%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP241-1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:26 PM UTC 2026
% Result : Unsatisfiable 10.68s 7.73s
% Output : CNFRefutation 10.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 48
% Syntax : Number of formulae : 402 ( 100 unt; 12 def)
% Number of atoms : 1503 ( 750 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 605 ( 182 ~; 423 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 0 ?; 56 :)
% 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,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = inverse(sk_c4)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c5)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f63,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f67]) ).
fof(f73,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != inverse(X2)
| multiply(X2,sk_c8) != X1
| sk_c7 != multiply(sk_c8,X1)
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| sk_c8 != inverse(sk_c7)
| inverse(sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f75]) ).
fof(f77,plain,
! [X2,X3,X0,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| sk_c8 != inverse(sk_c7)
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f76]) ).
fof(f78,plain,
! [X2,X3,X0,X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| sk_c8 != inverse(sk_c7)
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f77]) ).
tcf(c_88,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_126,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c7) != sk_c8 )
| ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(sk_c8,multiply(X3,sk_c8)) != sk_c7 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_459,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_126]) ).
tcf(c_460,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_126]) ).
tcf(c_461,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_126]) ).
tcf(c_462,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c8 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_126]) ).
tcf(c_463,definition,
iPr_def_13 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_464,definition,
iPr_def_14 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_465,definition,
iPr_def_15 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_466,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_467,definition,
iPr_def_17 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_468,definition,
iPr_def_18 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_469,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_470,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_471,definition,
iPr_def_21 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_472,definition,
iPr_def_22 = multiply(sk_c8,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_473,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_474,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_475,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c8 )
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_462,c_464,c_463]) ).
tcf(c_477,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_461]) ).
tcf(c_478,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_460]) ).
tcf(c_479,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_459]) ).
tcf(c_480,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_125,c_466,c_465]) ).
tcf(c_483,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122,c_469]) ).
tcf(c_484,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_121,c_470]) ).
tcf(c_485,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_120,c_471]) ).
tcf(c_488,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_489,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_490,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_472]) ).
tcf(c_492,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_493,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_494,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_473]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_500,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_474]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_503,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_504,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_505,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_508,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_515,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_516,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_521,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_515]) ).
tcf(c_766,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_484,c_483]) ).
tcf(c_831,plain,
( ( sk_c8 = iPr_def_15 )
| ( inverse(iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_490,c_464]) ).
tcf(c_893,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_495,c_490]) ).
tcf(c_912,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_495,c_469]) ).
tcf(c_941,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c3) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_480,c_472]) ).
tcf(c_942,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_489,c_472]) ).
tcf(c_943,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_488,c_472]) ).
tcf(c_984,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_516]) ).
tcf(c_989,plain,
multiply(iPr_def_13,sk_c8) = identity,
inference(superposition,[status(thm)],[c_463,c_89]) ).
tcf(c_990,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_470,c_89]) ).
tcf(c_991,plain,
multiply(iPr_def_15,sk_c5) = identity,
inference(superposition,[status(thm)],[c_465,c_89]) ).
tcf(c_992,plain,
multiply(iPr_def_14,sk_c7) = identity,
inference(superposition,[status(thm)],[c_464,c_89]) ).
tcf(c_993,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_473,c_89]) ).
tcf(c_994,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_466,c_89]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_516]) ).
tcf(c_1001,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c7 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1000]) ).
tcf(c_1040,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1000]) ).
tcf(c_1049,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c8,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_496,c_468]) ).
tcf(c_1103,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_498,c_474]) ).
tcf(c_1106,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_498,c_493]) ).
tcf(c_1153,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_499,c_474]) ).
tcf(c_1155,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_499,c_494]) ).
tcf(c_1159,plain,
( ( sk_c8 = iPr_def_20 )
| ( inverse(iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_499,c_464]) ).
tcf(c_1195,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_500,c_471]) ).
tcf(c_1201,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_500,c_480]) ).
tcf(c_1317,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_503,c_471]) ).
tcf(c_1374,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_504,c_471]) ).
tcf(c_1377,plain,
( ( sk_c8 = iPr_def_20 )
| ( inverse(iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_504,c_463]) ).
tcf(c_1432,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_505,c_471]) ).
tcf(c_1433,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,sk_c6) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_505,c_468]) ).
tcf(c_1523,plain,
( ( sk_c8 = iPr_def_14 )
| ( inverse(iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_507,c_464]) ).
tcf(c_1600,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_508,c_471]) ).
tcf(c_1664,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_509,c_508]) ).
tcf(c_1671,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_509,c_471]) ).
tcf(c_1837,plain,
( ( sk_c8 = iPr_def_15 )
| ( inverse(iPr_def_16) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_480,c_463]) ).
tcf(c_1873,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c8,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_511,c_468]) ).
tcf(c_1894,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_512,c_474]) ).
tcf(c_2096,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_514,c_469]) ).
tcf(c_2194,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_20 )
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_514,c_475]) ).
tcf(c_2195,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_513,c_475]) ).
tcf(c_2197,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_15 )
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_510,c_475]) ).
tcf(c_2333,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_474,c_478]) ).
tcf(c_2336,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_992,c_478]) ).
tcf(c_2358,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_23 )
| ( sk_c8 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2333,c_473]) ).
tcf(c_2530,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_469,c_479]) ).
tcf(c_2531,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_474,c_479]) ).
tcf(c_2556,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2531,c_473]) ).
tcf(c_2560,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2530,c_470]) ).
tcf(c_2707,plain,
( ~ iPr_def_12
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_467,c_477]) ).
tcf(c_2731,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_15 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2707,c_465]) ).
tcf(c_2852,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_89,c_90]) ).
tcf(c_2854,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_989,c_90]) ).
tcf(c_2855,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_990,c_90]) ).
tcf(c_2856,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_991,c_90]) ).
tcf(c_2857,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_992,c_90]) ).
tcf(c_2858,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_993,c_90]) ).
tcf(c_2859,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_994,c_90]) ).
tcf(c_2864,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2859,c_88]) ).
tcf(c_2865,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2858,c_88]) ).
tcf(c_2866,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2857,c_88]) ).
tcf(c_2867,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2856,c_88]) ).
tcf(c_2868,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2855,c_88]) ).
tcf(c_2869,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2854,c_88]) ).
tcf(c_2900,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_13 )
| ( X0 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_984]) ).
tcf(c_2901,plain,
( ( sk_c7 = sk_c8 )
| ( sk_c7 != iPr_def_13 )
| ( sk_c8 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_2900]) ).
tcf(c_2967,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_766,c_504]) ).
tcf(c_2968,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_766,c_503]) ).
tcf(c_3316,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1106,c_893]) ).
tcf(c_3420,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1155,c_893]) ).
tcf(c_3531,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_20 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1201,c_484]) ).
tcf(c_3793,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1664,c_766]) ).
tcf(c_4891,plain,
multiply(iPr_def_16,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_471,c_2864]) ).
tcf(c_4952,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_474,c_2865]) ).
tcf(c_4966,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_14,multiply(iPr_def_23,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_497,c_2866]) ).
tcf(c_5070,plain,
multiply(iPr_def_15,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_467,c_2867]) ).
tcf(c_5075,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_469,c_2868]) ).
tcf(c_5132,plain,
multiply(iPr_def_13,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_468,c_2869]) ).
tcf(c_6094,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_912,c_2868]) ).
tcf(c_6095,plain,
( ( sk_c7 = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6094,c_5075]) ).
tcf(c_6454,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_485,c_941]) ).
tcf(c_6456,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6454,c_4891]) ).
tcf(c_6496,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_24,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_504,c_942]) ).
tcf(c_6590,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_24,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_503,c_943]) ).
tcf(c_6874,plain,
( ( sk_c8 = iPr_def_15 )
| ( inverse(iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6456,c_463]) ).
tcf(c_8119,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_6874,c_831]) ).
tcf(c_8931,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1103,c_2865]) ).
tcf(c_8932,plain,
( ( sk_c7 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_8931,c_4952]) ).
tcf(c_9099,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1153,c_2865]) ).
tcf(c_9100,plain,
( ( sk_c7 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_9099,c_4952]) ).
tcf(c_9172,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1195,c_2864]) ).
tcf(c_9173,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_9172,c_4891]) ).
tcf(c_9604,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1317,c_2864]) ).
tcf(c_9605,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_9604,c_4891]) ).
tcf(c_9700,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1374,c_2864]) ).
tcf(c_9701,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_9700,c_4891]) ).
tcf(c_9776,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1432,c_2864]) ).
tcf(c_9777,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_9776,c_4891]) ).
tcf(c_10017,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_506,c_1433]) ).
tcf(c_10023,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_10017,c_5070]) ).
tcf(c_10157,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1600,c_2864]) ).
tcf(c_10158,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_10157,c_4891]) ).
tcf(c_10243,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10023,c_505]) ).
tcf(c_10252,plain,
( ( sk_c8 = iPr_def_14 )
| ( inverse(iPr_def_18) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10023,c_463]) ).
tcf(c_11129,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( inverse(iPr_def_14) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_10243,c_463]) ).
tcf(c_12077,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1671,c_2864]) ).
tcf(c_12078,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_12077,c_4891]) ).
tcf(c_12130,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10252,c_1523]) ).
tcf(c_12301,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( iPr_def_13 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_12130,c_8119]) ).
tcf(c_12793,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1894,c_2865]) ).
tcf(c_12794,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_12793,c_4952]) ).
tcf(c_15085,plain,
( iPr_def_12
| ( sk_c8 = iPr_def_20 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2194,c_2194,c_2358,c_9100,c_9701,c_12078]) ).
tcf(c_15086,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c8 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_15085]) ).
tcf(c_15093,plain,
( iPr_def_12
| ( sk_c8 = iPr_def_19 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2195,c_2195,c_2358,c_8932,c_9605,c_10158]) ).
tcf(c_15094,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c8 = iPr_def_19 ) ),
inference(renaming,[status(thm)],[c_15093]) ).
tcf(c_15165,plain,
( iPr_def_12
| ( sk_c8 = iPr_def_15 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2197,c_2197,c_2358,c_6095,c_9173,c_9777]) ).
tcf(c_15166,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c8 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_15165]) ).
tcf(c_15581,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2968,c_2967]) ).
tcf(c_15800,plain,
! [X0: $i] :
( ( multiply(X0,iPr_def_17) = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( multiply(X0,iPr_def_17) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1040]) ).
tcf(c_15803,plain,
( ( multiply(sk_c8,iPr_def_17) = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( multiply(sk_c8,iPr_def_17) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_15800]) ).
tcf(c_15861,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2852,c_88]) ).
tcf(c_15924,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_88,c_15861]) ).
tcf(c_15925,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_89,c_15861]) ).
tcf(c_16098,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2869,c_15861]) ).
tcf(c_16099,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2868,c_15861]) ).
tcf(c_16101,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2866,c_15861]) ).
tcf(c_16102,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2865,c_15861]) ).
tcf(c_16136,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_15861,c_15861]) ).
tcf(c_16747,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_15925,c_16136]) ).
tcf(c_16767,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_16747,c_15924]) ).
tcf(c_17723,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_20 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3531,c_504]) ).
tcf(c_17724,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_20 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_3531,c_503]) ).
tcf(c_19344,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_13,X0)) = X0,
inference(superposition,[status(thm)],[c_16098,c_15861]) ).
tcf(c_19345,plain,
multiply(sk_c8,identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_16098,c_16747]) ).
tcf(c_19902,plain,
inverse(iPr_def_13) = sk_c8,
inference(demodulation,[status(thm)],[c_19345,c_16747]) ).
tcf(c_19989,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(iPr_def_13) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_19344,c_477]) ).
tcf(c_20093,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_19989,c_19902]) ).
tcf(c_21732,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_514,c_20093]) ).
tcf(c_21735,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_510,c_20093]) ).
tcf(c_21738,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_499,c_20093]) ).
tcf(c_21739,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_498,c_20093]) ).
tcf(c_21741,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_495,c_20093]) ).
tcf(c_21745,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_490,c_20093]) ).
tcf(c_21846,plain,
( ( sk_c8 != iPr_def_13 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_21732,c_521,c_1001,c_1873,c_2731,c_2901,c_12794,c_15803,c_20093,c_21735]) ).
tcf(c_21847,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_13 ) ),
inference(renaming,[status(thm)],[c_21846]) ).
tcf(c_21898,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_12
| ( iPr_def_13 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_504,c_21847]) ).
tcf(c_22191,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 != iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_21738,c_2556,c_9701,c_15086,c_21738]) ).
tcf(c_22222,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_15 )
| ( iPr_def_22 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_6456,c_22191]) ).
tcf(c_22545,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 != iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_21739,c_2556,c_9605,c_15094,c_21739]) ).
tcf(c_22574,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 )
| ( iPr_def_22 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_6456,c_22545]) ).
tcf(c_22966,plain,
sk_c8 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_21741,c_893,c_2560,c_6456,c_15166,c_21745,c_22222,c_22574]) ).
tcf(c_22970,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_22545,c_22966]) ).
tcf(c_22972,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_15 != iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_22191,c_22966]) ).
tcf(c_22975,plain,
( ~ iPr_def_12
| ( iPr_def_13 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_21847,c_22966]) ).
tcf(c_23006,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_15 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_15086,c_22966]) ).
tcf(c_23015,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( multiply(iPr_def_24,iPr_def_21) = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_6590,c_22966]) ).
tcf(c_23016,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( multiply(iPr_def_24,iPr_def_21) = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_6496,c_22966]) ).
tcf(c_23019,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_13) = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_2096,c_22966]) ).
tcf(c_23048,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_10023,c_22966]) ).
tcf(c_23093,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1049,c_22966]) ).
tcf(c_23143,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( inverse(iPr_def_24) = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_1377,c_22966]) ).
tcf(c_23147,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( inverse(iPr_def_23) = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_1159,c_22966]) ).
tcf(c_23159,plain,
multiply(iPr_def_15,iPr_def_17) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5070,c_22966]) ).
tcf(c_23160,plain,
multiply(iPr_def_16,iPr_def_21) = iPr_def_15,
inference(demodulation,[status(thm)],[c_4891,c_22966]) ).
tcf(c_23174,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c7 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_475,c_22966]) ).
tcf(c_23185,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_502,c_22966]) ).
tcf(c_23186,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c6 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_501,c_22966]) ).
tcf(c_23190,plain,
multiply(iPr_def_13,iPr_def_15) = identity,
inference(demodulation,[status(thm)],[c_989,c_22966]) ).
tcf(c_23201,plain,
inverse(iPr_def_15) = iPr_def_13,
inference(demodulation,[status(thm)],[c_463,c_22966]) ).
tcf(c_23688,plain,
multiply(inverse(iPr_def_15),iPr_def_15) = iPr_def_17,
inference(superposition,[status(thm)],[c_23159,c_15861]) ).
tcf(c_23690,plain,
identity = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_23688,c_23190,c_23201]) ).
tcf(c_23694,plain,
inverse(iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_16767,c_23690]) ).
tcf(c_23695,plain,
! [X0: $i] : multiply(X0,iPr_def_17) = X0,
inference(demodulation,[status(thm)],[c_16747,c_23690]) ).
tcf(c_23712,plain,
multiply(iPr_def_14,sk_c7) = iPr_def_17,
inference(demodulation,[status(thm)],[c_992,c_23690]) ).
tcf(c_23715,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_17,
inference(demodulation,[status(thm)],[c_89,c_23690]) ).
tcf(c_24659,plain,
( ( iPr_def_15 = iPr_def_20 )
| ~ iPr_def_12
| ( iPr_def_13 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_21898,c_22966]) ).
tcf(c_24762,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_3316,c_22970]) ).
tcf(c_24834,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_15 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_3420,c_22972]) ).
tcf(c_25145,plain,
multiply(sk_c4,iPr_def_17) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_16099,c_23695]) ).
tcf(c_25200,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_4952,c_4966]) ).
tcf(c_25210,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_25200,c_23712]) ).
tcf(c_25336,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_25145,c_23695]) ).
tcf(c_25981,plain,
multiply(sk_c7,iPr_def_17) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_16101,c_23695]) ).
tcf(c_26054,plain,
inverse(iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_25981,c_23695]) ).
tcf(c_26057,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_11129,c_26054]) ).
tcf(c_26909,plain,
multiply(sk_c1,iPr_def_23) = iPr_def_17,
inference(superposition,[status(thm)],[c_16102,c_23715]) ).
tcf(c_26913,plain,
multiply(sk_c1,iPr_def_17) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_16102,c_23695]) ).
tcf(c_27122,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_26913,c_23695]) ).
tcf(c_27125,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c1 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_23147,c_27122]) ).
tcf(c_27766,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_27125,c_474]) ).
tcf(c_27769,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_27766,c_23712]) ).
tcf(c_28109,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( inverse(iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_27769,c_23143]) ).
tcf(c_28114,plain,
( ( iPr_def_15 = iPr_def_20 )
| ~ iPr_def_12
| ( iPr_def_13 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_27769,c_24659]) ).
tcf(c_28127,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_28109,c_23694]) ).
tcf(c_29044,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_17723,c_2560,c_17724,c_17723,c_23006,c_28127,c_28114]) ).
tcf(c_29188,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_29044,c_23016]) ).
tcf(c_29201,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_29188,c_23160]) ).
tcf(c_29329,plain,
sk_c8 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_1837,c_893,c_2560,c_6456,c_15166,c_21745,c_22222,c_22574]) ).
tcf(c_29349,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c7 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_514,c_29329]) ).
tcf(c_29444,plain,
iPr_def_15 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_29349,c_24834,c_29201]) ).
tcf(c_30236,plain,
iPr_def_15 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_23019,c_29444]) ).
tcf(c_30256,plain,
inverse(iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_25336,c_30236]) ).
tcf(c_30277,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_15581,c_30236]) ).
tcf(c_30299,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_3793,c_30236]) ).
tcf(c_30304,plain,
sk_c4 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_30256,c_23201]) ).
tcf(c_30325,plain,
multiply(iPr_def_13,sk_c7) = iPr_def_19,
inference(demodulation,[status(thm)],[c_469,c_30304]) ).
tcf(c_31389,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_30277,c_23015]) ).
tcf(c_31411,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_31389,c_23160]) ).
tcf(c_31422,plain,
iPr_def_15 = iPr_def_19,
inference(global_subsumption_just,[status(thm)],[c_30299,c_24762,c_31411]) ).
tcf(c_31430,plain,
multiply(iPr_def_13,sk_c7) = iPr_def_15,
inference(demodulation,[status(thm)],[c_30325,c_31422]) ).
tcf(c_31495,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( multiply(iPr_def_13,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_25210,c_31430]) ).
tcf(c_31497,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(iPr_def_13,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_23185,c_31430]) ).
tcf(c_31522,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_31497,c_5132]) ).
tcf(c_31528,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_31495,c_5132]) ).
tcf(c_31980,plain,
( ~ iPr_def_11
| ( sk_c8 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2336,c_26054]) ).
tcf(c_31981,plain,
( ~ iPr_def_11
| ( iPr_def_15 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_31980,c_22966,c_23690]) ).
tcf(c_32150,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_26057,c_23174]) ).
tcf(c_32517,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_31522,c_23186]) ).
tcf(c_33691,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_31528,c_496]) ).
tcf(c_33936,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_33691,c_474]) ).
tcf(c_33949,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_33936,c_26909]) ).
tcf(c_34936,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c7 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_23093,c_23695]) ).
tcf(c_34991,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_18 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_34936,c_492]) ).
tcf(c_35117,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_493,c_29329]) ).
tcf(c_35125,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( inverse(iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_35117,c_464]) ).
tcf(c_35129,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_494,c_29329]) ).
tcf(c_35173,plain,
iPr_def_15 = iPr_def_19,
inference(global_subsumption_just,[status(thm)],[c_35125,c_24762,c_31411]) ).
tcf(c_35175,plain,
multiply(sk_c4,sk_c7) = iPr_def_15,
inference(demodulation,[status(thm)],[c_469,c_35173]) ).
tcf(c_35214,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c7 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_499,c_29329]) ).
tcf(c_35224,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_35214,c_35129]) ).
tcf(c_35275,plain,
iPr_def_15 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_35224,c_24834,c_29201]) ).
tcf(c_35280,plain,
inverse(sk_c4) = iPr_def_15,
inference(demodulation,[status(thm)],[c_470,c_35275]) ).
tcf(c_35595,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != iPr_def_15 )
| ( multiply(X0,sk_c7) != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_479,c_29329]) ).
tcf(c_35605,plain,
( ~ iPr_def_10
| ( inverse(sk_c4) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_35175,c_35595]) ).
tcf(c_35616,plain,
~ iPr_def_10,
inference(ground_joinability,[status(thm)],[c_35605,c_35280]) ).
tcf(c_38714,plain,
iPr_def_15 = iPr_def_17,
inference(superposition,[status(thm)],[c_33949,c_32517]) ).
tcf(c_38721,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_31981,c_38714]) ).
tcf(c_38739,plain,
inverse(iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_23694,c_38714]) ).
tcf(c_38754,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c7 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_23174,c_38721]) ).
tcf(c_38765,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_38739,c_23201]) ).
tcf(c_38766,plain,
~ iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_22975,c_38765]) ).
tcf(c_38826,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_12301,c_38765]) ).
tcf(c_38827,plain,
( iPr_def_10
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c7 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_38754,c_38766]) ).
tcf(c_38965,plain,
iPr_def_15 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_34991,c_23048,c_32150,c_35616,c_38766,c_38721]) ).
tcf(c_38967,plain,
iPr_def_13 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_38965,c_38765]) ).
tcf(c_38976,plain,
sk_c7 = iPr_def_13,
inference(demodulation,[status(thm)],[c_512,c_38967]) ).
tcf(c_41675,plain,
iPr_def_14 != iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_38827,c_35616,c_38827,c_38976]) ).
tcf(c_41677,plain,
$false,
inference(ground_joinability,[status(thm)],[c_41675,c_38765,c_38826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP241-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.36 % Computer : n003.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 14:16:40 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.40 Running first-order theorem proving
% 0.11/5.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.41
% 0.11/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.41
% 0.11/5.41 % Detected problem language: tptp
% 0.11/5.43 % Proving...
% 10.68/7.73 % SZS status Started for theBenchmark.p
% 10.68/7.73 % SZS status Unsatisfiable for theBenchmark.p
% 10.68/7.73
% 10.68/7.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.68/7.73
% 10.68/7.73 % ------ iProver source info
% 10.68/7.73
% 10.68/7.73 % git: date: 2026-07-19 20:42:38 +0200
% 10.68/7.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.68/7.73 % git: non_committed_changes: false
% 10.68/7.73
% 10.68/7.73 % ------ Parsing...% successful
% 10.68/7.73
% 10.68/7.73
% 10.68/7.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.68/7.73
% 10.68/7.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.68/7.73
% 10.68/7.73 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.68/7.73
% 10.68/7.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.68/7.73 % ------ Proving...
% 10.68/7.73 % ------ Problem Properties
% 10.68/7.73
% 10.68/7.73 %
% 10.68/7.73 % clauses 54
% 10.68/7.73 % conjectures 39
% 10.68/7.73 % EPR 36
% 10.68/7.73 % Horn 18
% 10.68/7.73 % unary 15
% 10.68/7.73 % binary 35
% 10.68/7.73 % lits 99
% 10.68/7.73 % lits eq 93
% 10.68/7.73 % fd_pure 0
% 10.68/7.73 % fd_pseudo 0
% 10.68/7.73 % fd_cond 0
% 10.68/7.73 % fd_pseudo_cond 0
% 10.68/7.73 % AC symbols 0
% 10.68/7.73
% 10.68/7.73 % ------ Schedule dynamic 5 is on
% 10.68/7.73
% 10.68/7.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.68/7.73
% 10.68/7.73
% 10.68/7.73 % ------
% 10.68/7.73 % Current options:
% 10.68/7.73 % ------
% 10.68/7.73
% 10.68/7.73
% 10.68/7.73 %
% 10.68/7.73
% 10.68/7.73 % ------ Proving...
% 10.68/7.73 %
% 10.68/7.73
% 10.68/7.73 % SZS status Unsatisfiable for theBenchmark.p
% 10.68/7.73
% 10.68/7.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.68/7.74
% 10.68/7.74
%------------------------------------------------------------------------------