%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP308-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.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 01:32:47 PM UTC 2026
% Result : Unsatisfiable 10.56s 22.32s
% Output : CNFRefutation 10.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 54
% Syntax : Number of formulae : 398 ( 109 unt; 12 def)
% Number of atoms : 1371 ( 742 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 526 ( 147 ~; 379 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = inverse(sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c4)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c4)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c5)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0
| sk_c7 != multiply(sk_c8,X0)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X1,X4] :
( sk_c6 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f78]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_109,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_121,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c6,sk_c7) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X3,sk_c8) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_474,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_477,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_478,definition,
iPr_def_14 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,definition,
iPr_def_15 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_483,definition,
iPr_def_19 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_484,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,definition,
iPr_def_25 = multiply(sk_c8,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_490,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c6 )
| ( iPr_def_15 != sk_c8 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_477,c_480,c_479,c_478]) ).
tcf(c_491,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_492,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_474]) ).
tcf(c_494,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_127,c_482,c_481]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_126,c_483]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_125,c_484]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_124,c_485]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_123,c_486]) ).
tcf(c_500,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122,c_487]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_24 = sk_c2 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_121,c_488]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_24 = sk_c2 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_503,negated_conjecture,
( ( iPr_def_24 = sk_c2 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_504,negated_conjecture,
( ( iPr_def_24 = sk_c2 )
| ( iPr_def_21 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_505,negated_conjecture,
( ( iPr_def_24 = sk_c2 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_24 = sk_c2 )
| ( iPr_def_23 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_489]) ).
tcf(c_508,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_21 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_23 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_520,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_521,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_522,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_523,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_524,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_527,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_528,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_530,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_531,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_793,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_498,c_495]) ).
tcf(c_806,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_497,c_500]) ).
tcf(c_905,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c6,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_509,c_479]) ).
tcf(c_927,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_510,c_508]) ).
tcf(c_928,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c7 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_510,c_507]) ).
tcf(c_940,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_497,c_485]) ).
tcf(c_947,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_499,c_487]) ).
tcf(c_974,plain,
multiply(iPr_def_22,sk_c3) = identity,
inference(superposition,[status(thm)],[c_486,c_90]) ).
tcf(c_975,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_484,c_90]) ).
tcf(c_976,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_483,c_90]) ).
tcf(c_977,plain,
multiply(iPr_def_16,sk_c8) = identity,
inference(superposition,[status(thm)],[c_480,c_90]) ).
tcf(c_978,plain,
multiply(iPr_def_18,sk_c1) = identity,
inference(superposition,[status(thm)],[c_482,c_90]) ).
tcf(c_989,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c6,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_511,c_479]) ).
tcf(c_1005,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1016,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c6,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_512,c_479]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1074,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_514,c_479]) ).
tcf(c_1091,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_515,c_485]) ).
tcf(c_1124,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_516,c_513]) ).
tcf(c_1146,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_517,c_487]) ).
tcf(c_1149,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_517,c_478]) ).
tcf(c_1180,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1041]) ).
tcf(c_1193,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_518,c_515]) ).
tcf(c_1218,plain,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c6 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1005]) ).
tcf(c_1293,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_520,c_479]) ).
tcf(c_1412,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_522,c_520]) ).
tcf(c_1413,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_522,c_519]) ).
tcf(c_1713,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_526,c_479]) ).
tcf(c_1794,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_527,c_521]) ).
tcf(c_1863,plain,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_16 != iPr_def_16 )
| ( sk_c6 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1180]) ).
tcf(c_1864,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1865,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1889,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_528,c_526]) ).
tcf(c_1890,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_528,c_525]) ).
tcf(c_1982,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_529,c_523]) ).
tcf(c_2144,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_530,c_524]) ).
tcf(c_2315,plain,
( ~ iPr_def_11
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_89,c_493]) ).
tcf(c_2317,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(iPr_def_16) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_977,c_493]) ).
tcf(c_2626,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_478,c_91]) ).
tcf(c_2627,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_487,c_91]) ).
tcf(c_2629,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_481,c_91]) ).
tcf(c_2630,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_479,c_91]) ).
tcf(c_2632,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_488,c_91]) ).
tcf(c_2634,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2636,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_974,c_91]) ).
tcf(c_2637,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_975,c_91]) ).
tcf(c_2638,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_976,c_91]) ).
tcf(c_2639,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_977,c_91]) ).
tcf(c_2640,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_978,c_91]) ).
tcf(c_2646,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2640,c_89]) ).
tcf(c_2647,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2639,c_89]) ).
tcf(c_2648,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2638,c_89]) ).
tcf(c_2649,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2637,c_89]) ).
tcf(c_2650,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2636,c_89]) ).
tcf(c_3054,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_927,c_479]) ).
tcf(c_3086,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_928,c_479]) ).
tcf(c_3111,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_3363,plain,
! [X0: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1865]) ).
tcf(c_3493,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1124,c_793]) ).
tcf(c_3595,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1193,c_806]) ).
tcf(c_4408,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1794,c_485]) ).
tcf(c_4496,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1889,c_1412]) ).
tcf(c_4614,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1890,c_1413]) ).
tcf(c_4782,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1982,c_478]) ).
tcf(c_4833,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( iPr_def_16 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_3363]) ).
tcf(c_4970,plain,
multiply(iPr_def_16,iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_478,c_2647]) ).
tcf(c_4971,plain,
multiply(iPr_def_16,iPr_def_25) = sk_c2,
inference(superposition,[status(thm)],[c_489,c_2647]) ).
tcf(c_4972,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_16,multiply(iPr_def_22,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_1982,c_2647]) ).
tcf(c_5380,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_14,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4970,c_91]) ).
tcf(c_5384,plain,
multiply(iPr_def_19,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_481,c_2648]) ).
tcf(c_5387,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5384,c_91]) ).
tcf(c_5404,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_485,c_2649]) ).
tcf(c_5407,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_5404,c_91]) ).
tcf(c_5409,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c8,
inference(superposition,[status(thm)],[c_487,c_2650]) ).
tcf(c_5412,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_23,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5409,c_91]) ).
tcf(c_5630,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_521,c_905]) ).
tcf(c_5643,plain,
( ( sk_c2 = iPr_def_15 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5630,c_4971]) ).
tcf(c_5883,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_5643,c_503]) ).
tcf(c_6846,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_16,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_523,c_989]) ).
tcf(c_6861,plain,
( ( sk_c2 = iPr_def_15 )
| ( sk_c8 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_6846,c_4971]) ).
tcf(c_6991,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_16,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_524,c_1016]) ).
tcf(c_7007,plain,
( ( sk_c2 = iPr_def_15 )
| ( sk_c7 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_6991,c_4971]) ).
tcf(c_7074,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_6861,c_505]) ).
tcf(c_7169,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_7007,c_506]) ).
tcf(c_7228,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_7074,c_478]) ).
tcf(c_8005,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_515,c_1074]) ).
tcf(c_8293,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_518,c_1149]) ).
tcf(c_8302,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_8293,c_5409]) ).
tcf(c_10936,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_17,sk_c7),
inference(superposition,[status(thm)],[c_478,c_2629]) ).
tcf(c_12498,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_16,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1412,c_3054]) ).
tcf(c_12522,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c2 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_12498,c_4971]) ).
tcf(c_12661,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c6 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_12522,c_504]) ).
tcf(c_12663,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_12522,c_502]) ).
tcf(c_12703,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( multiply(iPr_def_16,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1413,c_3086]) ).
tcf(c_12728,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c2 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_12703,c_4971]) ).
tcf(c_12768,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c6 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_12728,c_504]) ).
tcf(c_12771,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_12728,c_501]) ).
tcf(c_13926,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2144,c_4782]) ).
tcf(c_13940,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_13926,c_5409]) ).
tcf(c_14373,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_16,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_13940,c_977]) ).
tcf(c_14398,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_14373,c_4970]) ).
tcf(c_14800,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_14398,c_1794]) ).
tcf(c_14812,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(sk_c6,identity) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14398,c_479]) ).
tcf(c_15494,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2634,c_89]) ).
tcf(c_15523,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_15494]) ).
tcf(c_15524,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_15494]) ).
tcf(c_15541,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(inverse(iPr_def_19),iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1713,c_15494]) ).
tcf(c_15542,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(inverse(iPr_def_19),iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1293,c_15494]) ).
tcf(c_15653,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2650,c_15494]) ).
tcf(c_15654,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2649,c_15494]) ).
tcf(c_15655,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2648,c_15494]) ).
tcf(c_15656,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2647,c_15494]) ).
tcf(c_15657,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2646,c_15494]) ).
tcf(c_15723,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_15494,c_15494]) ).
tcf(c_16534,plain,
( ~ iPr_def_13
| ( inverse(inverse(identity)) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15523,c_491]) ).
tcf(c_16569,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_15524,c_15723]) ).
tcf(c_16575,plain,
multiply(sk_c1,sk_c8) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_16569,c_2632]) ).
tcf(c_16583,plain,
multiply(sk_c7,identity) = multiply(iPr_def_16,iPr_def_14),
inference(superposition,[status(thm)],[c_16569,c_5380]) ).
tcf(c_16584,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_16569,c_2630]) ).
tcf(c_16586,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_16569,c_2626]) ).
tcf(c_16587,plain,
multiply(sk_c8,identity) = multiply(iPr_def_22,iPr_def_23),
inference(superposition,[status(thm)],[c_16569,c_5412]) ).
tcf(c_16588,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_16569,c_5407]) ).
tcf(c_16589,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_17),
inference(superposition,[status(thm)],[c_16569,c_5387]) ).
tcf(c_16597,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_16569,c_15523]) ).
tcf(c_16602,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_16588,c_5404]) ).
tcf(c_16604,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_16586,c_478]) ).
tcf(c_16606,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_16584,c_479]) ).
tcf(c_16610,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_16575,c_488]) ).
tcf(c_16695,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_16597,c_90]) ).
tcf(c_16818,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_7169,c_7228]) ).
tcf(c_16835,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_16818,c_5409]) ).
tcf(c_17285,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(iPr_def_16,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_16835,c_977]) ).
tcf(c_17310,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_17285,c_4970]) ).
tcf(c_17808,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(sk_c4,identity) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_17310,c_485]) ).
tcf(c_18132,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c8 )
| ( multiply(sk_c3,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15653,c_493]) ).
tcf(c_18134,plain,
multiply(sk_c3,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_15653,c_90]) ).
tcf(c_18138,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_15653,c_15494]) ).
tcf(c_18139,plain,
multiply(sk_c3,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_15653,c_16569]) ).
tcf(c_18157,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_23 )
| ( inverse(inverse(iPr_def_22)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_18132,c_487]) ).
tcf(c_18167,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1146,c_18134]) ).
tcf(c_18168,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_947,c_18134]) ).
tcf(c_18487,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( identity = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_18168,c_18167]) ).
tcf(c_18821,plain,
inverse(iPr_def_22) = sk_c3,
inference(demodulation,[status(thm)],[c_18139,c_16569]) ).
tcf(c_18849,plain,
multiply(sk_c3,sk_c8) = iPr_def_23,
inference(superposition,[status(thm)],[c_5409,c_18138]) ).
tcf(c_19242,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_15654,c_90]) ).
tcf(c_19245,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c4,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_15654,c_494]) ).
tcf(c_19246,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_15654,c_15494]) ).
tcf(c_19247,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_15654,c_16569]) ).
tcf(c_19248,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_19245,c_485]) ).
tcf(c_19262,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( identity = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_4408,c_19242]) ).
tcf(c_19263,plain,
( ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1091,c_19242]) ).
tcf(c_19264,plain,
( ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_940,c_19242]) ).
tcf(c_19417,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_19247,c_16569]) ).
tcf(c_19421,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm)],[c_975,c_19246]) ).
tcf(c_19422,plain,
multiply(sk_c4,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_5404,c_19246]) ).
tcf(c_19494,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_19262,c_14800]) ).
tcf(c_19810,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_19264,c_19263]) ).
tcf(c_20267,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_19494,c_4614]) ).
tcf(c_20667,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_19810,c_18487]) ).
tcf(c_20701,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_20267,c_8005]) ).
tcf(c_20758,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_20701,c_5384]) ).
tcf(c_21711,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_20667,c_3595]) ).
tcf(c_21827,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_20758,c_1982]) ).
tcf(c_21842,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_15,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_20758,c_478]) ).
tcf(c_22017,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_21711,c_3493]) ).
tcf(c_22723,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_15) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_21827,c_18821]) ).
tcf(c_22861,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_22017,c_8005]) ).
tcf(c_22918,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_22861,c_5384]) ).
tcf(c_26539,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_14812,c_16569]) ).
tcf(c_26620,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_26539,c_528]) ).
tcf(c_26626,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_26539,c_522]) ).
tcf(c_28250,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_16,identity) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_974,c_4972]) ).
tcf(c_33381,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_12663,c_12661]) ).
tcf(c_33882,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_12771,c_12768]) ).
tcf(c_34897,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c4 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_17808,c_16569]) ).
tcf(c_34922,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_34897,c_485]) ).
tcf(c_38367,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_26620,c_1218,c_1863,c_1864,c_3111,c_4833,c_26626,c_26620]) ).
tcf(c_38396,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_38367,c_4614]) ).
tcf(c_38397,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_38367,c_4496]) ).
tcf(c_46742,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2315,c_16597]) ).
tcf(c_48253,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c5,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15655,c_491]) ).
tcf(c_48255,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_19)) != sk_c6 )
| ( multiply(sk_c5,sk_c8) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_15655,c_492]) ).
tcf(c_48256,plain,
multiply(sk_c5,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_15655,c_90]) ).
tcf(c_48260,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_15655,c_15494]) ).
tcf(c_48261,plain,
multiply(sk_c5,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_15655,c_16569]) ).
tcf(c_48328,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_48256,c_2648]) ).
tcf(c_48367,plain,
inverse(iPr_def_19) = sk_c5,
inference(demodulation,[status(thm)],[c_48261,c_16569]) ).
tcf(c_48369,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_15) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_38397,c_48367]) ).
tcf(c_48747,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_15,identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_14398,c_21842]) ).
tcf(c_48979,plain,
multiply(sk_c5,sk_c8) = iPr_def_17,
inference(superposition,[status(thm)],[c_5384,c_48260]) ).
tcf(c_49078,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_16)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15656,c_491]) ).
tcf(c_49080,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c8,sk_c8) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_15656,c_492]) ).
tcf(c_49081,plain,
multiply(sk_c8,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_15656,c_90]) ).
tcf(c_49084,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_15656,c_494]) ).
tcf(c_49085,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_15656,c_15494]) ).
tcf(c_49086,plain,
multiply(sk_c8,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_15656,c_16569]) ).
tcf(c_49089,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_14 )
| ( inverse(inverse(iPr_def_16)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_49084,c_478]) ).
tcf(c_49171,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_16) = identity ) ),
inference(superposition,[status(thm)],[c_22918,c_49081]) ).
tcf(c_49172,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_15,iPr_def_16) = identity ) ),
inference(superposition,[status(thm)],[c_20758,c_49081]) ).
tcf(c_49182,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_16) = identity ) ),
inference(superposition,[status(thm)],[c_8302,c_49081]) ).
tcf(c_49197,plain,
multiply(sk_c1,identity) = multiply(iPr_def_24,iPr_def_16),
inference(superposition,[status(thm)],[c_49081,c_2632]) ).
tcf(c_49198,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_16),
inference(superposition,[status(thm)],[c_49081,c_2629]) ).
tcf(c_49199,plain,
multiply(sk_c3,identity) = multiply(iPr_def_23,iPr_def_16),
inference(superposition,[status(thm)],[c_49081,c_2627]) ).
tcf(c_49200,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(superposition,[status(thm)],[c_49081,c_2647]) ).
tcf(c_49674,plain,
inverse(iPr_def_16) = sk_c8,
inference(demodulation,[status(thm)],[c_49086,c_16569]) ).
tcf(c_49676,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c8 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_2317,c_49674]) ).
tcf(c_49683,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(equality_resolution_simp,[status(thm)],[c_49676]) ).
tcf(c_50600,plain,
multiply(sk_c8,sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_4970,c_49085]) ).
tcf(c_52937,plain,
multiply(iPr_def_24,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_49197,c_16569]) ).
tcf(c_54286,plain,
multiply(iPr_def_17,iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_49198,c_16569]) ).
tcf(c_54290,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_15,iPr_def_16) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_38396,c_54286]) ).
tcf(c_54294,plain,
multiply(sk_c8,iPr_def_16) = multiply(iPr_def_19,sk_c5),
inference(superposition,[status(thm)],[c_54286,c_5387]) ).
tcf(c_54320,plain,
multiply(iPr_def_23,iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_49199,c_16569]) ).
tcf(c_55498,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(iPr_def_21,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_5883,c_34922]) ).
tcf(c_55719,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c1,sk_c8) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_15657,c_492]) ).
tcf(c_55720,plain,
multiply(sk_c1,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_15657,c_90]) ).
tcf(c_55725,plain,
multiply(sk_c1,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_15657,c_16569]) ).
tcf(c_55747,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_24 )
| ( inverse(inverse(iPr_def_18)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_55719,c_488]) ).
tcf(c_56356,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_55747,c_55725,c_55720,c_55498,c_54320,c_54294,c_54290,c_54286,c_52937,c_50600,c_49683,c_49674,c_49200,c_49198,c_49197,c_49182,c_49172,c_49171,c_49089,c_49080,c_49078,c_49086,c_49081,c_48979,c_48747,c_48369,c_48367,c_48328,c_48255,c_48253,c_46742,c_38367,c_33882,c_33381,c_28250,c_22918,c_22723,c_19422,c_19421,c_19417,c_19262,c_19248,c_19242,c_18849,c_18821,c_18157,c_18134,c_16835,c_16610,c_16606,c_16604,c_16602,c_16589,c_16587,c_16584,c_16583,c_16575,c_16597,c_16534,c_15542,c_15541,c_10936,c_16695,c_526,c_500,c_499,c_498,c_497,c_496,c_495,c_490,c_486,c_484,c_483,c_482,c_480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP308-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/20.40 % Computer : n010.cluster.edu
% 0.09/20.40 % Model : x86_64 x86_64
% 0.09/20.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.40 % Memory : 8046.5625MB
% 0.09/20.40 % OS : Linux 6.8.0-71-generic
% 0.01/20.40 % CPULimit : 300
% 0.01/20.40 % WCLimit : 300
% 0.01/20.40 % DateTime : Wed Sep 23 14:26:35 UTC 2026
% 0.01/20.40 % CPUTime :
% 0.01/20.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.01/20.44 Running first-order theorem proving
% 0.01/20.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.01/20.45
% 0.01/20.45 % ======== iProver multi-core TPTP/SMT =========
% 0.01/20.45
% 0.01/20.45 % Detected problem language: tptp
% 0.01/20.46 % Proving...
% 10.56/22.32 % SZS status Started for theBenchmark.p
% 10.56/22.32 % SZS status Unsatisfiable for theBenchmark.p
% 10.56/22.32
% 10.56/22.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.56/22.32
% 10.56/22.32 % ------ iProver source info
% 10.56/22.32
% 10.56/22.32 % git: date: 2026-07-19 20:42:38 +0200
% 10.56/22.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.56/22.32 % git: non_committed_changes: false
% 10.56/22.32
% 10.56/22.32 % ------ Parsing...% successful
% 10.56/22.32
% 10.56/22.32
% 10.56/22.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.56/22.32
% 10.56/22.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.56/22.32
% 10.56/22.32 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.56/22.32
% 10.56/22.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.56/22.32 % ------ Proving...
% 10.56/22.32 % ------ Problem Properties
% 10.56/22.32
% 10.56/22.32 %
% 10.56/22.32 % clauses 56
% 10.56/22.32 % conjectures 41
% 10.56/22.32 % EPR 37
% 10.56/22.32 % Horn 19
% 10.56/22.32 % unary 15
% 10.56/22.32 % binary 36
% 10.56/22.32 % lits 106
% 10.56/22.32 % lits eq 98
% 10.56/22.32 % fd_pure 0
% 10.56/22.32 % fd_pseudo 0
% 10.56/22.32 % fd_cond 0
% 10.56/22.32 % fd_pseudo_cond 0
% 10.56/22.32 % AC symbols 0
% 10.56/22.32
% 10.56/22.32 % ------ Schedule dynamic 5 is on
% 10.56/22.32
% 10.56/22.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.56/22.32
% 10.56/22.32
% 10.56/22.32 % ------
% 10.56/22.32 % Current options:
% 10.56/22.32 % ------
% 10.56/22.32
% 10.56/22.32
% 10.56/22.32 %
% 10.56/22.32
% 10.56/22.32 % ------ Proving...
% 10.56/22.32 %
% 10.56/22.32
% 10.56/22.32 % SZS status Unsatisfiable for theBenchmark.p
% 10.56/22.32
% 10.56/22.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.56/22.33
% 10.56/22.33
%------------------------------------------------------------------------------