%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP343-1 : 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 : n011.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 01:33:17 PM UTC 2026
% Result : Unsatisfiable 10.55s 17.68s
% Output : CNFRefutation 10.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 53
% Syntax : Number of formulae : 470 ( 124 unt; 13 def)
% Number of atoms : 1700 ( 895 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 907 ( 340 ~; 567 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn 145 !; 0 ?; 122 :)
% 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_c9) = sk_c7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c4)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c6) = sk_c5
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c9 = inverse(sk_c5)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c5 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c8 = inverse(sk_c4)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( inverse(sk_c6) = sk_c5
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = inverse(sk_c5)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c5
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c9 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c5 = multiply(sk_c6,sk_c9)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( inverse(sk_c6) = sk_c5
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c9 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c5 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X4,sk_c9) != X5
| inverse(X5) != sk_c9
| inverse(X4) != X5
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X4,sk_c9) != X5
| sk_c9 != inverse(X5)
| inverse(X4) != X5
| sk_c8 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != inverse(X1)
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(reorient_equations,[],[f70]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != multiply(X4,sk_c9)
| sk_c9 != inverse(inverse(X4))
| sk_c8 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != inverse(X1)
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(equality_resolution,[],[f71]) ).
tcf(c_86,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_87,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_89,negated_conjecture,
multiply(sk_c8,sk_c9) = sk_c7,
inference(cnf_transformation,[],[f5]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c5 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c5 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_121,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c5 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_122,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c8 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c9 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( multiply(sk_c8,sk_c9) != sk_c7 )
| ( inverse(inverse(X0)) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( multiply(X3,sk_c9) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c8) != sk_c9 )
| ( multiply(X0,sk_c9) != inverse(X0) ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c8 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c9 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c9) != inverse(X0) )
| ( multiply(X1,sk_c8) != sk_c9 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X3,sk_c9) != sk_c8 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( inverse(inverse(X0)) != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_122,c_89,c_122]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c8 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c9 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( inverse(inverse(X0)) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( multiply(X3,sk_c9) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c8) != sk_c9 )
| ( multiply(X0,sk_c9) != inverse(X0) ) ),
inference(renaming,[status(thm)],[c_127]) ).
tcf(c_440,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_441,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_442,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_443,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_444,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(inverse(X0)) != sk_c9 )
| ( multiply(X0,sk_c9) != inverse(X0) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_128]) ).
tcf(c_445,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c9,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_446,definition,
iPr_def_15 = multiply(sk_c9,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_447,definition,
iPr_def_16 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_448,definition,
iPr_def_17 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_449,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_450,definition,
iPr_def_19 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_451,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_452,definition,
iPr_def_21 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_453,definition,
iPr_def_22 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_454,definition,
iPr_def_23 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_455,definition,
iPr_def_24 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_456,definition,
iPr_def_25 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_457,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_458,definition,
iPr_def_27 = multiply(sk_c8,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_459,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_445,c_446]) ).
tcf(c_460,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(inverse(X0)) != sk_c9 )
| ( multiply(X0,sk_c9) != inverse(X0) ) ),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_461,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_443]) ).
tcf(c_462,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_442]) ).
tcf(c_463,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_441]) ).
tcf(c_464,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_465,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_121,c_448,c_447]) ).
tcf(c_466,negated_conjecture,
( ( iPr_def_18 = sk_c9 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_120,c_449]) ).
tcf(c_467,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_119,c_450]) ).
tcf(c_468,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_118,c_451]) ).
tcf(c_469,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_117,c_452]) ).
tcf(c_470,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_471,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_453]) ).
tcf(c_472,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_454]) ).
tcf(c_473,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_113,c_455]) ).
tcf(c_474,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_475,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_476,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_477,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_478,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_479,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_480,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_23 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_481,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_105,c_456]) ).
tcf(c_482,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_483,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_19 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_484,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_485,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_486,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_487,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_488,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_23 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_489,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_97,c_457]) ).
tcf(c_490,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_491,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_19 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_492,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_493,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_494,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_23 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_497,negated_conjecture,
iPr_def_27 = sk_c7,
inference(demodulation,[status(thm)],[c_89,c_458]) ).
tcf(c_498,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_504,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_742,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_465,c_467]) ).
tcf(c_782,plain,
multiply(sk_c9,iPr_def_27) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_446,c_497]) ).
tcf(c_844,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_474,c_466]) ).
tcf(c_865,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_475,c_473]) ).
tcf(c_916,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_477,c_469]) ).
tcf(c_942,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_478,c_470]) ).
tcf(c_968,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_479,c_471]) ).
tcf(c_981,plain,
multiply(sk_c2,iPr_def_27) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_448,c_497]) ).
tcf(c_990,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_469,c_452]) ).
tcf(c_991,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_468,c_452]) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1051,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1057,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = inverse(X0) )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1054]) ).
tcf(c_1066,plain,
! [X0: $i] :
( ( sk_c8 = inverse(X0) )
| ( sk_c8 != sk_c8 )
| ( inverse(X0) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1057]) ).
tcf(c_1067,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_1069,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1073,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_24,sk_c9) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_476,c_458]) ).
tcf(c_1078,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_17,sk_c9) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_469,c_458]) ).
tcf(c_1111,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_18 )
| ( iPr_def_18 != inverse(sk_c5) )
| ( inverse(X0) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1063]) ).
tcf(c_1121,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_26 )
| ( iPr_def_26 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1063]) ).
tcf(c_1124,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_457,c_87]) ).
tcf(c_1125,plain,
multiply(iPr_def_22,sk_c3) = identity,
inference(superposition,[status(thm)],[c_453,c_87]) ).
tcf(c_1126,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_451,c_87]) ).
tcf(c_1128,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_449,c_87]) ).
tcf(c_1129,plain,
multiply(iPr_def_24,sk_c2) = identity,
inference(superposition,[status(thm)],[c_455,c_87]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_18 )
| ( inverse(X0) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1054]) ).
tcf(c_1201,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_482,c_454]) ).
tcf(c_1223,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_483,c_481]) ).
tcf(c_1225,plain,
( ( sk_c9 = iPr_def_25 )
| ( inverse(iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_483,c_449]) ).
tcf(c_1252,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_484,c_456]) ).
tcf(c_1303,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_26 )
| ( inverse(X0) != iPr_def_26 ) ),
inference(instantiation,[status(thm)],[c_1054]) ).
tcf(c_1310,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1069]) ).
tcf(c_1339,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_485,c_454]) ).
tcf(c_1367,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_486,c_484]) ).
tcf(c_1431,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1432,plain,
( ( sk_c9 = sk_c8 )
| ( sk_c9 != sk_c9 )
| ( sk_c8 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1431]) ).
tcf(c_1434,plain,
( ( sk_c8 = iPr_def_20 )
| ( iPr_def_20 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1310]) ).
tcf(c_1435,plain,
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1310]) ).
tcf(c_1456,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_487,c_454]) ).
tcf(c_1471,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( iPr_def_20 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1494,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_488,c_456]) ).
tcf(c_1551,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1557,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_26 )
| ( iPr_def_26 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_1558,plain,
( ( sk_c9 = iPr_def_26 )
| ( iPr_def_26 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1557]) ).
tcf(c_1604,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_26) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_490,c_454]) ).
tcf(c_1626,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c5) )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_501]) ).
tcf(c_1640,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_491,c_489]) ).
tcf(c_1643,plain,
( ( sk_c9 = iPr_def_26 )
| ( inverse(iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_491,c_449]) ).
tcf(c_1679,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_492,c_456]) ).
tcf(c_1833,plain,
( ( inverse(sk_c1) = iPr_def_26 )
| ( iPr_def_26 != inverse(sk_c1) )
| ( inverse(sk_c1) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_1834,plain,
inverse(sk_c1) = inverse(sk_c1),
inference(instantiation,[status(thm)],[c_1051]) ).
tcf(c_1848,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_26) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_493,c_454]) ).
tcf(c_1971,plain,
iPr_def_20 = iPr_def_20,
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_2047,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_26) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_495,c_454]) ).
tcf(c_2085,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_496,c_456]) ).
tcf(c_2146,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1069]) ).
tcf(c_2149,plain,
( ( sk_c8 = sk_c9 )
| ( sk_c9 != iPr_def_15 )
| ( sk_c8 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_2146]) ).
tcf(c_2215,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_494,c_459]) ).
tcf(c_2218,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_486,c_459]) ).
tcf(c_2220,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_23 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_480,c_459]) ).
tcf(c_2222,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_478,c_459]) ).
tcf(c_2368,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_21 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_452,c_461]) ).
tcf(c_2369,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_456,c_461]) ).
tcf(c_2370,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c9 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_86,c_461]) ).
tcf(c_2393,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_25 )
| ( sk_c8 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_2369,c_457]) ).
tcf(c_2397,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_21 )
| ( sk_c8 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2368,c_451]) ).
tcf(c_2607,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_21 )
| ( inverse(sk_c4) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_452,c_462]) ).
tcf(c_2608,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_456,c_462]) ).
tcf(c_2609,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c9 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_86,c_462]) ).
tcf(c_2632,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_26 )
| ( sk_c9 != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_2608,c_457]) ).
tcf(c_2636,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_21 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2607,c_451]) ).
tcf(c_2750,plain,
( ( inverse(iPr_def_19) = inverse(sk_c5) )
| ( iPr_def_19 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1626]) ).
tcf(c_2787,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ( iPr_def_20 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1471]) ).
tcf(c_2788,plain,
( ( sk_c9 = iPr_def_20 )
| ( iPr_def_20 != sk_c8 )
| ( sk_c9 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_2787]) ).
tcf(c_2796,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_23 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_454,c_463]) ).
tcf(c_2813,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2796,c_453]) ).
tcf(c_2861,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_26 )
| ( iPr_def_26 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_1557]) ).
tcf(c_2894,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_478,c_470]) ).
tcf(c_2909,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_27) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_464,c_497]) ).
tcf(c_2921,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_15 )
| ( inverse(sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_782,c_2909]) ).
tcf(c_3023,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_26 )
| ( inverse(sk_c1) != iPr_def_26 ) ),
inference(instantiation,[status(thm)],[c_1303]) ).
tcf(c_3024,plain,
( ( inverse(sk_c1) = sk_c9 )
| ( sk_c9 != iPr_def_26 )
| ( inverse(sk_c1) != iPr_def_26 ) ),
inference(instantiation,[status(thm)],[c_3023]) ).
tcf(c_3055,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c9,X0)) = multiply(iPr_def_27,X0),
inference(superposition,[status(thm)],[c_458,c_88]) ).
tcf(c_3056,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c9,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_454,c_88]) ).
tcf(c_3059,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_456,c_88]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_87,c_88]) ).
tcf(c_3063,plain,
! [X0: $i] : multiply(sk_c9,multiply(iPr_def_27,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_782,c_88]) ).
tcf(c_3064,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_27,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_981,c_88]) ).
tcf(c_3065,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1124,c_88]) ).
tcf(c_3066,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1125,c_88]) ).
tcf(c_3067,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1126,c_88]) ).
tcf(c_3069,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1128,c_88]) ).
tcf(c_3070,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1129,c_88]) ).
tcf(c_3076,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3070,c_86]) ).
tcf(c_3077,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3069,c_86]) ).
tcf(c_3079,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3067,c_86]) ).
tcf(c_3080,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3066,c_86]) ).
tcf(c_3081,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3065,c_86]) ).
tcf(c_3352,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_865,c_742]) ).
tcf(c_3472,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_916,c_458]) ).
tcf(c_3524,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c8 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_942,c_480]) ).
tcf(c_3531,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_942,c_476]) ).
tcf(c_3658,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_968,c_454]) ).
tcf(c_3660,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(iPr_def_22,iPr_def_27) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_968,c_782]) ).
tcf(c_3827,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1431]) ).
tcf(c_3829,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_1431]) ).
tcf(c_3844,plain,
( ~ iPr_def_14
| ( inverse(sk_c8) != iPr_def_27 )
| ( inverse(inverse(sk_c8)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_458,c_460]) ).
tcf(c_3846,plain,
( ~ iPr_def_14
| ( inverse(sk_c6) != iPr_def_16 )
| ( inverse(inverse(sk_c6)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_447,c_460]) ).
tcf(c_3863,plain,
( ~ iPr_def_14
| ( iPr_def_16 != iPr_def_19 )
| ( inverse(iPr_def_19) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3846,c_450]) ).
tcf(c_3954,plain,
! [X0: $i] :
( ( X0 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1551]) ).
tcf(c_4149,plain,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c8 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_3827]) ).
tcf(c_4150,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_4160,plain,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_20 != iPr_def_20 )
| ( sk_c8 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_3829]) ).
tcf(c_4257,plain,
multiply(iPr_def_24,sk_c2) = identity,
inference(superposition,[status(thm)],[c_455,c_87]) ).
tcf(c_5119,plain,
multiply(iPr_def_24,iPr_def_17) = iPr_def_27,
inference(superposition,[status(thm)],[c_981,c_3076]) ).
tcf(c_5122,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(iPr_def_17,X0)) = multiply(iPr_def_27,X0),
inference(superposition,[status(thm)],[c_5119,c_88]) ).
tcf(c_5270,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_452,c_3079]) ).
tcf(c_5273,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5270,c_88]) ).
tcf(c_5275,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c9,
inference(superposition,[status(thm)],[c_454,c_3080]) ).
tcf(c_5280,plain,
multiply(iPr_def_26,iPr_def_25) = sk_c8,
inference(superposition,[status(thm)],[c_456,c_3081]) ).
tcf(c_5283,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(iPr_def_25,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5280,c_88]) ).
tcf(c_5290,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_17,multiply(sk_c2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_3352,c_3076]) ).
tcf(c_5318,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_22 )
| ( iPr_def_22 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_5319,plain,
( ( sk_c9 = iPr_def_22 )
| ( iPr_def_22 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_5318]) ).
tcf(c_5431,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| ( sk_c9 = iPr_def_26 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2215,c_504,c_495,c_496,c_1067,c_1435,c_1558,c_2215,c_2813,c_5319]) ).
tcf(c_5432,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c9 = iPr_def_26 ) ),
inference(renaming,[status(thm)],[c_5431]) ).
tcf(c_5626,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_990,c_3079]) ).
tcf(c_5627,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5626,c_5270]) ).
tcf(c_5710,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_991,c_3079]) ).
tcf(c_5711,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5710,c_5270]) ).
tcf(c_6573,plain,
( ( sk_c8 = inverse(sk_c1) )
| ( sk_c8 != sk_c8 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1066]) ).
tcf(c_6577,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c8 )
| ( sk_c8 != X0 )
| ( inverse(sk_c1) != X0 ) ),
inference(instantiation,[status(thm)],[c_1015]) ).
tcf(c_6578,plain,
( ( inverse(sk_c1) = sk_c8 )
| ( sk_c8 != sk_c9 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_6577]) ).
tcf(c_6816,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_17,iPr_def_25) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_485,c_1078]) ).
tcf(c_7523,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1201,c_3080]) ).
tcf(c_7524,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_7523,c_5275]) ).
tcf(c_7694,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1252,c_3081]) ).
tcf(c_7695,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_7694,c_5280]) ).
tcf(c_7766,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1339,c_3080]) ).
tcf(c_7767,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_7766,c_5275]) ).
tcf(c_8180,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1456,c_3080]) ).
tcf(c_8181,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_8180,c_5275]) ).
tcf(c_8297,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1494,c_3081]) ).
tcf(c_8298,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c8 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_8297,c_5280]) ).
tcf(c_8619,plain,
( ( inverse(iPr_def_19) = iPr_def_18 )
| ( iPr_def_18 != inverse(sk_c5) )
| ( inverse(iPr_def_19) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1111]) ).
tcf(c_8632,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1604,c_3080]) ).
tcf(c_8633,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_8632,c_5275]) ).
tcf(c_8799,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1679,c_3081]) ).
tcf(c_8800,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_8799,c_5280]) ).
tcf(c_9189,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1848,c_3080]) ).
tcf(c_9190,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_9189,c_5275]) ).
tcf(c_9411,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_2047,c_3080]) ).
tcf(c_9412,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_9411,c_5275]) ).
tcf(c_9810,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_26,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_2085,c_3081]) ).
tcf(c_9811,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c8 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_9810,c_5280]) ).
tcf(c_10731,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_23,iPr_def_27),
inference(superposition,[status(thm)],[c_782,c_3056]) ).
tcf(c_11154,plain,
multiply(sk_c1,iPr_def_27) = multiply(iPr_def_25,sk_c9),
inference(superposition,[status(thm)],[c_458,c_3059]) ).
tcf(c_11326,plain,
multiply(iPr_def_26,multiply(iPr_def_25,sk_c9)) = iPr_def_27,
inference(superposition,[status(thm)],[c_11154,c_3081]) ).
tcf(c_13615,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3061,c_86]) ).
tcf(c_13630,plain,
multiply(inverse(sk_c8),iPr_def_27) = sk_c9,
inference(superposition,[status(thm)],[c_458,c_13615]) ).
tcf(c_13636,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_87,c_13615]) ).
tcf(c_13638,plain,
multiply(inverse(sk_c9),iPr_def_15) = iPr_def_27,
inference(superposition,[status(thm)],[c_782,c_13615]) ).
tcf(c_13784,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3081,c_13615]) ).
tcf(c_13785,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3080,c_13615]) ).
tcf(c_13786,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3079,c_13615]) ).
tcf(c_13788,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3077,c_13615]) ).
tcf(c_13789,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3076,c_13615]) ).
tcf(c_13845,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_13615,c_13615]) ).
tcf(c_14209,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1069]) ).
tcf(c_14212,plain,
( ( sk_c8 = sk_c9 )
| ( sk_c9 != iPr_def_17 )
| ( sk_c8 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_14209]) ).
tcf(c_14227,plain,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_15 != iPr_def_20 )
| ( sk_c8 != iPr_def_20 ) ),
inference(instantiation,[status(thm)],[c_3829]) ).
tcf(c_14284,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( iPr_def_17 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_3954]) ).
tcf(c_14511,plain,
! [X0: $i] :
( ( inverse(iPr_def_19) = X0 )
| ( X0 != iPr_def_18 )
| ( inverse(iPr_def_19) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1167]) ).
tcf(c_14512,plain,
( ( inverse(iPr_def_19) = sk_c9 )
| ( sk_c9 != iPr_def_18 )
| ( inverse(iPr_def_19) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_14511]) ).
tcf(c_14727,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_13636,c_13845]) ).
tcf(c_14739,plain,
multiply(sk_c2,iPr_def_27) = multiply(iPr_def_17,identity),
inference(superposition,[status(thm)],[c_14727,c_3064]) ).
tcf(c_14740,plain,
multiply(sk_c9,iPr_def_27) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_14727,c_3063]) ).
tcf(c_14743,plain,
multiply(sk_c8,sk_c9) = multiply(iPr_def_27,identity),
inference(superposition,[status(thm)],[c_14727,c_3055]) ).
tcf(c_14745,plain,
multiply(sk_c8,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_14727,c_5273]) ).
tcf(c_14749,plain,
multiply(sk_c8,identity) = multiply(iPr_def_26,iPr_def_25),
inference(superposition,[status(thm)],[c_14727,c_5283]) ).
tcf(c_14750,plain,
multiply(iPr_def_24,iPr_def_17) = multiply(iPr_def_27,identity),
inference(superposition,[status(thm)],[c_14727,c_5122]) ).
tcf(c_14758,plain,
multiply(iPr_def_27,identity) = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_14750,c_5119]) ).
tcf(c_14759,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_14749,c_5280]) ).
tcf(c_14768,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_14740,c_782]) ).
tcf(c_14773,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_2393,c_2397,c_2393,c_7695,c_7767]) ).
tcf(c_14801,plain,
( ( sk_c9 = iPr_def_26 )
| ~ iPr_def_13
| ( iPr_def_23 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_496,c_14773]) ).
tcf(c_14804,plain,
( ( sk_c9 = iPr_def_25 )
| ~ iPr_def_13
| ( iPr_def_23 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_488,c_14773]) ).
tcf(c_14813,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_13
| ( iPr_def_23 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_472,c_14773]) ).
tcf(c_14946,plain,
( ( sk_c9 = iPr_def_26 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_14801,c_2397,c_8800,c_9190]) ).
tcf(c_14952,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_10
| ( sk_c9 = iPr_def_26 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5432,c_14946]) ).
tcf(c_14961,plain,
( ( sk_c9 = iPr_def_25 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_14804,c_2397,c_7695,c_7767]) ).
tcf(c_14967,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_25 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2218,c_14961]) ).
tcf(c_15013,plain,
( iPr_def_10
| ( sk_c9 = iPr_def_25 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_14967,c_459,c_1223,c_1225,c_1367,c_2813,c_3863,c_7524,c_7695,c_8181,c_8298,c_14227,c_14512,c_14961]) ).
tcf(c_15014,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c9 = iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_15013]) ).
tcf(c_15021,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_14813,c_2397,c_5627,c_5711]) ).
tcf(c_15519,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_12
| ( sk_c9 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_485,c_2632]) ).
tcf(c_15684,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_15519,c_9190,c_15519]) ).
tcf(c_15691,plain,
( ( sk_c9 = iPr_def_26 )
| iPr_def_10
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_14952,c_1640,c_1643,c_3863,c_8633,c_14512,c_14952]) ).
tcf(c_15692,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c9 = iPr_def_26 ) ),
inference(renaming,[status(thm)],[c_15691]) ).
tcf(c_15718,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_3524,c_472,c_480,c_1067,c_1435,c_14284]) ).
tcf(c_15811,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(iPr_def_23,sk_c9) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_15718,c_458]) ).
tcf(c_15981,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_2636,c_2636,c_15684]) ).
tcf(c_16234,plain,
multiply(sk_c1,iPr_def_26) = identity,
inference(superposition,[status(thm)],[c_13784,c_87]) ).
tcf(c_16238,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_26)) != sk_c9 )
| ( multiply(sk_c1,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_13784,c_463]) ).
tcf(c_16240,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_26,X0)) = X0,
inference(superposition,[status(thm)],[c_13784,c_13615]) ).
tcf(c_16241,plain,
multiply(sk_c1,identity) = inverse(iPr_def_26),
inference(superposition,[status(thm)],[c_13784,c_14727]) ).
tcf(c_16299,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_4257,c_88]) ).
tcf(c_16305,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_16299,c_86]) ).
tcf(c_16349,plain,
inverse(iPr_def_26) = sk_c1,
inference(demodulation,[status(thm)],[c_16241,c_14727]) ).
tcf(c_16435,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_3531,c_468,c_476,c_1067,c_1434,c_14284]) ).
tcf(c_16491,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_16435,c_3472]) ).
tcf(c_16518,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_16435,c_942]) ).
tcf(c_16553,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c8 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_16491,c_5270]) ).
tcf(c_16963,plain,
multiply(sk_c1,sk_c8) = iPr_def_25,
inference(superposition,[status(thm)],[c_5280,c_16240]) ).
tcf(c_17268,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( iPr_def_17 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_16553,c_15718]) ).
tcf(c_17631,plain,
( ( iPr_def_17 = iPr_def_24 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_968,c_2813]) ).
tcf(c_17634,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_11
| ( iPr_def_22 != iPr_def_26 )
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_495,c_2813]) ).
tcf(c_18025,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_17268,c_3660]) ).
tcf(c_18049,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_18025,c_5275]) ).
tcf(c_18298,plain,
( ( iPr_def_17 = iPr_def_24 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_18049,c_15981]) ).
tcf(c_18689,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_17 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2894,c_459]) ).
tcf(c_19302,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_22)) != sk_c9 )
| ( multiply(sk_c3,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_13785,c_462]) ).
tcf(c_19304,plain,
multiply(sk_c3,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_13785,c_87]) ).
tcf(c_19308,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c9 )
| ( multiply(sk_c3,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_13785,c_463]) ).
tcf(c_19310,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_13785,c_13615]) ).
tcf(c_19311,plain,
multiply(sk_c3,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_13785,c_14727]) ).
tcf(c_19315,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_23 )
| ( inverse(inverse(iPr_def_22)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_19308,c_454]) ).
tcf(c_19330,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_3658,c_19304]) ).
tcf(c_19393,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19330,c_86]) ).
tcf(c_19452,plain,
inverse(iPr_def_22) = sk_c3,
inference(demodulation,[status(thm)],[c_19311,c_14727]) ).
tcf(c_19459,plain,
multiply(sk_c3,sk_c9) = iPr_def_23,
inference(superposition,[status(thm)],[c_5275,c_19310]) ).
tcf(c_19509,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_13786,c_87]) ).
tcf(c_19515,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_13786,c_13615]) ).
tcf(c_20625,plain,
multiply(sk_c4,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_5270,c_19515]) ).
tcf(c_23358,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_19393,c_15811]) ).
tcf(c_23576,plain,
( ( iPr_def_21 = iPr_def_27 )
| ( iPr_def_17 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_23358,c_916]) ).
tcf(c_23586,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_27) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_23358,c_454]) ).
tcf(c_25223,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(sk_c9,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_23576,c_782]) ).
tcf(c_25508,plain,
( ( sk_c8 = iPr_def_26 )
| ( iPr_def_26 != inverse(sk_c1) )
| ( sk_c8 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_2861]) ).
tcf(c_25810,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_2370,c_457,c_1067,c_1833,c_1834,c_3024,c_6573,c_6578,c_14773,c_14946,c_25508]) ).
tcf(c_25855,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_471,c_25810]) ).
tcf(c_26525,plain,
( ( sk_c9 != iPr_def_17 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_25855,c_14212,c_15021,c_25810]) ).
tcf(c_26526,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_26525]) ).
tcf(c_26559,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( iPr_def_17 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_485,c_26526]) ).
tcf(c_26719,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_13788,c_14727]) ).
tcf(c_26759,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_26719,c_14727]) ).
tcf(c_26839,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_22 )
| ( iPr_def_22 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_5318]) ).
tcf(c_26844,plain,
( ( sk_c8 = iPr_def_22 )
| ( iPr_def_22 != sk_c9 )
| ( sk_c8 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_26839]) ).
tcf(c_27159,plain,
( ( iPr_def_17 = iPr_def_24 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_23 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_23586,c_2909]) ).
tcf(c_27167,plain,
( ( iPr_def_17 = iPr_def_24 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_23 )
| ( sk_c8 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_27159,c_453]) ).
tcf(c_27683,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_2609,c_504,c_492,c_1432,c_1558,c_1971,c_2636,c_2632,c_2788,c_4160,c_7695,c_15684]) ).
tcf(c_28308,plain,
multiply(sk_c2,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_13789,c_87]) ).
tcf(c_28313,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_24)) != sk_c8 )
| ( multiply(sk_c2,iPr_def_27) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_13789,c_2909]) ).
tcf(c_28315,plain,
multiply(sk_c2,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_13789,c_14727]) ).
tcf(c_28348,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_17 )
| ( inverse(inverse(iPr_def_24)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_28313,c_981]) ).
tcf(c_28633,plain,
inverse(iPr_def_24) = sk_c2,
inference(demodulation,[status(thm)],[c_28315,c_14727]) ).
tcf(c_28915,plain,
( iPr_def_14
| ( iPr_def_17 = iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_18689,c_449,c_459,c_467,c_471,c_475,c_479,c_844,c_916,c_942,c_2149,c_2397,c_2750,c_3352,c_3863,c_4149,c_4150,c_8619,c_14284,c_14512,c_15718,c_16435,c_16518,c_17631,c_18049,c_18298,c_26844,c_27167]) ).
tcf(c_28917,plain,
iPr_def_17 = iPr_def_24,
inference(global_subsumption_just,[status(thm)],[c_28915,c_449,c_467,c_475,c_844,c_2750,c_3352,c_3863,c_8619,c_14284,c_14512,c_28915]) ).
tcf(c_28923,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(demodulation,[status(thm)],[c_16305,c_28917]) ).
tcf(c_29690,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_5290,c_28923]) ).
tcf(c_29692,plain,
multiply(iPr_def_17,iPr_def_17) = iPr_def_27,
inference(superposition,[status(thm)],[c_981,c_29690]) ).
tcf(c_29694,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_14727,c_29690]) ).
tcf(c_29700,plain,
multiply(iPr_def_17,identity) = iPr_def_24,
inference(superposition,[status(thm)],[c_28308,c_29690]) ).
tcf(c_29719,plain,
multiply(iPr_def_24,iPr_def_27) = multiply(iPr_def_27,iPr_def_17),
inference(superposition,[status(thm)],[c_29692,c_5122]) ).
tcf(c_29720,plain,
iPr_def_17 = iPr_def_24,
inference(global_subsumption_just,[status(thm)],[c_25223,c_28917]) ).
tcf(c_29722,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_28633,c_29720]) ).
tcf(c_29723,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(demodulation,[status(thm)],[c_28308,c_29720]) ).
tcf(c_29817,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_17,sk_c9) = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_1073,c_29720]) ).
tcf(c_29849,plain,
inverse(sk_c2) = iPr_def_17,
inference(demodulation,[status(thm)],[c_455,c_29720]) ).
tcf(c_29873,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_29723,c_88]) ).
tcf(c_29876,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_29873,c_86]) ).
tcf(c_29882,plain,
multiply(inverse(iPr_def_17),identity) = sk_c2,
inference(superposition,[status(thm)],[c_29694,c_13615]) ).
tcf(c_29884,plain,
multiply(sk_c2,identity) = sk_c2,
inference(light_normalisation,[status(thm)],[c_29882,c_29722]) ).
tcf(c_30040,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_2220,c_459,c_2222,c_4149,c_4150]) ).
tcf(c_30042,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_30040,c_29720]) ).
tcf(c_30080,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_27) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_6816,c_29876]) ).
tcf(c_30089,plain,
( ( iPr_def_17 = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_30080,c_981]) ).
tcf(c_30165,plain,
multiply(iPr_def_17,iPr_def_27) = multiply(iPr_def_27,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_29719,c_29720]) ).
tcf(c_30169,plain,
multiply(sk_c2,multiply(iPr_def_17,iPr_def_27)) = multiply(iPr_def_17,iPr_def_17),
inference(superposition,[status(thm)],[c_30165,c_3064]) ).
tcf(c_30171,plain,
multiply(sk_c2,multiply(iPr_def_17,iPr_def_27)) = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_30169,c_29692]) ).
tcf(c_30619,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13 ),
inference(backward_subsumption_resolution,[status(thm)],[c_26559,c_30089]) ).
tcf(c_30850,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_20 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2397,c_30619]) ).
tcf(c_31126,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_27) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_29817,c_29876]) ).
tcf(c_31127,plain,
( ( sk_c9 = iPr_def_17 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_31126,c_981]) ).
tcf(c_31228,plain,
~ iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_30850,c_26526,c_30850,c_31127]) ).
tcf(c_31230,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_17 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_30042,c_31228]) ).
tcf(c_31231,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_459,c_31228]) ).
tcf(c_48675,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_26 )
| ( multiply(sk_c1,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_16238,c_457,c_16349]) ).
tcf(c_49727,plain,
( ( sk_c8 != iPr_def_23 )
| ( iPr_def_22 != iPr_def_26 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_17634,c_2813,c_17634]) ).
tcf(c_49728,plain,
( ~ iPr_def_11
| ( iPr_def_22 != iPr_def_26 )
| ( sk_c8 != iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_49727]) ).
tcf(c_49754,plain,
( ( sk_c9 = iPr_def_26 )
| ~ iPr_def_11
| ( iPr_def_22 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_496,c_49728]) ).
tcf(c_49810,plain,
( ( sk_c9 = iPr_def_26 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_49754,c_2813,c_9412,c_9811]) ).
tcf(c_49816,plain,
( ~ iPr_def_11
| ( multiply(sk_c1,sk_c9) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_48675,c_49810]) ).
tcf(c_50113,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_22 )
| ( multiply(sk_c3,sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_19302,c_453,c_19452]) ).
tcf(c_51538,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_50113,c_49816,c_31231,c_31230,c_30171,c_30169,c_29884,c_29723,c_29722,c_29700,c_29849,c_29720,c_28633,c_28348,c_27683,c_26759,c_20625,c_19509,c_19459,c_19452,c_19315,c_19311,c_19304,c_16963,c_16234,c_15692,c_15014,c_14768,c_14759,c_14758,c_14749,c_14745,c_14743,c_14740,c_14739,c_13638,c_13630,c_11326,c_10731,c_3863,c_3844,c_2921,c_472,c_471,c_470,c_469,c_468,c_467,c_466,c_465,c_453,c_449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP343-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.43 % CPULimit : 300
% 0.09/15.43 % WCLimit : 300
% 0.09/15.43 % DateTime : Wed Sep 23 14:31:27 UTC 2026
% 0.09/15.43 % CPUTime :
% 0.09/15.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/15.46 Running first-order theorem proving
% 0.09/15.46 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
% 0.09/15.47
% 0.09/15.47 % ======== iProver multi-core TPTP/SMT =========
% 0.09/15.47
% 0.09/15.47 % Detected problem language: tptp
% 0.09/15.49 % Proving...
% 10.55/17.68 % SZS status Started for theBenchmark.p
% 10.55/17.68 % SZS status Unsatisfiable for theBenchmark.p
% 10.55/17.68
% 10.55/17.68 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.55/17.68
% 10.55/17.68 % ------ iProver source info
% 10.55/17.68
% 10.55/17.68 % git: date: 2026-07-19 20:42:38 +0200
% 10.55/17.68 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.55/17.68 % git: non_committed_changes: false
% 10.55/17.68
% 10.55/17.68 % ------ Parsing...% successful
% 10.55/17.68
% 10.55/17.68
% 10.55/17.68 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.55/17.68
% 10.55/17.68 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.55/17.68
% 10.55/17.68 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.55/17.68
% 10.55/17.68 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.55/17.68 % ------ Proving...
% 10.55/17.68 % ------ Problem Properties
% 10.55/17.68
% 10.55/17.68 %
% 10.55/17.68 % clauses 55
% 10.55/17.68 % conjectures 39
% 10.55/17.68 % EPR 34
% 10.55/17.68 % Horn 22
% 10.55/17.68 % unary 17
% 10.55/17.68 % binary 32
% 10.55/17.68 % lits 102
% 10.55/17.68 % lits eq 92
% 10.55/17.68 % fd_pure 0
% 10.55/17.68 % fd_pseudo 0
% 10.55/17.68 % fd_cond 0
% 10.55/17.68 % fd_pseudo_cond 0
% 10.55/17.68 % AC symbols 0
% 10.55/17.68
% 10.55/17.68 % ------ Schedule dynamic 5 is on
% 10.55/17.68
% 10.55/17.68 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.55/17.68
% 10.55/17.68
% 10.55/17.68 % ------
% 10.55/17.68 % Current options:
% 10.55/17.68 % ------
% 10.55/17.68
% 10.55/17.68
% 10.55/17.68 %
% 10.55/17.68
% 10.55/17.68 % ------ Proving...
% 10.55/17.68 %
% 10.55/17.68
% 10.55/17.68 % SZS status Unsatisfiable for theBenchmark.p
% 10.55/17.68
% 10.55/17.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.55/17.68
% 10.55/17.68
%------------------------------------------------------------------------------