tcf(c_21984,plain,
multiply(iPr_def_12,iPr_def_12) = multiply(iPr_def_13,sk_c6),
inference(demodulation,[status(thm)],[c_10091,c_21917]) ).
tcf(c_21985,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(sk_c7,X0)) = multiply(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_1966,c_21917]) ).
tcf(c_21995,plain,
( ( iPr_def_12 = iPr_def_15 )
| ( multiply(iPr_def_22,iPr_def_14) = iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_2935,c_21917]) ).
tcf(c_22032,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_12,iPr_def_17) = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_923,c_21917]) ).
tcf(c_22043,plain,
( ( iPr_def_12 = iPr_def_22 )
| ( iPr_def_12 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_3362,c_21917]) ).
tcf(c_22078,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_12,X0)) = X0,
inference(demodulation,[status(thm)],[c_1984,c_21917]) ).
tcf(c_22085,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != iPr_def_12 )
| ( multiply(iPr_def_12,multiply(X0,iPr_def_12)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_422,c_21917]) ).
tcf(c_22086,plain,
( iPr_def_11
| iPr_def_10
| ( iPr_def_12 != iPr_def_12 )
| ( sk_c6 != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_419,c_21917]) ).
tcf(c_22087,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != iPr_def_12 )
| ( multiply(X0,iPr_def_12) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_421,c_21917]) ).
tcf(c_22095,plain,
( ( iPr_def_12 = iPr_def_19 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_444,c_21917]) ).
tcf(c_22096,plain,
( ( iPr_def_12 = iPr_def_15 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_441,c_21917]) ).
tcf(c_22097,plain,
multiply(iPr_def_14,iPr_def_12) = identity,
inference(demodulation,[status(thm)],[c_852,c_21917]) ).
tcf(c_22098,plain,
multiply(iPr_def_12,sk_c2) = iPr_def_22,
inference(demodulation,[status(thm)],[c_418,c_21917]) ).
tcf(c_22099,plain,
multiply(sk_c1,iPr_def_12) = iPr_def_21,
inference(demodulation,[status(thm)],[c_417,c_21917]) ).
tcf(c_22100,plain,
multiply(sk_c3,iPr_def_12) = iPr_def_20,
inference(demodulation,[status(thm)],[c_416,c_21917]) ).
tcf(c_22101,plain,
( ( iPr_def_12 = iPr_def_19 )
| ( sk_c7 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_438,c_21917]) ).
tcf(c_22103,plain,
( ( iPr_def_12 = iPr_def_19 )
| ( sk_c2 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_432,c_21917]) ).
tcf(c_22104,plain,
multiply(iPr_def_12,sk_c5) = iPr_def_18,
inference(demodulation,[status(thm)],[c_414,c_21917]) ).
tcf(c_22105,plain,
multiply(sk_c4,iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_413,c_21917]) ).
tcf(c_22106,plain,
multiply(iPr_def_12,sk_c7) = iPr_def_13,
inference(demodulation,[status(thm)],[c_409,c_21917]) ).
tcf(c_22107,plain,
inverse(iPr_def_12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_410,c_21917]) ).
tcf(c_22290,plain,
( iPr_def_11
| iPr_def_10
| ( sk_c6 != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(equality_resolution_simp,[status(thm)],[c_22086]) ).
tcf(c_22371,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1973,c_83]) ).
tcf(c_22379,plain,
multiply(inverse(sk_c7),iPr_def_12) = sk_c6,
inference(superposition,[status(thm)],[c_408,c_22371]) ).
tcf(c_22380,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_22371]) ).
tcf(c_22381,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_22371]) ).
tcf(c_22415,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1986,c_22371]) ).
tcf(c_22416,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1985,c_22371]) ).
tcf(c_22417,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1983,c_22371]) ).
tcf(c_22418,plain,
multiply(inverse(iPr_def_14),sk_c7) = iPr_def_13,
inference(superposition,[status(thm)],[c_2081,c_22371]) ).
tcf(c_22419,plain,
multiply(inverse(iPr_def_14),sk_c5) = iPr_def_18,
inference(superposition,[status(thm)],[c_2082,c_22371]) ).
tcf(c_22420,plain,
multiply(inverse(iPr_def_14),sk_c2) = iPr_def_22,
inference(superposition,[status(thm)],[c_2083,c_22371]) ).
tcf(c_22435,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_22371,c_22371]) ).
tcf(c_22725,plain,
multiply(inverse(iPr_def_12),iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_22104,c_22371]) ).
tcf(c_22836,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_12,iPr_def_12) = multiply(iPr_def_13,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_446,c_21984]) ).
tcf(c_22837,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_12,iPr_def_12) = multiply(iPr_def_13,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_445,c_21984]) ).
tcf(c_22838,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_12,iPr_def_12) = multiply(iPr_def_13,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_443,c_21984]) ).
tcf(c_22840,plain,
multiply(inverse(iPr_def_13),multiply(iPr_def_12,iPr_def_12)) = sk_c6,
inference(superposition,[status(thm)],[c_21984,c_22371]) ).
tcf(c_22842,plain,
multiply(iPr_def_14,multiply(iPr_def_12,iPr_def_12)) = multiply(sk_c7,sk_c6),
inference(superposition,[status(thm)],[c_21984,c_2171]) ).
tcf(c_22843,plain,
multiply(iPr_def_14,multiply(iPr_def_12,iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_22842,c_408]) ).
tcf(c_22944,plain,
( ( iPr_def_12 = iPr_def_19 )
| ( multiply(inverse(iPr_def_14),iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_22101,c_22418]) ).
tcf(c_22947,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(iPr_def_14),iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_439,c_22418]) ).
tcf(c_22949,plain,
multiply(inverse(inverse(iPr_def_14)),iPr_def_13) = sk_c7,
inference(superposition,[status(thm)],[c_22418,c_22371]) ).
tcf(c_22968,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(inverse(iPr_def_14),iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_436,c_22419]) ).
tcf(c_22969,plain,
( ( sk_c2 = iPr_def_21 )
| ( multiply(inverse(iPr_def_14),iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_430,c_22419]) ).
tcf(c_22981,plain,
( ( iPr_def_12 = iPr_def_19 )
| ( multiply(inverse(iPr_def_14),iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22103,c_22420]) ).
tcf(c_22984,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(inverse(iPr_def_14),iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_3419,c_22420]) ).
tcf(c_22986,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(iPr_def_14),iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_433,c_22420]) ).
tcf(c_22988,plain,
multiply(inverse(inverse(iPr_def_14)),iPr_def_22) = sk_c2,
inference(superposition,[status(thm)],[c_22420,c_22371]) ).
tcf(c_23005,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(inverse(iPr_def_14)),iPr_def_13) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22947,c_22371]) ).
tcf(c_23062,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(inverse(iPr_def_14)),iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_22986,c_22371]) ).
tcf(c_23082,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(inverse(iPr_def_13),multiply(iPr_def_12,iPr_def_12)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_22836,c_22371]) ).
tcf(c_23085,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c6 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_23082,c_22840]) ).
tcf(c_23136,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_22078,c_22371]) ).
tcf(c_23150,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_22381,c_22435]) ).
tcf(c_23163,plain,
multiply(sk_c5,identity) = multiply(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_23150,c_2173]) ).
tcf(c_23165,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_23150,c_1965]) ).
tcf(c_23167,plain,
multiply(sk_c2,identity) = multiply(iPr_def_14,iPr_def_22),
inference(superposition,[status(thm)],[c_23150,c_2175]) ).
tcf(c_23171,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_23150,c_22380]) ).
tcf(c_23172,plain,
multiply(sk_c2,identity) = sk_c2,
inference(light_normalisation,[status(thm)],[c_23167,c_2083]) ).
tcf(c_23175,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_23163,c_2082]) ).
tcf(c_23211,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(iPr_def_13),multiply(iPr_def_12,iPr_def_12)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_22837,c_22371]) ).
tcf(c_23214,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_23211,c_22840]) ).
tcf(c_23226,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(inverse(iPr_def_13),multiply(iPr_def_12,iPr_def_12)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_22838,c_22371]) ).
tcf(c_23229,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_23226,c_22840]) ).
tcf(c_23436,plain,
multiply(sk_c3,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_22415,c_84]) ).
tcf(c_23440,plain,
multiply(sk_c3,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_22415,c_23150]) ).
tcf(c_23483,plain,
inverse(iPr_def_19) = sk_c3,
inference(demodulation,[status(thm)],[c_23440,c_23150]) ).
tcf(c_23552,plain,
multiply(sk_c4,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_22416,c_84]) ).
tcf(c_23790,plain,
multiply(sk_c1,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_22417,c_84]) ).
tcf(c_23794,plain,
multiply(sk_c1,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_22417,c_23150]) ).
tcf(c_23821,plain,
inverse(iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_23794,c_23150]) ).
tcf(c_24184,plain,
multiply(iPr_def_12,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_23136,c_84]) ).
tcf(c_24188,plain,
multiply(iPr_def_12,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_23136,c_23150]) ).
tcf(c_24287,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(superposition,[status(thm)],[c_24184,c_22078]) ).
tcf(c_24306,plain,
inverse(iPr_def_14) = iPr_def_12,
inference(demodulation,[status(thm)],[c_24188,c_23150]) ).
tcf(c_24370,plain,
( ~ iPr_def_10
| ( identity != iPr_def_12 )
| ( multiply(iPr_def_12,iPr_def_12) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1744,c_21917,c_23171]) ).
tcf(c_24380,plain,
( ~ iPr_def_10
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_1746,c_21917,c_24306]) ).
tcf(c_24381,plain,
( ~ iPr_def_10
| ( multiply(iPr_def_12,identity) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_24380,c_21917]) ).
tcf(c_24382,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_24381,c_23150]) ).
tcf(c_24392,plain,
( ( iPr_def_12 = iPr_def_19 )
| ~ iPr_def_10
| ( iPr_def_12 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22101,c_24382]) ).
tcf(c_24395,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_10
| ( iPr_def_12 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_439,c_24382]) ).
tcf(c_24594,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(iPr_def_12)) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_84,c_22087]) ).
tcf(c_24598,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c3) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_22100,c_22087]) ).
tcf(c_24605,plain,
( ~ iPr_def_11
| ( iPr_def_12 != iPr_def_19 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_24598,c_415]) ).
tcf(c_24616,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(ground_joinability,[status(thm)],[c_24594,c_22107,c_24306]) ).
tcf(c_24669,plain,
( ( iPr_def_12 = iPr_def_19 )
| ~ iPr_def_11
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22101,c_24616]) ).
tcf(c_24672,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_11
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_439,c_24616]) ).
tcf(c_24751,plain,
( ( identity != iPr_def_22 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_24672,c_24605,c_24672,c_24669]) ).
tcf(c_24752,plain,
( ~ iPr_def_11
| ( identity != iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_24751]) ).
tcf(c_24996,plain,
( ~ iPr_def_10
| ( inverse(identity) != iPr_def_12 )
| ( multiply(iPr_def_12,iPr_def_12) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_22085]) ).
tcf(c_25823,plain,
multiply(sk_c1,multiply(iPr_def_12,iPr_def_12)) = multiply(iPr_def_21,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_12508,c_21984]) ).
tcf(c_26533,plain,
multiply(iPr_def_12,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_23150,c_21963]) ).
tcf(c_26693,plain,
multiply(iPr_def_12,identity) = multiply(iPr_def_15,iPr_def_17),
inference(superposition,[status(thm)],[c_23150,c_21965]) ).
tcf(c_26707,plain,
multiply(iPr_def_12,identity) = multiply(iPr_def_16,iPr_def_21),
inference(superposition,[status(thm)],[c_23150,c_21971]) ).
tcf(c_26772,plain,
multiply(sk_c1,identity) = multiply(iPr_def_21,iPr_def_14),
inference(superposition,[status(thm)],[c_24184,c_21977]) ).
tcf(c_26773,plain,
multiply(sk_c1,iPr_def_12) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_23150,c_21977]) ).
tcf(c_26780,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_26773,c_22099]) ).
tcf(c_26796,plain,
multiply(iPr_def_12,sk_c2) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_23150,c_21978]) ).
tcf(c_26804,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_12,multiply(iPr_def_21,X0)) = multiply(iPr_def_22,X0) ) ),
inference(superposition,[status(thm)],[c_433,c_21978]) ).
tcf(c_26811,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_26796,c_22098]) ).
tcf(c_26870,plain,
multiply(iPr_def_21,iPr_def_14) = sk_c1,
inference(demodulation,[status(thm)],[c_26772,c_23150]) ).
tcf(c_26873,plain,
multiply(iPr_def_12,iPr_def_14) = multiply(iPr_def_16,sk_c1),
inference(superposition,[status(thm)],[c_26870,c_21971]) ).
tcf(c_27036,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_12,iPr_def_21) = multiply(iPr_def_22,identity) ) ),
inference(superposition,[status(thm)],[c_23150,c_26804]) ).
tcf(c_27037,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_12,sk_c1) = multiply(iPr_def_22,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_26870,c_26804]) ).
tcf(c_27519,plain,
multiply(sk_c4,identity) = multiply(iPr_def_17,iPr_def_14),
inference(superposition,[status(thm)],[c_24184,c_21980]) ).
tcf(c_27520,plain,
multiply(sk_c4,iPr_def_12) = multiply(iPr_def_17,identity),
inference(superposition,[status(thm)],[c_23150,c_21980]) ).
tcf(c_27529,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_27520,c_22105]) ).
tcf(c_28583,plain,
multiply(iPr_def_12,sk_c5) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_23150,c_21981]) ).
tcf(c_28588,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_12,multiply(iPr_def_17,X0)) = multiply(iPr_def_18,X0) ) ),
inference(superposition,[status(thm)],[c_442,c_21981]) ).
tcf(c_28597,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_28583,c_22104]) ).
tcf(c_28615,plain,
multiply(sk_c3,identity) = multiply(iPr_def_20,iPr_def_14),
inference(superposition,[status(thm)],[c_24184,c_21983]) ).
tcf(c_28616,plain,
multiply(sk_c3,iPr_def_12) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_23150,c_21983]) ).
tcf(c_28625,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_28616,c_22100]) ).
tcf(c_28691,plain,
multiply(iPr_def_12,sk_c7) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_23150,c_21985]) ).
tcf(c_28698,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_12,multiply(iPr_def_22,X0)) = multiply(iPr_def_13,X0) ) ),
inference(superposition,[status(thm)],[c_439,c_21985]) ).
tcf(c_28699,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_12,multiply(iPr_def_22,X0)) = multiply(iPr_def_13,X0) ) ),
inference(superposition,[status(thm)],[c_437,c_21985]) ).
tcf(c_28707,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_28691,c_22106]) ).
tcf(c_28753,plain,
multiply(iPr_def_17,iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_27519,c_23150]) ).
tcf(c_28756,plain,
multiply(iPr_def_12,iPr_def_14) = multiply(iPr_def_15,sk_c4),
inference(superposition,[status(thm)],[c_28753,c_21965]) ).
tcf(c_28927,plain,
multiply(iPr_def_20,iPr_def_14) = sk_c3,
inference(demodulation,[status(thm)],[c_28615,c_23150]) ).
tcf(c_28977,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_12,sk_c4) = multiply(iPr_def_18,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_28753,c_28588]) ).
tcf(c_29358,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_12,iPr_def_22) = multiply(iPr_def_13,identity) ) ),
inference(superposition,[status(thm)],[c_23150,c_28698]) ).
tcf(c_29527,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_12,iPr_def_22) = multiply(iPr_def_13,identity) ) ),
inference(superposition,[status(thm)],[c_23150,c_28699]) ).
tcf(c_29669,plain,
( ( iPr_def_12 = iPr_def_15 )
| ( multiply(iPr_def_12,iPr_def_14) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_22043,c_21995]) ).
tcf(c_29678,plain,
( ( iPr_def_12 = iPr_def_15 )
| ( identity = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_29669,c_24184]) ).
tcf(c_31273,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(inverse(iPr_def_12),iPr_def_18) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_22032,c_22371]) ).
tcf(c_31615,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_31273,c_29678,c_29527,c_29358,c_28977,c_28927,c_28756,c_28707,c_28691,c_28625,c_28616,c_28597,c_28583,c_27529,c_27520,c_27037,c_27036,c_26873,c_26870,c_26811,c_26796,c_26780,c_26773,c_26707,c_26693,c_26533,c_25823,c_24996,c_24752,c_24605,c_24395,c_24392,c_24370,c_24306,c_24287,c_24188,c_24184,c_23821,c_23790,c_23552,c_23483,c_23436,c_23229,c_23214,c_23175,c_23172,c_23167,c_23165,c_23163,c_23171,c_23085,c_23062,c_23005,c_22988,c_22984,c_22981,c_22969,c_22968,c_22949,c_22944,c_22843,c_22725,c_22379,c_22290,c_22107,c_22097,c_22096,c_22095,c_22101,c_21984,c_21917,c_14930,c_13381,c_10412,c_9775,c_4335,c_4097,c_1768,c_1530,c_428,c_427,c_426,c_425,c_424,c_423,c_415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP359-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 14:29:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41
% 0.15/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.41
% 0.15/0.41 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 18.38/3.19 % SZS status Started for theBenchmark.p
% 18.38/3.19 % SZS status Unsatisfiable for theBenchmark.p
% 18.38/3.19
% 18.38/3.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.38/3.19
% 18.38/3.19 % ------ iProver source info
% 18.38/3.19
% 18.38/3.19 % git: date: 2026-07-19 20:42:38 +0200
% 18.38/3.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.38/3.19 % git: non_committed_changes: false
% 18.38/3.19
% 18.38/3.19 % ------ Parsing...% successful
% 18.38/3.19
% 18.38/3.19
% 18.38/3.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.38/3.19
% 18.38/3.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 18.38/3.19
% 18.38/3.19 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.38/3.19
% 18.38/3.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 18.38/3.19 % ------ Proving...
% 18.38/3.19 % ------ Problem Properties
% 18.38/3.19
% 18.38/3.19 %
% 18.38/3.19 % clauses 47
% 18.38/3.19 % conjectures 33
% 18.38/3.19 % EPR 31
% 18.38/3.19 % Horn 16
% 18.38/3.19 % unary 14
% 18.38/3.19 % binary 30
% 18.38/3.19 % lits 85
% 18.38/3.19 % lits eq 81
% 18.38/3.19 % fd_pure 0
% 18.38/3.19 % fd_pseudo 0
% 18.38/3.19 % fd_cond 0
% 18.38/3.19 % fd_pseudo_cond 0
% 18.38/3.19 % AC symbols 0
% 18.38/3.19
% 18.38/3.19 % ------ Schedule dynamic 5 is on
% 18.38/3.19
% 18.38/3.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.38/3.19
% 18.38/3.19
% 18.38/3.19 % ------
% 18.38/3.19 % Current options:
% 18.38/3.19 % ------
% 18.38/3.19
% 18.38/3.19
% 18.38/3.19 %
% 18.38/3.19
% 18.38/3.19 % ------ Proving...
% 18.38/3.19 %
% 18.38/3.19
% 18.38/3.19 % SZS status Unsatisfiable for theBenchmark.p
% 18.38/3.19
% 18.38/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.38/3.20
% 18.38/3.20
%------------------------------------------------------------------------------