%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP256-1 : 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 : 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 01:32:36 PM UTC 2026
% Result : Unsatisfiable 19.17s 3.39s
% Output : CNFRefutation 19.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 54
% Syntax : Number of formulae : 360 ( 107 unt; 13 def)
% Number of atoms : 1112 ( 659 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 554 ( 196 ~; 358 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?; 67 :)
% 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_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c6)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = inverse(sk_c6)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = inverse(sk_c6)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5
| sk_c8 != multiply(sk_c9,X5)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c9 != inverse(X6)
| sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(equality_resolution,[],[f90]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c9,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c7 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_128,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_130,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_132,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_133,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_135,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_137,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_138,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c8 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(X5,sk_c9) != sk_c8 )
| ( multiply(X4,sk_c9) != sk_c8 )
| ( multiply(X2,sk_c8) != sk_c9 )
| ( multiply(X1,sk_c10) != sk_c9 )
| ( multiply(X0,sk_c10) != sk_c9 )
| ( multiply(sk_c9,multiply(X3,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_537,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_140]) ).
tcf(c_538,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_140]) ).
tcf(c_539,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_140]) ).
tcf(c_540,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_140]) ).
tcf(c_541,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_140]) ).
tcf(c_542,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_543,definition,
iPr_def_15 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_544,definition,
iPr_def_16 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_545,definition,
iPr_def_17 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_546,definition,
iPr_def_18 = multiply(sk_c9,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_547,definition,
iPr_def_19 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_548,definition,
iPr_def_20 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_549,definition,
iPr_def_21 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_550,definition,
iPr_def_22 = multiply(sk_c4,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_551,definition,
iPr_def_23 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_552,definition,
iPr_def_24 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_553,definition,
iPr_def_25 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_554,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_555,definition,
iPr_def_27 = multiply(sk_c1,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_556,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_542]) ).
tcf(c_557,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_541]) ).
tcf(c_558,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_540]) ).
tcf(c_560,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_539]) ).
tcf(c_561,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_538]) ).
tcf(c_562,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_537]) ).
tcf(c_563,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_139,c_544,c_543]) ).
tcf(c_564,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_138,c_545]) ).
tcf(c_565,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_137,c_546]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_136,c_547]) ).
tcf(c_567,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_135,c_548]) ).
tcf(c_568,negated_conjecture,
( ( iPr_def_21 = sk_c10 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_134,c_549]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_133,c_550]) ).
tcf(c_570,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_132,c_551]) ).
tcf(c_571,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_572,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_573,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_574,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_575,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_577,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_125,c_552]) ).
tcf(c_578,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_580,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_581,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_584,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_118,c_553]) ).
tcf(c_585,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_587,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_588,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_591,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111,c_554]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_594,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_596,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_597,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_598,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_104,c_555]) ).
tcf(c_599,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_600,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_601,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_602,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_603,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_604,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_605,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_611,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_605]) ).
tcf(c_1094,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c9,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_571,c_546]) ).
tcf(c_1103,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_574,c_548]) ).
tcf(c_1110,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_565,c_548]) ).
tcf(c_1138,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_577,c_553]) ).
tcf(c_1147,plain,
multiply(iPr_def_21,sk_c4) = identity,
inference(superposition,[status(thm)],[c_549,c_96]) ).
tcf(c_1148,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_547,c_96]) ).
tcf(c_1149,plain,
multiply(iPr_def_16,sk_c6) = identity,
inference(superposition,[status(thm)],[c_544,c_96]) ).
tcf(c_1150,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_554,c_96]) ).
tcf(c_1151,plain,
multiply(iPr_def_24,sk_c2) = identity,
inference(superposition,[status(thm)],[c_552,c_96]) ).
tcf(c_1152,plain,
multiply(iPr_def_23,sk_c3) = identity,
inference(superposition,[status(thm)],[c_551,c_96]) ).
tcf(c_1165,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c9,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_578,c_546]) ).
tcf(c_1228,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_605]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_1245,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_580,c_579]) ).
tcf(c_1309,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_553]) ).
tcf(c_1372,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_584,c_548]) ).
tcf(c_1422,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1230]) ).
tcf(c_1471,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_586,c_572]) ).
tcf(c_1539,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_587,c_573]) ).
tcf(c_1602,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_588,c_548]) ).
tcf(c_1748,plain,
( ( iPr_def_21 = iPr_def_26 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_591,c_575]) ).
tcf(c_1795,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_593,c_555]) ).
tcf(c_1797,plain,
( ( iPr_def_21 = iPr_def_26 )
| ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_593,c_575]) ).
tcf(c_1825,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_594,c_555]) ).
tcf(c_1903,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_596,c_555]) ).
tcf(c_1942,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_597,c_555]) ).
tcf(c_2110,plain,
( ( sk_c8 = iPr_def_18 )
| ( iPr_def_18 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1422]) ).
tcf(c_2175,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_601,c_600]) ).
tcf(c_2739,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( inverse(sk_c2) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_553,c_558]) ).
tcf(c_2740,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_15 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_543,c_558]) ).
tcf(c_2755,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_23 )
| ( sk_c8 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2740,c_551]) ).
tcf(c_2759,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( sk_c8 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2739,c_552]) ).
tcf(c_2866,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_17 )
| ( inverse(sk_c6) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_545,c_560]) ).
tcf(c_2867,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_25 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_553,c_560]) ).
tcf(c_2868,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_15 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_543,c_560]) ).
tcf(c_2869,plain,
( ~ iPr_def_12
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_560]) ).
tcf(c_2883,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_15 )
| ( sk_c9 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2868,c_551]) ).
tcf(c_2887,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2867,c_552]) ).
tcf(c_2891,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_17 )
| ( sk_c9 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2866,c_544]) ).
tcf(c_2997,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_27 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_555,c_561]) ).
tcf(c_2998,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_550,c_561]) ).
tcf(c_3015,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( sk_c10 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2998,c_549]) ).
tcf(c_3019,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_27 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_2997,c_554]) ).
tcf(c_3116,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_548,c_562]) ).
tcf(c_3118,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_96,c_562]) ).
tcf(c_3142,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3116,c_547]) ).
tcf(c_3473,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1245,c_553]) ).
tcf(c_3476,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1245,c_543]) ).
tcf(c_3826,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_546,c_97]) ).
tcf(c_3827,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c9,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_545,c_97]) ).
tcf(c_3831,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_3833,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1147,c_97]) ).
tcf(c_3834,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1148,c_97]) ).
tcf(c_3835,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1149,c_97]) ).
tcf(c_3836,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1150,c_97]) ).
tcf(c_3837,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1151,c_97]) ).
tcf(c_3838,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1152,c_97]) ).
tcf(c_3845,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3838,c_95]) ).
tcf(c_3846,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3837,c_95]) ).
tcf(c_3847,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3836,c_95]) ).
tcf(c_3848,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3835,c_95]) ).
tcf(c_3849,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3834,c_95]) ).
tcf(c_3850,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3833,c_95]) ).
tcf(c_4226,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1539,c_1471]) ).
tcf(c_4823,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_4824,plain,
( ( sk_c9 = iPr_def_16 )
| ( iPr_def_16 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_4823]) ).
tcf(c_4935,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2175,c_1245]) ).
tcf(c_5740,plain,
multiply(iPr_def_23,iPr_def_15) = sk_c9,
inference(superposition,[status(thm)],[c_543,c_3845]) ).
tcf(c_5746,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_15,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_5740,c_97]) ).
tcf(c_5748,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_553,c_3846]) ).
tcf(c_5795,plain,
multiply(iPr_def_26,iPr_def_27) = sk_c10,
inference(superposition,[status(thm)],[c_555,c_3847]) ).
tcf(c_6089,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(iPr_def_27,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_5795,c_97]) ).
tcf(c_6091,plain,
multiply(iPr_def_16,iPr_def_17) = sk_c9,
inference(superposition,[status(thm)],[c_545,c_3848]) ).
tcf(c_6116,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_17,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_6091,c_97]) ).
tcf(c_6118,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_548,c_3849]) ).
tcf(c_6154,plain,
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1422]) ).
tcf(c_6157,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_6118,c_97]) ).
tcf(c_6159,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c10,
inference(superposition,[status(thm)],[c_550,c_3850]) ).
tcf(c_6215,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_6159,c_97]) ).
tcf(c_6229,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1110,c_3849]) ).
tcf(c_6230,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6229,c_6118]) ).
tcf(c_6540,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1309,c_3846]) ).
tcf(c_6541,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6540,c_5748]) ).
tcf(c_7070,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1602,c_3849]) ).
tcf(c_7071,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_7070,c_6118]) ).
tcf(c_9962,plain,
multiply(sk_c6,iPr_def_18) = multiply(iPr_def_17,sk_c7),
inference(superposition,[status(thm)],[c_546,c_3827]) ).
tcf(c_10689,plain,
( ( sk_c9 = iPr_def_16 )
| ( sk_c8 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_1748,c_611,c_570,c_1228,c_4824,c_6154]) ).
tcf(c_10690,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_16 ) ),
inference(renaming,[status(thm)],[c_10689]) ).
tcf(c_10860,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_1797,c_572,c_1228,c_2110,c_6154]) ).
tcf(c_10861,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_18 ) ),
inference(renaming,[status(thm)],[c_10860]) ).
tcf(c_12065,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3831,c_95]) ).
tcf(c_12074,plain,
multiply(inverse(sk_c5),iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_548,c_12065]) ).
tcf(c_12075,plain,
multiply(inverse(sk_c9),iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_546,c_12065]) ).
tcf(c_12079,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_12065]) ).
tcf(c_12080,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_12065]) ).
tcf(c_12103,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(inverse(sk_c5),iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1103,c_12065]) ).
tcf(c_12136,plain,
multiply(inverse(iPr_def_23),identity) = sk_c3,
inference(superposition,[status(thm)],[c_1152,c_12065]) ).
tcf(c_12138,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(inverse(sk_c5),iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1602,c_12065]) ).
tcf(c_12141,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(inverse(sk_c5),iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1372,c_12065]) ).
tcf(c_12226,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3850,c_12065]) ).
tcf(c_12227,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3849,c_12065]) ).
tcf(c_12228,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3848,c_12065]) ).
tcf(c_12229,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3847,c_12065]) ).
tcf(c_12230,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3846,c_12065]) ).
tcf(c_12233,plain,
multiply(inverse(iPr_def_23),sk_c9) = iPr_def_15,
inference(superposition,[status(thm)],[c_5740,c_12065]) ).
tcf(c_12250,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_12065,c_12065]) ).
tcf(c_12403,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_12103,c_547,c_6118]) ).
tcf(c_12667,plain,
( ~ iPr_def_14
| ( inverse(inverse(identity)) != sk_c9 )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12079,c_557]) ).
tcf(c_12787,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_12080,c_12250]) ).
tcf(c_12798,plain,
multiply(sk_c10,identity) = multiply(iPr_def_26,iPr_def_27),
inference(superposition,[status(thm)],[c_12787,c_6089]) ).
tcf(c_12801,plain,
multiply(sk_c10,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_12787,c_6215]) ).
tcf(c_12802,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_12787,c_6157]) ).
tcf(c_12804,plain,
multiply(sk_c9,sk_c7) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_12787,c_3826]) ).
tcf(c_12805,plain,
multiply(sk_c9,identity) = multiply(iPr_def_16,iPr_def_17),
inference(superposition,[status(thm)],[c_12787,c_6116]) ).
tcf(c_12810,plain,
multiply(sk_c9,identity) = multiply(iPr_def_23,iPr_def_15),
inference(superposition,[status(thm)],[c_12787,c_5746]) ).
tcf(c_12817,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12787,c_12079]) ).
tcf(c_12818,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_12810,c_5740]) ).
tcf(c_12824,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_12804,c_546]) ).
tcf(c_12826,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_12802,c_6118]) ).
tcf(c_12827,plain,
multiply(sk_c10,identity) = sk_c10,
inference(light_normalisation,[status(thm)],[c_12801,c_6159]) ).
tcf(c_12835,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_12817,c_96]) ).
tcf(c_12928,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_567,c_2755]) ).
tcf(c_12931,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_563,c_2755]) ).
tcf(c_13036,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12928,c_12403,c_12928]) ).
tcf(c_13059,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12931,c_10690,c_12931]) ).
tcf(c_13108,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_586,c_2759]) ).
tcf(c_13219,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_13108,c_2755,c_6230,c_10861]) ).
tcf(c_13547,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_12
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_567,c_2883]) ).
tcf(c_13693,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_13547,c_2887,c_6541,c_7071]) ).
tcf(c_14148,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c10 )
| ( multiply(sk_c4,sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_12226,c_561]) ).
tcf(c_14149,plain,
multiply(sk_c4,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_12226,c_96]) ).
tcf(c_14156,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_12226,c_12065]) ).
tcf(c_14157,plain,
multiply(sk_c4,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_12226,c_12787]) ).
tcf(c_14167,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( inverse(inverse(iPr_def_21)) != sk_c10 ) ),
inference(light_normalisation,[status(thm)],[c_14148,c_550]) ).
tcf(c_14236,plain,
inverse(iPr_def_21) = sk_c4,
inference(demodulation,[status(thm)],[c_14157,c_12787]) ).
tcf(c_15094,plain,
multiply(sk_c4,sk_c10) = iPr_def_22,
inference(superposition,[status(thm)],[c_6159,c_14156]) ).
tcf(c_15426,plain,
multiply(sk_c5,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_12227,c_96]) ).
tcf(c_15429,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c5,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_12227,c_562]) ).
tcf(c_15432,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c5,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12227,c_558]) ).
tcf(c_15433,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_12227,c_12065]) ).
tcf(c_15434,plain,
multiply(sk_c5,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_12227,c_12787]) ).
tcf(c_15441,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_15429,c_548]) ).
tcf(c_15615,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_15426,c_3849]) ).
tcf(c_16173,plain,
inverse(iPr_def_19) = sk_c5,
inference(demodulation,[status(thm)],[c_15434,c_12787]) ).
tcf(c_16178,plain,
multiply(sk_c5,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_6118,c_15433]) ).
tcf(c_16607,plain,
multiply(sk_c6,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_12228,c_96]) ).
tcf(c_16611,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_16)) != sk_c9 )
| ( multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12228,c_557]) ).
tcf(c_16612,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_16)) != sk_c9 )
| ( multiply(sk_c6,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12228,c_560]) ).
tcf(c_16614,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_12228,c_12065]) ).
tcf(c_16615,plain,
multiply(sk_c6,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_12228,c_12787]) ).
tcf(c_16627,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_16)) != sk_c9 )
| ( multiply(sk_c9,iPr_def_17) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_16611,c_545]) ).
tcf(c_16673,plain,
inverse(iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_16615,c_12787]) ).
tcf(c_16996,plain,
multiply(sk_c6,sk_c9) = iPr_def_17,
inference(superposition,[status(thm)],[c_6091,c_16614]) ).
tcf(c_18863,plain,
multiply(sk_c1,iPr_def_26) = identity,
inference(superposition,[status(thm)],[c_12229,c_96]) ).
tcf(c_18888,plain,
( ( identity = iPr_def_27 )
| ( sk_c9 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1942,c_18863]) ).
tcf(c_18889,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1903,c_18863]) ).
tcf(c_18891,plain,
( ( identity = iPr_def_27 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1825,c_18863]) ).
tcf(c_18892,plain,
( ( identity = iPr_def_27 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1795,c_18863]) ).
tcf(c_18936,plain,
multiply(iPr_def_26,identity) = iPr_def_26,
inference(superposition,[status(thm)],[c_18863,c_3847]) ).
tcf(c_19299,plain,
( ( identity = iPr_def_27 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_18889,c_550]) ).
tcf(c_19300,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_19299,c_14149]) ).
tcf(c_19881,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_18892,c_18891]) ).
tcf(c_21151,plain,
multiply(sk_c2,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_12230,c_96]) ).
tcf(c_21158,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_12230,c_12065]) ).
tcf(c_21159,plain,
multiply(sk_c2,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_12230,c_12787]) ).
tcf(c_21180,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_3473,c_21151]) ).
tcf(c_21182,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1309,c_21151]) ).
tcf(c_21183,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1138,c_21151]) ).
tcf(c_21204,plain,
inverse(iPr_def_24) = sk_c2,
inference(demodulation,[status(thm)],[c_21159,c_12787]) ).
tcf(c_21922,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_21180,c_19881]) ).
tcf(c_22451,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1151,c_21158]) ).
tcf(c_22452,plain,
multiply(sk_c2,sk_c9) = iPr_def_25,
inference(superposition,[status(thm)],[c_5748,c_21158]) ).
tcf(c_22784,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_21183,c_1165]) ).
tcf(c_22786,plain,
( ( identity = iPr_def_25 )
| ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_21183,c_1094]) ).
tcf(c_24758,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_21922,c_4935]) ).
tcf(c_28708,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_24758,c_4226]) ).
tcf(c_30500,plain,
( ~ iPr_def_12
| ( sk_c9 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2869,c_12817]) ).
tcf(c_32113,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_28708,c_3476]) ).
tcf(c_32410,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_25)) != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_588,c_3118]) ).
tcf(c_32411,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_25)) != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_587,c_3118]) ).
tcf(c_37511,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_32411,c_32410,c_32113,c_30500,c_22786,c_22784,c_22452,c_22451,c_21204,c_21182,c_19300,c_18936,c_18888,c_16996,c_16673,c_16627,c_16612,c_16615,c_16607,c_16178,c_16173,c_15615,c_15441,c_15432,c_15434,c_15426,c_15094,c_14236,c_14167,c_14149,c_13693,c_13219,c_13059,c_13036,c_12827,c_12826,c_12824,c_12818,c_12805,c_12804,c_12802,c_12798,c_12817,c_12667,c_12233,c_12141,c_12138,c_12136,c_12075,c_12074,c_9962,c_12835,c_3142,c_3019,c_3015,c_2891,c_2755,c_1149,c_1148,c_1094,c_604,c_603,c_602,c_601,c_600,c_599,c_598,c_585,c_569,c_568,c_567,c_566,c_565,c_564,c_563,c_552,c_551,c_549,c_547,c_544,c_556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP256-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 14:18:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 19.17/3.39 % SZS status Started for theBenchmark.p
% 19.17/3.39 % SZS status Unsatisfiable for theBenchmark.p
% 19.17/3.39
% 19.17/3.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.17/3.39
% 19.17/3.39 % ------ iProver source info
% 19.17/3.39
% 19.17/3.39 % git: date: 2026-07-19 20:42:38 +0200
% 19.17/3.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.17/3.39 % git: non_committed_changes: false
% 19.17/3.39
% 19.17/3.39 % ------ Parsing...% successful
% 19.17/3.39
% 19.17/3.39
% 19.17/3.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.17/3.39
% 19.17/3.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 19.17/3.39
% 19.17/3.39 % ------ Preprocessing... gs_s sp: 6 0s gs_e snvd_s sp: 0 0s snvd_e %
% 19.17/3.39
% 19.17/3.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 19.17/3.39 % ------ Proving...
% 19.17/3.39 % ------ Problem Properties
% 19.17/3.39
% 19.17/3.39 %
% 19.17/3.39 % clauses 64
% 19.17/3.39 % conjectures 48
% 19.17/3.39 % EPR 43
% 19.17/3.39 % Horn 21
% 19.17/3.39 % unary 16
% 19.17/3.39 % binary 42
% 19.17/3.39 % lits 120
% 19.17/3.39 % lits eq 110
% 19.17/3.39 % fd_pure 0
% 19.17/3.39 % fd_pseudo 0
% 19.17/3.39 % fd_cond 0
% 19.17/3.39 % fd_pseudo_cond 0
% 19.17/3.39 % AC symbols 0
% 19.17/3.39
% 19.17/3.39 % ------ Schedule dynamic 5 is on
% 19.17/3.39
% 19.17/3.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 19.17/3.39
% 19.17/3.39
% 19.17/3.39 % ------
% 19.17/3.39 % Current options:
% 19.17/3.39 % ------
% 19.17/3.39
% 19.17/3.39
% 19.17/3.39 %
% 19.17/3.39
% 19.17/3.39 % ------ Proving...
% 19.17/3.39 %
% 19.17/3.39
% 19.17/3.39 % SZS status Unsatisfiable for theBenchmark.p
% 19.17/3.39
% 19.17/3.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.17/3.39
% 19.17/3.39
%------------------------------------------------------------------------------