%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP252-1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:28 PM UTC 2026
% Result : Unsatisfiable 18.68s 3.33s
% Output : CNFRefutation 18.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 56
% Syntax : Number of formulae : 472 ( 100 unt; 13 def)
% Number of atoms : 1629 ( 889 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 778 ( 273 ~; 505 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 111 !; 0 ?; 85 :)
% 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_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c6)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c6)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c10 = inverse(sk_c4)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f65,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c6)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c4)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c8 = inverse(sk_c6)
| sk_c9 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c9
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c8 != inverse(X6)
| multiply(X6,sk_c8) != X5
| sk_c9 != multiply(sk_c8,X5)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c8 != inverse(X6)
| sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(equality_resolution,[],[f90]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c8,sk_c7) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_128,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_130,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_132,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_133,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_135,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_137,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_138,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c9 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(X5,sk_c9) != sk_c8 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( multiply(X3,sk_c8) != sk_c9 )
| ( multiply(X1,sk_c10) != sk_c9 )
| ( multiply(X0,sk_c10) != sk_c9 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c9 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_537,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_140]) ).
tcf(c_538,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_140]) ).
tcf(c_539,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_140]) ).
tcf(c_540,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_140]) ).
tcf(c_541,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_140]) ).
tcf(c_542,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_543,definition,
iPr_def_15 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_544,definition,
iPr_def_16 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_545,definition,
iPr_def_17 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_546,definition,
iPr_def_18 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_547,definition,
iPr_def_19 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_548,definition,
iPr_def_20 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_549,definition,
iPr_def_21 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_550,definition,
iPr_def_22 = multiply(sk_c4,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_551,definition,
iPr_def_23 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_552,definition,
iPr_def_24 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_553,definition,
iPr_def_25 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_554,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_555,definition,
iPr_def_27 = multiply(sk_c1,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_556,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_542]) ).
tcf(c_557,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_541]) ).
tcf(c_558,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_540]) ).
tcf(c_560,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_539]) ).
tcf(c_561,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_538]) ).
tcf(c_562,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_537]) ).
tcf(c_563,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_139,c_544,c_543]) ).
tcf(c_564,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_138,c_545]) ).
tcf(c_565,negated_conjecture,
( ( iPr_def_18 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_137,c_546]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_136,c_547]) ).
tcf(c_567,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_135,c_548]) ).
tcf(c_568,negated_conjecture,
( ( iPr_def_21 = sk_c10 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_134,c_549]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_133,c_550]) ).
tcf(c_570,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_132,c_551]) ).
tcf(c_571,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_572,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_573,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_574,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_577,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_125,c_552]) ).
tcf(c_578,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_580,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_581,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_582,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_583,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_584,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_118,c_553]) ).
tcf(c_585,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_587,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_588,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_590,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_591,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_554]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_594,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_595,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_596,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_597,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_598,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104,c_555]) ).
tcf(c_600,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_601,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_602,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_603,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_604,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_605,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_611,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_605]) ).
tcf(c_896,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_563,c_566]) ).
tcf(c_904,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_565,c_567]) ).
tcf(c_980,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_573,c_570]) ).
tcf(c_982,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_573,c_543]) ).
tcf(c_1040,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_577,c_543]) ).
tcf(c_1052,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_577,c_546]) ).
tcf(c_1054,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_570,c_546]) ).
tcf(c_1056,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_563,c_546]) ).
tcf(c_1076,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_566,c_548]) ).
tcf(c_1095,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_574,c_553]) ).
tcf(c_1096,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_572,c_553]) ).
tcf(c_1098,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_567,c_553]) ).
tcf(c_1118,plain,
multiply(iPr_def_21,sk_c4) = identity,
inference(superposition,[status(thm)],[c_549,c_96]) ).
tcf(c_1119,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_547,c_96]) ).
tcf(c_1120,plain,
multiply(iPr_def_16,sk_c6) = identity,
inference(superposition,[status(thm)],[c_544,c_96]) ).
tcf(c_1121,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_554,c_96]) ).
tcf(c_1122,plain,
multiply(iPr_def_24,sk_c2) = identity,
inference(superposition,[status(thm)],[c_552,c_96]) ).
tcf(c_1123,plain,
multiply(iPr_def_23,sk_c3) = identity,
inference(superposition,[status(thm)],[c_551,c_96]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_1127,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_605]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_1149,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_579,c_553]) ).
tcf(c_1152,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_579,c_572]) ).
tcf(c_1185,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_580,c_548]) ).
tcf(c_1187,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_580,c_577]) ).
tcf(c_1206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1130]) ).
tcf(c_1210,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_605]) ).
tcf(c_1212,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_1223,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_553]) ).
tcf(c_1225,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_581,c_574]) ).
tcf(c_1256,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c5) )
| ( inverse(X0) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1206]) ).
tcf(c_1260,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c3) )
| ( inverse(X0) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_1206]) ).
tcf(c_1272,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_582,c_550]) ).
tcf(c_1287,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_583,c_553]) ).
tcf(c_1318,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_584,c_548]) ).
tcf(c_1363,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1212]) ).
tcf(c_1364,plain,
( ( sk_c8 = sk_c9 )
| ( sk_c8 != sk_c8 )
| ( sk_c9 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1363]) ).
tcf(c_1375,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(sk_c8,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_585,c_546]) ).
tcf(c_1380,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != iPr_def_19 )
| ( inverse(X0) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1124]) ).
tcf(c_1395,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_586,c_548]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_23 )
| ( inverse(X0) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1130]) ).
tcf(c_1453,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_587,c_548]) ).
tcf(c_1459,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_587,c_543]) ).
tcf(c_1511,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_588,c_548]) ).
tcf(c_1517,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_588,c_543]) ).
tcf(c_1583,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_19 )
| ( iPr_def_19 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_1655,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_591,c_555]) ).
tcf(c_1704,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_593,c_555]) ).
tcf(c_1743,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_594,c_555]) ).
tcf(c_1768,plain,
( ( inverse(sk_c5) = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c5) )
| ( inverse(sk_c5) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1256]) ).
tcf(c_1769,plain,
inverse(sk_c5) = inverse(sk_c5),
inference(instantiation,[status(thm)],[c_1127]) ).
tcf(c_1782,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_595,c_555]) ).
tcf(c_1821,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_596,c_555]) ).
tcf(c_1846,plain,
( ( inverse(sk_c3) = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c3) )
| ( inverse(sk_c3) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_1847,plain,
inverse(sk_c3) = inverse(sk_c3),
inference(instantiation,[status(thm)],[c_1127]) ).
tcf(c_1860,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_597,c_555]) ).
tcf(c_1960,plain,
( ( sk_c8 = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1363]) ).
tcf(c_2053,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_601,c_598]) ).
tcf(c_2059,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_601,c_548]) ).
tcf(c_2170,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_27) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_602,c_553]) ).
tcf(c_2232,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_603,c_555]) ).
tcf(c_2289,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_27) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_604,c_553]) ).
tcf(c_2438,plain,
! [X0: $i] :
( ( inverse(sk_c3) = X0 )
| ( X0 != iPr_def_23 )
| ( inverse(sk_c3) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1437]) ).
tcf(c_2439,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( sk_c9 != iPr_def_23 )
| ( inverse(sk_c3) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_2438]) ).
tcf(c_2507,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_27 )
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_904,c_602]) ).
tcf(c_2508,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_27 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_904,c_600]) ).
tcf(c_2820,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_553,c_558]) ).
tcf(c_2821,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_558]) ).
tcf(c_2822,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_96,c_558]) ).
tcf(c_2842,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2820,c_552]) ).
tcf(c_2982,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_548,c_560]) ).
tcf(c_2984,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_15 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_543,c_560]) ).
tcf(c_2985,plain,
( ~ iPr_def_12
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_560]) ).
tcf(c_3003,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_23 )
| ( sk_c9 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2984,c_551]) ).
tcf(c_3011,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_20 )
| ( sk_c9 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2982,c_547]) ).
tcf(c_3130,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_27 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_555,c_561]) ).
tcf(c_3131,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_550,c_561]) ).
tcf(c_3148,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( sk_c10 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3131,c_549]) ).
tcf(c_3152,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_27 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_3130,c_554]) ).
tcf(c_3259,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_548,c_562]) ).
tcf(c_3261,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_15 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_543,c_562]) ).
tcf(c_3262,plain,
( ~ iPr_def_10
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_562]) ).
tcf(c_3280,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_23 )
| ( sk_c9 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3261,c_551]) ).
tcf(c_3288,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3259,c_547]) ).
tcf(c_3412,plain,
( ~ iPr_def_14
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,iPr_def_20) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_548,c_557]) ).
tcf(c_3441,plain,
( ~ iPr_def_14
| ( sk_c8 != iPr_def_19 )
| ( multiply(sk_c8,iPr_def_20) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3412,c_547]) ).
tcf(c_3887,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1187,c_980]) ).
tcf(c_3896,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1187,c_553]) ).
tcf(c_3938,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_546,c_97]) ).
tcf(c_3941,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_543,c_97]) ).
tcf(c_3943,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_3946,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1118,c_97]) ).
tcf(c_3947,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1119,c_97]) ).
tcf(c_3948,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1120,c_97]) ).
tcf(c_3949,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1121,c_97]) ).
tcf(c_3950,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1122,c_97]) ).
tcf(c_3951,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1123,c_97]) ).
tcf(c_3958,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3951,c_95]) ).
tcf(c_3959,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3950,c_95]) ).
tcf(c_3960,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3949,c_95]) ).
tcf(c_3961,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3948,c_95]) ).
tcf(c_3962,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3947,c_95]) ).
tcf(c_3963,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3946,c_95]) ).
tcf(c_4039,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_4040,plain,
( ( sk_c9 = iPr_def_23 )
| ( iPr_def_23 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_4039]) ).
tcf(c_4101,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1225,c_1152]) ).
tcf(c_4694,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2053,c_896]) ).
tcf(c_5535,plain,
multiply(iPr_def_23,iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_543,c_3958]) ).
tcf(c_5559,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_15,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5535,c_97]) ).
tcf(c_5561,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_553,c_3959]) ).
tcf(c_5614,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_25) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_3887,c_5561]) ).
tcf(c_5640,plain,
multiply(iPr_def_26,iPr_def_27) = sk_c10,
inference(superposition,[status(thm)],[c_555,c_3960]) ).
tcf(c_5648,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(iPr_def_23,iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_982,c_3958]) ).
tcf(c_5649,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_5648,c_5535]) ).
tcf(c_5698,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_23,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1040,c_3958]) ).
tcf(c_5699,plain,
( ( sk_c8 = iPr_def_16 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_5698,c_5535]) ).
tcf(c_5712,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_578,c_1052]) ).
tcf(c_5760,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_571,c_1054]) ).
tcf(c_5848,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_564,c_1056]) ).
tcf(c_5916,plain,
multiply(iPr_def_16,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_545,c_3961]) ).
tcf(c_5977,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5916,c_97]) ).
tcf(c_5979,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_548,c_3962]) ).
tcf(c_5982,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5979,c_97]) ).
tcf(c_5984,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c10,
inference(superposition,[status(thm)],[c_550,c_3963]) ).
tcf(c_5995,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_25) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_4101,c_5561]) ).
tcf(c_6111,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1076,c_3962]) ).
tcf(c_6112,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6111,c_5979]) ).
tcf(c_6232,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1095,c_3959]) ).
tcf(c_6233,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6232,c_5561]) ).
tcf(c_6248,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1096,c_3959]) ).
tcf(c_6249,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6248,c_5561]) ).
tcf(c_6356,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1098,c_3959]) ).
tcf(c_6357,plain,
( ( sk_c9 = iPr_def_20 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6356,c_5561]) ).
tcf(c_6440,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1149,c_3959]) ).
tcf(c_6441,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6440,c_5561]) ).
tcf(c_6452,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1185,c_3962]) ).
tcf(c_6453,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_6452,c_5979]) ).
tcf(c_6506,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1223,c_3959]) ).
tcf(c_6507,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6506,c_5561]) ).
tcf(c_6593,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1287,c_3959]) ).
tcf(c_6594,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_6593,c_5561]) ).
tcf(c_6605,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1318,c_3962]) ).
tcf(c_6606,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6605,c_5979]) ).
tcf(c_6697,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1395,c_3962]) ).
tcf(c_6698,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6697,c_5979]) ).
tcf(c_6875,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1453,c_3962]) ).
tcf(c_6876,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_6875,c_5979]) ).
tcf(c_6927,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1511,c_3962]) ).
tcf(c_6928,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6927,c_5979]) ).
tcf(c_7416,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1821,c_3960]) ).
tcf(c_7417,plain,
( ( sk_c10 = iPr_def_26 )
| ( sk_c10 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_7416,c_5640]) ).
tcf(c_7625,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1860,c_3960]) ).
tcf(c_7626,plain,
( ( sk_c9 = iPr_def_22 )
| ( sk_c10 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_7625,c_5640]) ).
tcf(c_7901,plain,
( ~ iPr_def_10
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c5,sk_c8) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_562]) ).
tcf(c_8601,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2059,c_3962]) ).
tcf(c_8602,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c9 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_8601,c_5979]) ).
tcf(c_8656,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2170,c_3959]) ).
tcf(c_8657,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_8656,c_5561]) ).
tcf(c_8668,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_2232,c_3960]) ).
tcf(c_8669,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c10 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_8668,c_5640]) ).
tcf(c_8699,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2289,c_3959]) ).
tcf(c_8700,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c9 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_8699,c_5561]) ).
tcf(c_8948,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_5712,c_5916]) ).
tcf(c_9003,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_8948,c_543]) ).
tcf(c_9421,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_5760,c_5916]) ).
tcf(c_10235,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5848,c_5916]) ).
tcf(c_10297,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_10235,c_566]) ).
tcf(c_11120,plain,
multiply(sk_c3,iPr_def_18) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_546,c_3941]) ).
tcf(c_12462,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_4039]) ).
tcf(c_12466,plain,
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != sk_c9 )
| ( sk_c8 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_12462]) ).
tcf(c_12801,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_15,sk_c7) = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9003,c_11120]) ).
tcf(c_12811,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_578,c_12801]) ).
tcf(c_12815,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c8,sk_c7) = multiply(iPr_def_23,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_12801,c_5559]) ).
tcf(c_12904,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c8,iPr_def_17) = multiply(iPr_def_23,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_12811,c_5559]) ).
tcf(c_13309,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3943,c_95]) ).
tcf(c_13318,plain,
multiply(inverse(sk_c5),iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_548,c_13309]) ).
tcf(c_13321,plain,
multiply(inverse(sk_c2),iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_553,c_13309]) ).
tcf(c_13322,plain,
multiply(inverse(sk_c3),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_543,c_13309]) ).
tcf(c_13323,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_13309]) ).
tcf(c_13324,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_13309]) ).
tcf(c_13420,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(inverse(sk_c3),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1517,c_13309]) ).
tcf(c_13421,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c3),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1459,c_13309]) ).
tcf(c_13440,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(inverse(sk_c2),iPr_def_25) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2170,c_13309]) ).
tcf(c_13456,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3963,c_13309]) ).
tcf(c_13457,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3962,c_13309]) ).
tcf(c_13458,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3961,c_13309]) ).
tcf(c_13459,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3960,c_13309]) ).
tcf(c_13460,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3959,c_13309]) ).
tcf(c_13519,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_13309,c_13309]) ).
tcf(c_13998,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c3,sk_c8) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_562]) ).
tcf(c_14001,plain,
! [X0: $i] :
( ( inverse(sk_c3) = sk_c8 )
| ( sk_c8 != X0 )
| ( inverse(sk_c3) != X0 ) ),
inference(instantiation,[status(thm)],[c_1124]) ).
tcf(c_14002,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( sk_c8 != sk_c9 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_14001]) ).
tcf(c_14167,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_13324,c_13519]) ).
tcf(c_14179,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_14167,c_5982]) ).
tcf(c_14183,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_14167,c_3938]) ).
tcf(c_14184,plain,
multiply(sk_c8,identity) = multiply(iPr_def_16,iPr_def_17),
inference(superposition,[status(thm)],[c_14167,c_5977]) ).
tcf(c_14187,plain,
multiply(sk_c8,identity) = multiply(iPr_def_23,iPr_def_15),
inference(superposition,[status(thm)],[c_14167,c_5559]) ).
tcf(c_14194,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_14167,c_13323]) ).
tcf(c_14195,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_14187,c_5535]) ).
tcf(c_14199,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_14183,c_546]) ).
tcf(c_14212,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_14194,c_96]) ).
tcf(c_14527,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2508,c_2507]) ).
tcf(c_17468,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_2842]) ).
tcf(c_17469,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_579,c_2842]) ).
tcf(c_17765,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_17468,c_6928,c_17468]) ).
tcf(c_17771,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_17469,c_6698,c_17469]) ).
tcf(c_18512,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_3011,c_3011,c_3003,c_6233,c_6357]) ).
tcf(c_18556,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_12
| ( iPr_def_19 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_600,c_18512]) ).
tcf(c_18563,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_12
| ( iPr_def_19 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_569,c_18512]) ).
tcf(c_18565,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_12
| ( iPr_def_18 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_565,c_18512]) ).
tcf(c_18783,plain,
multiply(sk_c4,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_13456,c_96]) ).
tcf(c_18790,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_13456,c_13309]) ).
tcf(c_18810,plain,
( ( identity = iPr_def_22 )
| ( sk_c9 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1272,c_18783]) ).
tcf(c_18836,plain,
multiply(sk_c4,sk_c10) = iPr_def_22,
inference(superposition,[status(thm)],[c_5984,c_18790]) ).
tcf(c_18849,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_18556,c_3003,c_6249,c_10297,c_18565]) ).
tcf(c_20205,plain,
( ( sk_c9 = iPr_def_15 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_18563,c_10297,c_18565]) ).
tcf(c_20211,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_23 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3003,c_20205]) ).
tcf(c_20781,plain,
multiply(sk_c5,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_13457,c_96]) ).
tcf(c_20785,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c5,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_13457,c_562]) ).
tcf(c_20788,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_13457,c_13309]) ).
tcf(c_20789,plain,
multiply(sk_c5,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_13457,c_14167]) ).
tcf(c_20797,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_20785,c_548]) ).
tcf(c_20828,plain,
inverse(iPr_def_19) = sk_c5,
inference(demodulation,[status(thm)],[c_20789,c_14167]) ).
tcf(c_20841,plain,
multiply(sk_c5,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_5979,c_20788]) ).
tcf(c_22737,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_16)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c6,sk_c8)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_13458,c_557]) ).
tcf(c_22741,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_13458,c_13309]) ).
tcf(c_22742,plain,
multiply(sk_c6,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_13458,c_14167]) ).
tcf(c_22885,plain,
inverse(iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_22742,c_14167]) ).
tcf(c_22894,plain,
multiply(sk_c6,sk_c8) = iPr_def_17,
inference(superposition,[status(thm)],[c_5916,c_22741]) ).
tcf(c_26550,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_3148,c_3152,c_3148,c_7417,c_8669]) ).
tcf(c_26552,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_26550,c_3152,c_7626,c_8700,c_26550]) ).
tcf(c_26554,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_556,c_26552]) ).
tcf(c_26770,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_3280,c_3288,c_3280,c_6112,c_6357]) ).
tcf(c_26794,plain,
( ( sk_c9 = iPr_def_27 )
| ~ iPr_def_10
| ( iPr_def_19 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_601,c_26770]) ).
tcf(c_26801,plain,
( ( sk_c9 = iPr_def_24 )
| ~ iPr_def_10
| ( iPr_def_19 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_580,c_26770]) ).
tcf(c_26803,plain,
( ( sk_c9 = iPr_def_23 )
| ~ iPr_def_10
| ( iPr_def_19 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_573,c_26770]) ).
tcf(c_26877,plain,
( ( sk_c9 = iPr_def_27 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_26794,c_3288,c_8602,c_8657]) ).
tcf(c_27017,plain,
multiply(sk_c1,iPr_def_26) = identity,
inference(superposition,[status(thm)],[c_13459,c_96]) ).
tcf(c_27040,plain,
( ( identity = iPr_def_27 )
| ( sk_c9 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1782,c_27017]) ).
tcf(c_27041,plain,
( ( identity = iPr_def_27 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1743,c_27017]) ).
tcf(c_27042,plain,
( ( identity = iPr_def_27 )
| ( sk_c9 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1704,c_27017]) ).
tcf(c_27043,plain,
( ( identity = iPr_def_27 )
| ( sk_c8 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1655,c_27017]) ).
tcf(c_27061,plain,
! [X0: $i] :
( ( X0 = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1583]) ).
tcf(c_27062,plain,
( ( sk_c9 = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( sk_c9 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_27061]) ).
tcf(c_27085,plain,
( ( sk_c9 = iPr_def_24 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_26801,c_3288,c_6453,c_6507]) ).
tcf(c_27093,plain,
( ( sk_c9 = iPr_def_23 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_26803,c_3288,c_5649,c_6233]) ).
tcf(c_27498,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c5) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1380]) ).
tcf(c_28368,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_27042,c_27040]) ).
tcf(c_28577,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_27043,c_27041]) ).
tcf(c_29431,plain,
multiply(sk_c2,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_13460,c_96]) ).
tcf(c_29434,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_24)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c2,sk_c8)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_13460,c_557]) ).
tcf(c_29437,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_24)) != sk_c9 )
| ( multiply(sk_c2,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_13460,c_558]) ).
tcf(c_29438,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_13460,c_13309]) ).
tcf(c_29439,plain,
multiply(sk_c2,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_13460,c_14167]) ).
tcf(c_29480,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( inverse(inverse(iPr_def_24)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_29437,c_553]) ).
tcf(c_29498,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_3896,c_29431]) ).
tcf(c_29500,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1223,c_29431]) ).
tcf(c_29501,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1149,c_29431]) ).
tcf(c_29843,plain,
inverse(iPr_def_24) = sk_c2,
inference(demodulation,[status(thm)],[c_29439,c_14167]) ).
tcf(c_29895,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1122,c_29438]) ).
tcf(c_29896,plain,
multiply(sk_c2,sk_c9) = iPr_def_25,
inference(superposition,[status(thm)],[c_5561,c_29438]) ).
tcf(c_31056,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( iPr_def_16 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_29498,c_28577]) ).
tcf(c_31703,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( identity = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_29501,c_29500]) ).
tcf(c_32390,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_31056,c_4694]) ).
tcf(c_32996,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_31703,c_28368]) ).
tcf(c_35774,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_15) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_32390,c_5614]) ).
tcf(c_35799,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_35774,c_5535]) ).
tcf(c_37891,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_32996,c_14527]) ).
tcf(c_44617,plain,
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2821,c_14194]) ).
tcf(c_44639,plain,
( ( sk_c9 = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_18 )
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_8948,c_44617]) ).
tcf(c_44851,plain,
( ~ iPr_def_12
| ( sk_c9 != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_2985,c_611,c_573,c_4040,c_18512,c_20211,c_27062]) ).
tcf(c_44868,plain,
( ( sk_c9 = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c9 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_9421,c_44851]) ).
tcf(c_44878,plain,
( ( sk_c9 = iPr_def_27 )
| ~ iPr_def_12
| ( sk_c9 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_598,c_44851]) ).
tcf(c_45119,plain,
~ iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_44878,c_18849,c_20211,c_44868]) ).
tcf(c_45121,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_26554,c_45119]) ).
tcf(c_45913,plain,
( ~ iPr_def_10
| ( sk_c9 != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_3262,c_135,c_547,c_551,c_573,c_1210,c_1364,c_1768,c_1769,c_1846,c_1847,c_1960,c_2439,c_7901,c_12466,c_13998,c_14002,c_26770,c_27093,c_27498]) ).
tcf(c_45941,plain,
( ( sk_c9 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_590,c_45913]) ).
tcf(c_45942,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_588,c_45913]) ).
tcf(c_45943,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_587,c_45913]) ).
tcf(c_45976,plain,
( ( sk_c9 != iPr_def_25 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_45941,c_3288,c_45943,c_45942]) ).
tcf(c_45977,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(renaming,[status(thm)],[c_45976]) ).
tcf(c_46788,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(sk_c5,sk_c9) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_35799,c_548]) ).
tcf(c_47017,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_15) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_37891,c_5995]) ).
tcf(c_47874,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(inverse(sk_c5),iPr_def_20) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_46788,c_13309]) ).
tcf(c_49024,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_47874,c_47017,c_45977,c_45121,c_44639,c_44617,c_29896,c_29895,c_29843,c_29480,c_29434,c_29431,c_27085,c_27041,c_27040,c_27017,c_26877,c_22894,c_22885,c_22737,c_20841,c_20828,c_20797,c_20781,c_18836,c_18810,c_18783,c_17771,c_17765,c_14199,c_14195,c_14187,c_14184,c_14183,c_14179,c_13440,c_13421,c_13420,c_13322,c_13321,c_13318,c_12904,c_12815,c_8602,c_6876,c_6606,c_6594,c_6453,c_6441,c_5699,c_5649,c_3441,c_3288,c_14212,c_2842,c_2822,c_1782,c_1743,c_1375,c_569,c_568,c_567,c_566,c_565,c_564,c_563,c_552,c_551,c_547,c_544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Wed Sep 23 14:18:33 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 0.13/0.45
% 0.13/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.45
% 0.13/0.45 % Detected problem language: tptp
% 0.18/0.46 % Proving...
% 18.68/3.33 % SZS status Started for theBenchmark.p
% 18.68/3.33 % SZS status Unsatisfiable for theBenchmark.p
% 18.68/3.33
% 18.68/3.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.68/3.33
% 18.68/3.33 % ------ iProver source info
% 18.68/3.33
% 18.68/3.33 % git: date: 2026-07-19 20:42:38 +0200
% 18.68/3.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.68/3.33 % git: non_committed_changes: false
% 18.68/3.33
% 18.68/3.33 % ------ Parsing...% successful
% 18.68/3.33
% 18.68/3.33
% 18.68/3.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.68/3.33
% 18.68/3.33 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 18.68/3.33
% 18.68/3.33 % ------ Preprocessing... gs_s sp: 6 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.68/3.33
% 18.68/3.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 18.68/3.33 % ------ Proving...
% 18.68/3.33 % ------ Problem Properties
% 18.68/3.33
% 18.68/3.33 %
% 18.68/3.33 % clauses 64
% 18.68/3.33 % conjectures 48
% 18.68/3.33 % EPR 43
% 18.68/3.33 % Horn 21
% 18.68/3.33 % unary 16
% 18.68/3.33 % binary 42
% 18.68/3.33 % lits 120
% 18.68/3.33 % lits eq 110
% 18.68/3.33 % fd_pure 0
% 18.68/3.33 % fd_pseudo 0
% 18.68/3.33 % fd_cond 0
% 18.68/3.33 % fd_pseudo_cond 0
% 18.68/3.33 % AC symbols 0
% 18.68/3.33
% 18.68/3.33 % ------ Schedule dynamic 5 is on
% 18.68/3.33
% 18.68/3.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.68/3.33
% 18.68/3.33
% 18.68/3.33 % ------
% 18.68/3.33 % Current options:
% 18.68/3.33 % ------
% 18.68/3.33
% 18.68/3.33
% 18.68/3.33 %
% 18.68/3.33
% 18.68/3.33 % ------ Proving...
% 18.68/3.33 %
% 18.68/3.33
% 18.68/3.33 % SZS status Unsatisfiable for theBenchmark.p
% 18.68/3.33
% 18.68/3.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.68/3.34
% 18.68/3.34
%------------------------------------------------------------------------------