%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP319-1 : 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 01:32:50 PM UTC 2026
% Result : Unsatisfiable 10.31s 2.17s
% Output : CNFRefutation 10.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 54
% Syntax : Number of formulae : 388 ( 104 unt; 12 def)
% Number of atoms : 1299 ( 718 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 631 ( 192 ~; 439 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 65 :)
% 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_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = inverse(sk_c4)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = inverse(sk_c6)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = inverse(sk_c4)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c6)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X5,sk_c9) != sk_c7
| inverse(X5) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c7 != inverse(X5)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X2)
| multiply(X2,sk_c9) != X1
| sk_c8 != multiply(sk_c9,X1)
| inverse(X0) != sk_c8
| sk_c9 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X4,X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c7 != inverse(X5)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| inverse(X0) != sk_c8
| sk_c9 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c9) != sk_c7 ),
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_c4,sk_c9) = sk_c8 )
| ( multiply(sk_c8,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c8,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c8,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c7 )
| ( multiply(sk_c8,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c4,sk_c9) = sk_c8 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c7 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c7 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_121,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X1) != sk_c9 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,sk_c9) != sk_c7 )
| ( multiply(X4,sk_c9) != sk_c7 )
| ( multiply(X3,sk_c8) != sk_c7 )
| ( multiply(X2,sk_c9) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 )
| ( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
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_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
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_c7 )
| ( multiply(X0,sk_c9) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_477,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_128]) ).
tcf(c_478,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c8,sk_c9) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_479,definition,
iPr_def_15 = multiply(sk_c8,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = inverse(sk_c6),
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 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = multiply(sk_c4,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = multiply(sk_c9,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_490,definition,
iPr_def_26 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_491,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_478,c_479]) ).
tcf(c_492,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_477]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c9) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_494,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_495,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_496,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_127,c_481,c_480]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_126,c_482]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_125,c_483]) ).
tcf(c_500,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_124,c_484]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123,c_485]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_122,c_486]) ).
tcf(c_503,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_121,c_487]) ).
tcf(c_504,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_505,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_508,negated_conjecture,
( ( iPr_def_23 = sk_c3 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_488]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_109,c_489]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_520,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_521,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103,c_490]) ).
tcf(c_522,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_523,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_524,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_527,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_528,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_530,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_531,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_532,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_533,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_874,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_510,c_509]) ).
tcf(c_907,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_512,c_510]) ).
tcf(c_922,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_508,c_488]) ).
tcf(c_923,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_507,c_488]) ).
tcf(c_924,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_506,c_488]) ).
tcf(c_925,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_505,c_488]) ).
tcf(c_926,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_504,c_488]) ).
tcf(c_927,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c9,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_503,c_488]) ).
tcf(c_942,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_511,c_490]) ).
tcf(c_951,plain,
multiply(iPr_def_21,sk_c4) = identity,
inference(superposition,[status(thm)],[c_485,c_90]) ).
tcf(c_952,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_483,c_90]) ).
tcf(c_953,plain,
multiply(iPr_def_18,sk_c6) = identity,
inference(superposition,[status(thm)],[c_482,c_90]) ).
tcf(c_954,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_489,c_90]) ).
tcf(c_955,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_481,c_90]) ).
tcf(c_962,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_513,c_490]) ).
tcf(c_985,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_514,c_490]) ).
tcf(c_987,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_24,sk_c9) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_514,c_479]) ).
tcf(c_1050,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_517,c_490]) ).
tcf(c_1076,plain,
! [X0: $i] :
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_15 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_534]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_534]) ).
tcf(c_1080,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1079]) ).
tcf(c_1081,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_533]) ).
tcf(c_1091,plain,
( ( sk_c7 = iPr_def_16 )
| ( iPr_def_16 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1080]) ).
tcf(c_1092,plain,
( ( sk_c7 = iPr_def_18 )
| ( iPr_def_18 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1080]) ).
tcf(c_1105,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c8 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_518,c_516]) ).
tcf(c_1106,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c8 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_518,c_515]) ).
tcf(c_1126,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_519,c_490]) ).
tcf(c_1129,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,sk_c9) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_519,c_479]) ).
tcf(c_1147,plain,
( ( sk_c7 = iPr_def_15 )
| ( iPr_def_15 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1080]) ).
tcf(c_1159,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_520,c_490]) ).
tcf(c_1162,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_25,sk_c9) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_520,c_479]) ).
tcf(c_1227,plain,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c7 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1076]) ).
tcf(c_1283,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_523,c_490]) ).
tcf(c_1338,plain,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_15 != iPr_def_16 )
| ( sk_c7 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1076]) ).
tcf(c_1355,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_524,c_522]) ).
tcf(c_1356,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_524,c_521]) ).
tcf(c_1373,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_26) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_525,c_487]) ).
tcf(c_1413,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c9 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_526,c_523]) ).
tcf(c_1419,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_526,c_490]) ).
tcf(c_1592,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_529,c_528]) ).
tcf(c_1593,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_529,c_527]) ).
tcf(c_1679,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_530,c_528]) ).
tcf(c_1680,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_530,c_527]) ).
tcf(c_1715,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_531,c_530]) ).
tcf(c_1717,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c7 = iPr_def_15 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_531,c_527]) ).
tcf(c_1831,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_532,c_530]) ).
tcf(c_1833,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_532,c_527]) ).
tcf(c_1921,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_531,c_491]) ).
tcf(c_1922,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_530,c_491]) ).
tcf(c_1923,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_529,c_491]) ).
tcf(c_1925,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_527,c_491]) ).
tcf(c_2127,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_15 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_479,c_493]) ).
tcf(c_2129,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_16 )
| ( inverse(sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_480,c_493]) ).
tcf(c_2142,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_18 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2129,c_482]) ).
tcf(c_2211,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_484,c_494]) ).
tcf(c_2212,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_26 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_490,c_494]) ).
tcf(c_2228,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_26 )
| ( sk_c8 != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_2212,c_489]) ).
tcf(c_2232,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2211,c_483]) ).
tcf(c_2327,plain,
( ~ iPr_def_11
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_89,c_495]) ).
tcf(c_2536,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c9,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_479,c_91]) ).
tcf(c_2538,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_484,c_91]) ).
tcf(c_2541,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c3,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_488,c_91]) ).
tcf(c_2544,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2546,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_951,c_91]) ).
tcf(c_2547,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_952,c_91]) ).
tcf(c_2548,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_953,c_91]) ).
tcf(c_2549,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_954,c_91]) ).
tcf(c_2550,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_955,c_91]) ).
tcf(c_2555,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2550,c_89]) ).
tcf(c_2556,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2549,c_89]) ).
tcf(c_2557,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2548,c_89]) ).
tcf(c_2558,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2547,c_89]) ).
tcf(c_2559,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2546,c_89]) ).
tcf(c_2755,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_533]) ).
tcf(c_2819,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_874,c_490]) ).
tcf(c_2882,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_907,c_490]) ).
tcf(c_3061,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( inverse(sk_c4) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_486,c_496]) ).
tcf(c_3064,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c9 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_89,c_496]) ).
tcf(c_3065,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_90,c_496]) ).
tcf(c_3084,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_21 )
| ( sk_c8 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_3061,c_485]) ).
tcf(c_3182,plain,
( ~ iPr_def_14
| ( inverse(inverse(sk_c9)) != sk_c9 )
| ( multiply(sk_c9,identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_90,c_492]) ).
tcf(c_4391,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1679,c_491]) ).
tcf(c_4595,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1680,c_491]) ).
tcf(c_4705,plain,
multiply(iPr_def_17,iPr_def_23) = sk_c9,
inference(superposition,[status(thm)],[c_487,c_2555]) ).
tcf(c_4708,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_23,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4705,c_91]) ).
tcf(c_4758,plain,
( iPr_def_14
| iPr_def_13
| ( iPr_def_18 = iPr_def_20 )
| iPr_def_10
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_4391,c_491,c_1105,c_1227,c_1355,c_1679,c_2228,c_2755]) ).
tcf(c_4759,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_4758]) ).
tcf(c_4770,plain,
( iPr_def_14
| iPr_def_13
| ( iPr_def_16 = iPr_def_20 )
| iPr_def_10
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_4595,c_1106,c_1356,c_2228,c_4595]) ).
tcf(c_4771,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_4770]) ).
tcf(c_4944,plain,
multiply(iPr_def_25,iPr_def_26) = sk_c8,
inference(superposition,[status(thm)],[c_490,c_2556]) ).
tcf(c_4947,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(iPr_def_26,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4944,c_91]) ).
tcf(c_4949,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c9,
inference(superposition,[status(thm)],[c_480,c_2557]) ).
tcf(c_4955,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4949,c_91]) ).
tcf(c_4967,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_484,c_2558]) ).
tcf(c_4970,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4967,c_91]) ).
tcf(c_4972,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c9,
inference(superposition,[status(thm)],[c_486,c_2559]) ).
tcf(c_4975,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4972,c_91]) ).
tcf(c_5958,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1050,c_2556]) ).
tcf(c_5959,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5958,c_4944]) ).
tcf(c_6096,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1126,c_2556]) ).
tcf(c_6097,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c8 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_6096,c_4944]) ).
tcf(c_6138,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_525,c_1129]) ).
tcf(c_6144,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6138,c_4944]) ).
tcf(c_6191,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1159,c_2556]) ).
tcf(c_6192,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_6191,c_4944]) ).
tcf(c_6220,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1413,c_1162]) ).
tcf(c_6265,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6220,c_4944]) ).
tcf(c_6341,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1283,c_2556]) ).
tcf(c_6342,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_6341,c_4944]) ).
tcf(c_6390,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_6144,c_484]) ).
tcf(c_7140,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_17,iPr_def_23) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1373,c_2555]) ).
tcf(c_7141,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_7140,c_4705]) ).
tcf(c_7354,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1419,c_2556]) ).
tcf(c_7355,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c8 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_7354,c_4944]) ).
tcf(c_8403,plain,
multiply(sk_c5,iPr_def_15) = multiply(iPr_def_20,sk_c9),
inference(superposition,[status(thm)],[c_479,c_2538]) ).
tcf(c_9381,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c7 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1592,c_527,c_1081,c_1091,c_1147,c_1338,c_1593]) ).
tcf(c_9382,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_19 ) ),
inference(renaming,[status(thm)],[c_9381]) ).
tcf(c_10100,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1715,c_527,c_1081,c_1091,c_1147,c_1338,c_1717]) ).
tcf(c_10101,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c9 = iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_10100]) ).
tcf(c_10997,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1831,c_527,c_1081,c_1091,c_1147,c_1338,c_1833]) ).
tcf(c_10998,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_10997]) ).
tcf(c_11182,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2544,c_89]) ).
tcf(c_11188,plain,
multiply(inverse(sk_c8),iPr_def_15) = sk_c9,
inference(superposition,[status(thm)],[c_479,c_11182]) ).
tcf(c_11192,plain,
multiply(inverse(sk_c1),iPr_def_26) = sk_c8,
inference(superposition,[status(thm)],[c_490,c_11182]) ).
tcf(c_11195,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_11182]) ).
tcf(c_11196,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_11182]) ).
tcf(c_11239,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( multiply(inverse(sk_c1),iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2882,c_11182]) ).
tcf(c_11240,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(inverse(sk_c1),iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2819,c_11182]) ).
tcf(c_11241,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(inverse(sk_c1),iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_985,c_11182]) ).
tcf(c_11242,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(inverse(sk_c1),iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_962,c_11182]) ).
tcf(c_11243,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c1),iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_942,c_11182]) ).
tcf(c_11309,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2559,c_11182]) ).
tcf(c_11310,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2558,c_11182]) ).
tcf(c_11311,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2557,c_11182]) ).
tcf(c_11312,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2556,c_11182]) ).
tcf(c_11313,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2555,c_11182]) ).
tcf(c_11329,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11182,c_11182]) ).
tcf(c_11759,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11196,c_11329]) ).
tcf(c_11770,plain,
multiply(sk_c8,sk_c9) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_11759,c_2536]) ).
tcf(c_11773,plain,
multiply(sk_c9,sk_c3) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_11759,c_2541]) ).
tcf(c_11779,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_11759,c_11195]) ).
tcf(c_11780,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_11773,c_488]) ).
tcf(c_11783,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_11770,c_479]) ).
tcf(c_11791,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_11779,c_90]) ).
tcf(c_12135,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_21)) != sk_c8 )
| ( multiply(sk_c4,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11309,c_494]) ).
tcf(c_12136,plain,
multiply(sk_c4,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_11309,c_90]) ).
tcf(c_12140,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_21)) != sk_c9 )
| ( multiply(sk_c4,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11309,c_496]) ).
tcf(c_12142,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_11309,c_11182]) ).
tcf(c_12143,plain,
multiply(sk_c4,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_11309,c_11759]) ).
tcf(c_12148,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( inverse(inverse(iPr_def_21)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_12140,c_486]) ).
tcf(c_12638,plain,
inverse(iPr_def_21) = sk_c4,
inference(demodulation,[status(thm)],[c_12143,c_11759]) ).
tcf(c_12645,plain,
multiply(sk_c4,sk_c9) = iPr_def_22,
inference(superposition,[status(thm)],[c_4972,c_12142]) ).
tcf(c_12682,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c5,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11310,c_495]) ).
tcf(c_12684,plain,
multiply(sk_c5,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_11310,c_90]) ).
tcf(c_12690,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_11310,c_11182]) ).
tcf(c_12691,plain,
multiply(sk_c5,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_11310,c_11759]) ).
tcf(c_12702,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_12682,c_484]) ).
tcf(c_13551,plain,
inverse(iPr_def_19) = sk_c5,
inference(demodulation,[status(thm)],[c_12691,c_11759]) ).
tcf(c_13575,plain,
multiply(sk_c5,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_4967,c_12690]) ).
tcf(c_13761,plain,
multiply(sk_c9,identity) = multiply(iPr_def_17,iPr_def_23),
inference(superposition,[status(thm)],[c_11759,c_4708]) ).
tcf(c_13764,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_13761,c_4705]) ).
tcf(c_13799,plain,
multiply(sk_c8,identity) = multiply(iPr_def_25,iPr_def_26),
inference(superposition,[status(thm)],[c_11759,c_4947]) ).
tcf(c_13806,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_13799,c_4944]) ).
tcf(c_13985,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c6,sk_c9) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11311,c_493]) ).
tcf(c_13986,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_11311,c_11182]) ).
tcf(c_13987,plain,
multiply(sk_c6,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11311,c_11759]) ).
tcf(c_14034,plain,
inverse(iPr_def_18) = sk_c6,
inference(demodulation,[status(thm)],[c_13987,c_11759]) ).
tcf(c_14056,plain,
multiply(sk_c9,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_11759,c_4955]) ).
tcf(c_14062,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_11759,c_4970]) ).
tcf(c_14074,plain,
multiply(sk_c9,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_11759,c_4975]) ).
tcf(c_14320,plain,
multiply(sk_c6,sk_c9) = iPr_def_16,
inference(superposition,[status(thm)],[c_4949,c_13986]) ).
tcf(c_14364,plain,
multiply(sk_c1,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_11312,c_90]) ).
tcf(c_14368,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_25)) != sk_c9 )
| ( multiply(sk_c1,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11312,c_496]) ).
tcf(c_14370,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_11312,c_11182]) ).
tcf(c_14371,plain,
multiply(sk_c1,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_11312,c_11759]) ).
tcf(c_14408,plain,
( ( identity = iPr_def_26 )
| ( sk_c8 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1159,c_14364]) ).
tcf(c_14409,plain,
( ( identity = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1126,c_14364]) ).
tcf(c_14410,plain,
( ( identity = iPr_def_26 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1050,c_14364]) ).
tcf(c_14935,plain,
inverse(iPr_def_25) = sk_c1,
inference(demodulation,[status(thm)],[c_14371,c_11759]) ).
tcf(c_14967,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_954,c_14370]) ).
tcf(c_14974,plain,
multiply(sk_c1,sk_c8) = iPr_def_26,
inference(superposition,[status(thm)],[c_4944,c_14370]) ).
tcf(c_15709,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_20,sk_c9) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6390,c_8403]) ).
tcf(c_15733,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_525,c_15709]) ).
tcf(c_15735,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(inverse(iPr_def_20),iPr_def_20) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_15709,c_11182]) ).
tcf(c_15740,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c8,sk_c9) = multiply(iPr_def_19,iPr_def_20) ) ),
inference(superposition,[status(thm)],[c_15709,c_4970]) ).
tcf(c_15809,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c2,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11313,c_495]) ).
tcf(c_15811,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_11313,c_90]) ).
tcf(c_15817,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_11313,c_11182]) ).
tcf(c_15818,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_11313,c_11759]) ).
tcf(c_15857,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_15818,c_11759]) ).
tcf(c_15869,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(inverse(iPr_def_20),iPr_def_20) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_15733,c_11182]) ).
tcf(c_16346,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_955,c_15817]) ).
tcf(c_16351,plain,
multiply(sk_c2,sk_c9) = iPr_def_23,
inference(superposition,[status(thm)],[c_4705,c_15817]) ).
tcf(c_17900,plain,
( ~ iPr_def_13
| ( inverse(sk_c8) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_2127,c_527,c_528,c_1081,c_1091,c_1092,c_1147,c_2142,c_2127]) ).
tcf(c_17921,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( inverse(iPr_def_15) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6144,c_17900]) ).
tcf(c_17932,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_13
| ( inverse(iPr_def_25) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_520,c_17900]) ).
tcf(c_17964,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c7 != sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_17932,c_14935]) ).
tcf(c_18773,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2327,c_11779]) ).
tcf(c_18789,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( sk_c8 != identity ) ),
inference(superposition,[status(thm)],[c_532,c_18773]) ).
tcf(c_18790,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( sk_c8 != identity ) ),
inference(superposition,[status(thm)],[c_531,c_18773]) ).
tcf(c_18791,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != identity ) ),
inference(superposition,[status(thm)],[c_530,c_18773]) ).
tcf(c_18792,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( sk_c8 != identity ) ),
inference(superposition,[status(thm)],[c_529,c_18773]) ).
tcf(c_19053,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( sk_c8 != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3064,c_11779]) ).
tcf(c_19080,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_10
| ( identity != iPr_def_26 )
| ( sk_c8 != sk_c9 ) ),
inference(superposition,[status(thm)],[c_525,c_19053]) ).
tcf(c_19179,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_1922,c_491,c_1227,c_1922,c_2755]) ).
tcf(c_19220,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1925,c_491,c_1227,c_1925,c_2755]) ).
tcf(c_24593,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_19220,c_19179,c_19080,c_18791,c_18792,c_18790,c_18789,c_17964,c_17921,c_17900,c_16351,c_16346,c_15869,c_15857,c_15809,c_15811,c_15740,c_15735,c_14974,c_14967,c_14935,c_14410,c_14409,c_14408,c_14368,c_14320,c_14074,c_14062,c_14056,c_14034,c_13985,c_13806,c_13764,c_13761,c_13575,c_13551,c_12702,c_12684,c_12645,c_12638,c_12148,c_12135,c_12136,c_11783,c_11780,c_11770,c_11779,c_11243,c_11242,c_11241,c_11240,c_11239,c_11192,c_11188,c_10998,c_10101,c_9382,c_8403,c_7355,c_7141,c_6342,c_6265,c_6192,c_6144,c_6097,c_5959,c_4771,c_4759,c_3182,c_3084,c_3065,c_2232,c_2228,c_1923,c_1921,c_11791,c_1373,c_987,c_985,c_927,c_926,c_925,c_924,c_923,c_922,c_530,c_502,c_501,c_500,c_499,c_498,c_497,c_491,c_489,c_485,c_483,c_482,c_481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP319-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 14:29:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 10.31/2.17 % SZS status Started for theBenchmark.p
% 10.31/2.17 % SZS status Unsatisfiable for theBenchmark.p
% 10.31/2.17
% 10.31/2.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.31/2.17
% 10.31/2.17 % ------ iProver source info
% 10.31/2.17
% 10.31/2.17 % git: date: 2026-07-19 20:42:38 +0200
% 10.31/2.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.31/2.17 % git: non_committed_changes: false
% 10.31/2.17
% 10.31/2.17 % ------ Parsing...% successful
% 10.31/2.17
% 10.31/2.17
% 10.31/2.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.31/2.17
% 10.31/2.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.31/2.17
% 10.31/2.17 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.31/2.17
% 10.31/2.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.31/2.17 % ------ Proving...
% 10.31/2.17 % ------ Problem Properties
% 10.31/2.17
% 10.31/2.17 %
% 10.31/2.17 % clauses 57
% 10.31/2.17 % conjectures 42
% 10.31/2.17 % EPR 37
% 10.31/2.17 % Horn 20
% 10.31/2.17 % unary 15
% 10.31/2.17 % binary 36
% 10.31/2.17 % lits 108
% 10.31/2.17 % lits eq 98
% 10.31/2.17 % fd_pure 0
% 10.31/2.17 % fd_pseudo 0
% 10.31/2.17 % fd_cond 0
% 10.31/2.17 % fd_pseudo_cond 0
% 10.31/2.17 % AC symbols 0
% 10.31/2.17
% 10.31/2.17 % ------ Schedule dynamic 5 is on
% 10.31/2.17
% 10.31/2.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.31/2.17
% 10.31/2.17
% 10.31/2.17 % ------
% 10.31/2.17 % Current options:
% 10.31/2.17 % ------
% 10.31/2.17
% 10.31/2.17
% 10.31/2.17 %
% 10.31/2.17
% 10.31/2.17 % ------ Proving...
% 10.31/2.17 %
% 10.31/2.17
% 10.31/2.17 % SZS status Unsatisfiable for theBenchmark.p
% 10.31/2.17
% 10.31/2.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.31/2.18
% 10.31/2.18
%------------------------------------------------------------------------------