%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP383-1 : 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 : n019.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 01:33:36 PM UTC 2026
% Result : Unsatisfiable 33.22s 5.36s
% Output : CNFRefutation 33.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 46
% Syntax : Number of formulae : 339 ( 113 unt; 12 def)
% Number of atoms : 1108 ( 617 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 439 ( 132 ~; 307 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 92 !; 0 ?; 72 :)
% 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_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = inverse(sk_c4)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = inverse(sk_c5)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f28]) ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f44,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c7 = inverse(sk_c5)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c7,sk_c6)
| inverse(sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f74]) ).
fof(f76,plain,
! [X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c7 != multiply(X1,inverse(X1))
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c7,sk_c6)
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f75]) ).
tcf(c_88,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_121,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_123,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_125,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_126,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(inverse(X2),sk_c8) != sk_c7 )
| ( multiply(X2,inverse(X2)) != sk_c7 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_463,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_126]) ).
tcf(c_464,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_126]) ).
tcf(c_465,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c8) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_126]) ).
tcf(c_466,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_126]) ).
tcf(c_467,definition,
iPr_def_13 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_468,definition,
iPr_def_14 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_469,definition,
iPr_def_15 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_470,definition,
iPr_def_16 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_471,definition,
iPr_def_17 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_472,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_473,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_474,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_475,definition,
iPr_def_21 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_476,definition,
iPr_def_22 = multiply(sk_c2,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_477,definition,
iPr_def_23 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_478,definition,
iPr_def_24 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_479,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c8 )
| ( iPr_def_13 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_466,c_469,c_468,c_467]) ).
tcf(c_480,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c8) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_465]) ).
tcf(c_481,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_464]) ).
tcf(c_483,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_463]) ).
tcf(c_484,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_125,c_471,c_470]) ).
tcf(c_485,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124,c_472]) ).
tcf(c_486,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_123,c_473]) ).
tcf(c_487,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_122,c_474]) ).
tcf(c_488,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_489,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_120,c_475]) ).
tcf(c_490,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_491,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_492,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_493,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_494,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_476]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_14 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_519,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_884,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_497,c_496]) ).
tcf(c_885,plain,
( ( sk_c7 = iPr_def_22 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_497,c_469]) ).
tcf(c_899,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c7,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_498,c_468]) ).
tcf(c_978,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_493,c_476]) ).
tcf(c_979,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_492,c_476]) ).
tcf(c_980,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_491,c_476]) ).
tcf(c_981,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_490,c_476]) ).
tcf(c_982,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_489,c_476]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_520]) ).
tcf(c_995,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_994]) ).
tcf(c_996,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_519]) ).
tcf(c_1006,plain,
( ( sk_c8 = iPr_def_19 )
| ( iPr_def_19 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_1007,plain,
( ( sk_c8 = iPr_def_20 )
| ( iPr_def_20 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_1021,plain,
multiply(iPr_def_15,sk_c8) = identity,
inference(superposition,[status(thm)],[c_469,c_89]) ).
tcf(c_1022,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_474,c_89]) ).
tcf(c_1023,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_472,c_89]) ).
tcf(c_1025,plain,
multiply(iPr_def_21,sk_c2) = identity,
inference(superposition,[status(thm)],[c_475,c_89]) ).
tcf(c_1027,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_994]) ).
tcf(c_1452,plain,
( ( sk_c8 = iPr_def_23 )
| ( iPr_def_23 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_1453,plain,
( ( sk_c8 = iPr_def_24 )
| ( iPr_def_24 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_1457,plain,
( ( sk_c8 = iPr_def_14 )
| ( iPr_def_14 != sk_c8 )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_1656,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( sk_c7 = iPr_def_16 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_511,c_509]) ).
tcf(c_1800,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_512,c_1021]) ).
tcf(c_1804,plain,
( ( sk_c8 = iPr_def_14 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_512,c_469]) ).
tcf(c_1896,plain,
( ( sk_c8 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 )
| ( sk_c8 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_1901,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_13) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_513,c_470]) ).
tcf(c_1902,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_513,c_468]) ).
tcf(c_1925,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_514,c_468]) ).
tcf(c_1926,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c8) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_514,c_467]) ).
tcf(c_1979,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_515,c_514]) ).
tcf(c_1984,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_18,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_515,c_468]) ).
tcf(c_1985,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_18,sk_c8) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_515,c_467]) ).
tcf(c_2054,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_15,iPr_def_19) = identity ) ),
inference(superposition,[status(thm)],[c_516,c_1021]) ).
tcf(c_2172,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_517,c_516]) ).
tcf(c_2187,plain,
( ( sk_c7 = iPr_def_15 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_517,c_469]) ).
tcf(c_2289,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_13) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_518,c_470]) ).
tcf(c_2315,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_89,c_481]) ).
tcf(c_2397,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_473,c_483]) ).
tcf(c_2398,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_477,c_483]) ).
tcf(c_2410,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2398,c_478]) ).
tcf(c_2414,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2397,c_474]) ).
tcf(c_2699,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_467,c_90]) ).
tcf(c_2700,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_473,c_90]) ).
tcf(c_2702,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_468,c_90]) ).
tcf(c_2705,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_471,c_90]) ).
tcf(c_2707,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_89,c_90]) ).
tcf(c_2709,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1021,c_90]) ).
tcf(c_2710,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1022,c_90]) ).
tcf(c_2711,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1023,c_90]) ).
tcf(c_2713,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1025,c_90]) ).
tcf(c_2718,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2713,c_88]) ).
tcf(c_2720,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2711,c_88]) ).
tcf(c_2721,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2710,c_88]) ).
tcf(c_2722,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2709,c_88]) ).
tcf(c_2894,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_884,c_467]) ).
tcf(c_3846,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1979,c_495]) ).
tcf(c_3847,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_22 )
| ( sk_c7 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1979,c_494]) ).
tcf(c_4271,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_470,c_2720]) ).
tcf(c_4274,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4271,c_90]) ).
tcf(c_4288,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_473,c_2721]) ).
tcf(c_4291,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4288,c_90]) ).
tcf(c_9301,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_518,c_1925]) ).
tcf(c_9326,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_516,c_1926]) ).
tcf(c_9382,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_18,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_518,c_1984]) ).
tcf(c_9407,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_516,c_1985]) ).
tcf(c_9950,plain,
multiply(sk_c4,iPr_def_13) = multiply(iPr_def_19,sk_c8),
inference(superposition,[status(thm)],[c_467,c_2700]) ).
tcf(c_9951,plain,
multiply(sk_c4,iPr_def_14) = multiply(iPr_def_19,sk_c6),
inference(superposition,[status(thm)],[c_468,c_2700]) ).
tcf(c_10190,plain,
multiply(iPr_def_20,multiply(iPr_def_19,sk_c6)) = iPr_def_14,
inference(superposition,[status(thm)],[c_9951,c_2721]) ).
tcf(c_13139,plain,
( ( sk_c8 = iPr_def_14 )
| ( sk_c7 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1656,c_511,c_996,c_1006,c_1457,c_1656,c_1896]) ).
tcf(c_13140,plain,
( ( sk_c7 = iPr_def_16 )
| ( sk_c8 = iPr_def_14 ) ),
inference(renaming,[status(thm)],[c_13139]) ).
tcf(c_13757,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c6,iPr_def_19) = multiply(iPr_def_18,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_9326,c_4274]) ).
tcf(c_13758,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c6,iPr_def_13) = multiply(iPr_def_18,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_9301,c_4274]) ).
tcf(c_13862,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2707,c_88]) ).
tcf(c_13889,plain,
multiply(inverse(sk_c7),iPr_def_13) = sk_c8,
inference(superposition,[status(thm)],[c_467,c_13862]) ).
tcf(c_13892,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_468,c_13862]) ).
tcf(c_13896,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_88,c_13862]) ).
tcf(c_13897,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_89,c_13862]) ).
tcf(c_13898,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_90,c_13862]) ).
tcf(c_13989,plain,
multiply(inverse(iPr_def_15),identity) = sk_c8,
inference(superposition,[status(thm)],[c_1021,c_13862]) ).
tcf(c_14059,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2722,c_13862]) ).
tcf(c_14060,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2721,c_13862]) ).
tcf(c_14061,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2720,c_13862]) ).
tcf(c_14063,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2718,c_13862]) ).
tcf(c_14111,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_13862,c_13862]) ).
tcf(c_15053,plain,
( ~ iPr_def_12
| ( inverse(inverse(identity)) != sk_c7 )
| ( multiply(inverse(inverse(identity)),sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_13896,c_480]) ).
tcf(c_15065,plain,
multiply(sk_c8,identity) = sk_c8,
inference(demodulation,[status(thm)],[c_13989,c_14059]) ).
tcf(c_15112,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_15065,c_2699]) ).
tcf(c_15115,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_15112,c_467]) ).
tcf(c_15394,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_13897,c_14111]) ).
tcf(c_15421,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_15394,c_4291]) ).
tcf(c_15424,plain,
multiply(sk_c6,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_15394,c_4274]) ).
tcf(c_15425,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_15394,c_2702]) ).
tcf(c_15434,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15394,c_13896]) ).
tcf(c_15439,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_15425,c_468]) ).
tcf(c_15440,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_15424,c_4271]) ).
tcf(c_15457,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_15434,c_89]) ).
tcf(c_16293,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_2410,c_501,c_502,c_996,c_1006,c_1007,c_1452,c_2414,c_2410]) ).
tcf(c_16295,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_16293,c_506,c_507,c_996,c_1006,c_1007,c_1453,c_2414,c_16293]) ).
tcf(c_16297,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c6 != iPr_def_13 )
| ( sk_c7 != iPr_def_15 )
| ( sk_c8 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_479,c_16295]) ).
tcf(c_16311,plain,
multiply(sk_c8,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_14059,c_89]) ).
tcf(c_16315,plain,
multiply(sk_c8,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_14059,c_15394]) ).
tcf(c_16359,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_19,iPr_def_15) = identity ) ),
inference(superposition,[status(thm)],[c_511,c_16311]) ).
tcf(c_16376,plain,
multiply(sk_c3,identity) = multiply(iPr_def_17,iPr_def_15),
inference(superposition,[status(thm)],[c_16311,c_2705]) ).
tcf(c_16377,plain,
multiply(sk_c7,identity) = multiply(iPr_def_13,iPr_def_15),
inference(superposition,[status(thm)],[c_16311,c_2699]) ).
tcf(c_16566,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_15) = multiply(iPr_def_20,identity) ) ),
inference(superposition,[status(thm)],[c_16359,c_4291]) ).
tcf(c_16756,plain,
inverse(iPr_def_15) = sk_c8,
inference(demodulation,[status(thm)],[c_16315,c_15394]) ).
tcf(c_16759,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_15,sk_c8) != sk_c7 )
| ( multiply(inverse(iPr_def_15),sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_16756,c_480]) ).
tcf(c_17051,plain,
multiply(iPr_def_17,iPr_def_15) = sk_c3,
inference(demodulation,[status(thm)],[c_16376,c_15394]) ).
tcf(c_17052,plain,
multiply(inverse(iPr_def_17),sk_c3) = iPr_def_15,
inference(superposition,[status(thm)],[c_17051,c_13862]) ).
tcf(c_17065,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),multiply(sk_c3,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_17052,c_90]) ).
tcf(c_17227,plain,
multiply(inverse(iPr_def_17),iPr_def_17) = multiply(iPr_def_15,sk_c8),
inference(superposition,[status(thm)],[c_471,c_17065]) ).
tcf(c_17250,plain,
multiply(inverse(iPr_def_17),sk_c3) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_15394,c_17065]) ).
tcf(c_17264,plain,
multiply(inverse(iPr_def_17),iPr_def_17) = identity,
inference(light_normalisation,[status(thm)],[c_17227,c_1021]) ).
tcf(c_17315,plain,
multiply(iPr_def_13,iPr_def_15) = sk_c7,
inference(demodulation,[status(thm)],[c_16377,c_15394]) ).
tcf(c_17318,plain,
multiply(inverse(iPr_def_13),sk_c7) = iPr_def_15,
inference(superposition,[status(thm)],[c_17315,c_13862]) ).
tcf(c_17340,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(iPr_def_13),iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_514,c_17318]) ).
tcf(c_17346,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_17318,c_90]) ).
tcf(c_17587,plain,
multiply(inverse(iPr_def_13),iPr_def_14) = multiply(iPr_def_15,sk_c6),
inference(superposition,[status(thm)],[c_468,c_17346]) ).
tcf(c_17602,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(inverse(iPr_def_13),iPr_def_14) = multiply(iPr_def_15,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_899,c_17346]) ).
tcf(c_17617,plain,
multiply(inverse(iPr_def_13),sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_15394,c_17346]) ).
tcf(c_18373,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_14060,c_89]) ).
tcf(c_18374,plain,
( ~ iPr_def_11
| ( multiply(sk_c4,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_20)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14060,c_481]) ).
tcf(c_18376,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_14060,c_13862]) ).
tcf(c_18377,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_14060,c_15394]) ).
tcf(c_18433,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(superposition,[status(thm)],[c_18373,c_2721]) ).
tcf(c_18438,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_18377,c_15394]) ).
tcf(c_18441,plain,
( ( sk_c4 = iPr_def_15 )
| ( sk_c7 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_2187,c_18438]) ).
tcf(c_18442,plain,
( ( sk_c4 = iPr_def_15 )
| ( sk_c8 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_1804,c_18438]) ).
tcf(c_18443,plain,
( ( sk_c4 = iPr_def_15 )
| ( sk_c7 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_885,c_18438]) ).
tcf(c_18480,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm)],[c_1022,c_18376]) ).
tcf(c_18485,plain,
multiply(sk_c4,sk_c7) = iPr_def_19,
inference(superposition,[status(thm)],[c_4288,c_18376]) ).
tcf(c_19077,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_15,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_18441,c_473]) ).
tcf(c_19124,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_18442,c_473]) ).
tcf(c_19439,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_15,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_18443,c_473]) ).
tcf(c_19968,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_14061,c_89]) ).
tcf(c_19969,plain,
( ~ iPr_def_11
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_18)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14061,c_481]) ).
tcf(c_19971,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_14061,c_13862]) ).
tcf(c_19972,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_14061,c_15394]) ).
tcf(c_19988,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_19972,c_15394]) ).
tcf(c_20145,plain,
multiply(sk_c5,identity) = sk_c5,
inference(superposition,[status(thm)],[c_1023,c_19971]) ).
tcf(c_20148,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_9407,c_19971]) ).
tcf(c_20150,plain,
multiply(sk_c5,sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_4271,c_19971]) ).
tcf(c_20743,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_3847,c_3846]) ).
tcf(c_24518,plain,
multiply(sk_c2,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_14063,c_89]) ).
tcf(c_24529,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_982,c_24518]) ).
tcf(c_24530,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_981,c_24518]) ).
tcf(c_24531,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_980,c_24518]) ).
tcf(c_24532,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_979,c_24518]) ).
tcf(c_24533,plain,
( ( identity = iPr_def_22 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_978,c_24518]) ).
tcf(c_25673,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24530,c_24529]) ).
tcf(c_26236,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24532,c_24531]) ).
tcf(c_26298,plain,
( ( identity = iPr_def_22 )
| ( inverse(iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_24532,c_469]) ).
tcf(c_26303,plain,
( ( identity = iPr_def_22 )
| ( sk_c4 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_26298,c_18438]) ).
tcf(c_26471,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c7,iPr_def_13) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_24533,c_468]) ).
tcf(c_26919,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_25673,c_15434]) ).
tcf(c_26964,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_26236,c_88]) ).
tcf(c_27014,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_15,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_26303,c_473]) ).
tcf(c_28885,plain,
( ( identity = iPr_def_22 )
| ( multiply(inverse(iPr_def_13),iPr_def_14) = multiply(iPr_def_15,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_26471,c_17346]) ).
tcf(c_32509,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_26964,c_2894]) ).
tcf(c_32976,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_13,iPr_def_15) = identity ) ),
inference(superposition,[status(thm)],[c_32509,c_16311]) ).
tcf(c_33053,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_32976,c_17315]) ).
tcf(c_34103,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_33053,c_2172]) ).
tcf(c_34117,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c4,identity) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_33053,c_473]) ).
tcf(c_34403,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_15) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_34103,c_15434]) ).
tcf(c_34408,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_34403,c_16756]) ).
tcf(c_35469,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c4 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_34117,c_15394]) ).
tcf(c_35516,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_35469,c_474]) ).
tcf(c_35607,plain,
( ( iPr_def_19 = iPr_def_20 )
| ~ iPr_def_12
| ( multiply(iPr_def_19,iPr_def_20) != sk_c7 )
| ( multiply(inverse(iPr_def_19),sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_35516,c_480]) ).
tcf(c_47364,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_15) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_20743,c_26919]) ).
tcf(c_47371,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_47364,c_16756]) ).
tcf(c_89074,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_13)) = sk_c8,
inference(superposition,[status(thm)],[c_467,c_13898]) ).
tcf(c_89077,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),multiply(X0,iPr_def_16)) = sk_c6,
inference(superposition,[status(thm)],[c_20150,c_13898]) ).
tcf(c_89079,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_14)) = sk_c6,
inference(superposition,[status(thm)],[c_468,c_13898]) ).
tcf(c_89126,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(multiply(X0,sk_c5)),multiply(X0,iPr_def_16)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1901,c_13898]) ).
tcf(c_89190,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_15)),multiply(X0,identity)) = sk_c8,
inference(superposition,[status(thm)],[c_1021,c_13898]) ).
tcf(c_89202,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(multiply(X0,iPr_def_15)),multiply(X0,identity)) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1800,c_13898]) ).
tcf(c_89207,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,iPr_def_15)),multiply(X0,identity)) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2054,c_13898]) ).
tcf(c_89257,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,iPr_def_16)),multiply(X0,iPr_def_14)) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1925,c_13898]) ).
tcf(c_89385,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,iPr_def_16)),multiply(X0,iPr_def_14)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9301,c_13898]) ).
tcf(c_89431,plain,
! [X0: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_13))),multiply(X0,iPr_def_15)) = sk_c7,
inference(superposition,[status(thm)],[c_17318,c_13898]) ).
tcf(c_89464,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,inverse(iPr_def_13))),multiply(X0,iPr_def_15)) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_17340,c_13898]) ).
tcf(c_89522,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_15)),X0) = sk_c8,
inference(light_normalisation,[status(thm)],[c_89190,c_15394]) ).
tcf(c_90055,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,iPr_def_15)),X0) = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_89207,c_15394]) ).
tcf(c_90067,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(multiply(X0,iPr_def_15)),X0) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_89202,c_15394]) ).
tcf(c_93642,plain,
multiply(inverse(identity),multiply(inverse(sk_c7),iPr_def_13)) = sk_c8,
inference(superposition,[status(thm)],[c_89,c_89074]) ).
tcf(c_93738,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(multiply(sk_c7,sk_c7)),iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_1902,c_89074]) ).
tcf(c_93780,plain,
multiply(identity,sk_c8) = sk_c8,
inference(light_normalisation,[status(thm)],[c_93642,c_13889,c_15434]) ).
tcf(c_95337,plain,
multiply(inverse(identity),multiply(inverse(sk_c7),iPr_def_14)) = sk_c6,
inference(superposition,[status(thm)],[c_89,c_89079]) ).
tcf(c_95429,plain,
multiply(inverse(multiply(inverse(iPr_def_14),sk_c7)),identity) = sk_c6,
inference(superposition,[status(thm)],[c_89,c_89079]) ).
tcf(c_95472,plain,
multiply(identity,sk_c6) = sk_c6,
inference(light_normalisation,[status(thm)],[c_95337,c_13892,c_15434]) ).
tcf(c_96357,plain,
inverse(multiply(inverse(iPr_def_14),sk_c7)) = sk_c6,
inference(demodulation,[status(thm)],[c_95429,c_15394]) ).
tcf(c_96433,plain,
( ~ iPr_def_12
| ( multiply(multiply(inverse(iPr_def_14),sk_c7),sk_c6) != sk_c7 )
| ( multiply(inverse(multiply(inverse(iPr_def_14),sk_c7)),sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_96357,c_480]) ).
tcf(c_96434,plain,
multiply(sk_c6,multiply(inverse(iPr_def_14),sk_c7)) = identity,
inference(superposition,[status(thm)],[c_96357,c_89]) ).
tcf(c_96609,plain,
( ~ iPr_def_12
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(multiply(inverse(iPr_def_14),sk_c7),sk_c6) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_96433,c_96357]) ).
tcf(c_122862,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_96609,c_96434,c_96357,c_93738,c_89464,c_89431,c_90067,c_90055,c_89522,c_89385,c_89257,c_89126,c_89077,c_47371,c_35607,c_34408,c_28885,c_27014,c_95472,c_20150,c_20148,c_20145,c_19988,c_19969,c_19968,c_19439,c_19124,c_19077,c_18485,c_18480,c_18438,c_18433,c_18374,c_17617,c_17602,c_17587,c_17318,c_17315,c_17264,c_17250,c_17227,c_17051,c_16759,c_16756,c_16566,c_16377,c_16311,c_16297,c_15440,c_15439,c_15425,c_15424,c_15421,c_15434,c_15115,c_15112,c_15053,c_13892,c_13889,c_13758,c_13757,c_13140,c_10190,c_9951,c_9950,c_9407,c_9382,c_2315,c_2289,c_15457,c_1022,c_93780,c_488,c_487,c_486,c_485,c_484,c_474,c_472,c_469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:38:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 33.22/5.36 % SZS status Started for theBenchmark.p
% 33.22/5.36 % SZS status Unsatisfiable for theBenchmark.p
% 33.22/5.36
% 33.22/5.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.22/5.36
% 33.22/5.36 % ------ iProver source info
% 33.22/5.36
% 33.22/5.36 % git: date: 2026-07-19 20:42:38 +0200
% 33.22/5.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.22/5.36 % git: non_committed_changes: false
% 33.22/5.36
% 33.22/5.36 % ------ Parsing...% successful
% 33.22/5.36
% 33.22/5.36
% 33.22/5.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 33.22/5.36
% 33.22/5.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 33.22/5.36
% 33.22/5.36 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 33.22/5.36
% 33.22/5.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 33.22/5.36 % ------ Proving...
% 33.22/5.36 % ------ Problem Properties
% 33.22/5.36
% 33.22/5.36 %
% 33.22/5.36 % clauses 54
% 33.22/5.36 % conjectures 39
% 33.22/5.36 % EPR 36
% 33.22/5.36 % Horn 18
% 33.22/5.36 % unary 15
% 33.22/5.36 % binary 35
% 33.22/5.36 % lits 100
% 33.22/5.36 % lits eq 94
% 33.22/5.36 % fd_pure 0
% 33.22/5.36 % fd_pseudo 0
% 33.22/5.36 % fd_cond 0
% 33.22/5.36 % fd_pseudo_cond 0
% 33.22/5.36 % AC symbols 0
% 33.22/5.36
% 33.22/5.36 % ------ Schedule dynamic 5 is on
% 33.22/5.36
% 33.22/5.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 33.22/5.36
% 33.22/5.36
% 33.22/5.36 % ------
% 33.22/5.36 % Current options:
% 33.22/5.36 % ------
% 33.22/5.36
% 33.22/5.36
% 33.22/5.36 %
% 33.22/5.36
% 33.22/5.36 % ------ Proving...
% 33.22/5.36 %
% 33.22/5.36
% 33.22/5.36 % SZS status Unsatisfiable for theBenchmark.p
% 33.22/5.36
% 33.22/5.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 33.22/5.37
% 33.22/5.37
%------------------------------------------------------------------------------