TSTP Solution File: GRP300-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP300-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:58:18 EDT 2024
% Result : Unsatisfiable 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 35
% Syntax : Number of formulae : 258 ( 41 unt; 0 def)
% Number of atoms : 919 ( 455 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1239 ( 578 ~; 654 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 159 ( 159 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1098,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f141,f155,f465,f507,f607,f650,f704,f1007,f1026,f1030,f1032,f1036,f1044,f1047,f1097]) ).
fof(f1097,plain,
( spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1096]) ).
fof(f1096,plain,
( $false
| spl0_4
| ~ spl0_7 ),
inference(global_subsumption,[],[f24,f6,f1,f2,f18,f3,f28,f8,f5,f4,f20,f17,f16,f9,f21,f19,f7,f55,f365,f23,f26,f22,f27,f25,f13,f361,f15,f10,f14,f11,f12,f649,f362,f814,f594,f817,f818,f815,f807,f851,f864,f376,f876,f880,f881,f883,f884,f875,f931,f909,f938,f898,f952,f953,f874,f974,f1005,f986,f1087,f1093,f1095]) ).
fof(f1095,plain,
( sk_c6 != sk_c4
| spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1094,f875]) ).
fof(f1094,plain,
( sk_c4 != multiply(sk_c6,identity)
| spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f149,f649]) ).
fof(f149,plain,
( multiply(sk_c6,sk_c5) != sk_c4
| spl0_4 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl0_4
<=> multiply(sk_c6,sk_c5) = sk_c4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1093,plain,
( sk_c6 = sk_c4
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f1092]) ).
fof(f1092,plain,
( sk_c6 = sk_c4
| sk_c6 = sk_c4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1091,f875]) ).
fof(f1091,plain,
( sk_c4 = multiply(sk_c6,identity)
| sk_c6 = sk_c4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1090,f649]) ).
fof(f1090,plain,
( sk_c6 = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1089,f1]) ).
fof(f1089,plain,
( sk_c6 = multiply(identity,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f4,f649]) ).
fof(f1087,plain,
( sk_c6 = sk_c4
| identity = multiply(sk_c2,sk_c6)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1086,f875]) ).
fof(f1086,plain,
( sk_c4 = multiply(sk_c6,identity)
| identity = multiply(sk_c2,sk_c6)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1085,f649]) ).
fof(f1085,plain,
( identity = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5,f649]) ).
fof(f986,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f3,f874]) ).
fof(f1005,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f984,f1]) ).
fof(f984,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f874]) ).
fof(f974,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f874,f3]) ).
fof(f874,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f376,f2]) ).
fof(f953,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f2,f898]) ).
fof(f952,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f55,f898]) ).
fof(f898,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f875,f362]) ).
fof(f938,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f923,f875]) ).
fof(f923,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f376,f875]) ).
fof(f909,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f362,f875]) ).
fof(f931,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f906,f875]) ).
fof(f906,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f875,f376]) ).
fof(f875,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f376,f362]) ).
fof(f884,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f55,f376]) ).
fof(f883,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f362,f376]) ).
fof(f881,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
inference(superposition,[],[f55,f376]) ).
fof(f880,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f2,f376]) ).
fof(f876,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f376,f55]) ).
fof(f376,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[],[f55,f55]) ).
fof(f864,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f852,f1]) ).
fof(f852,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)),
inference(superposition,[],[f3,f807]) ).
fof(f851,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f55,f807]) ).
fof(f807,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f55,f362]) ).
fof(f815,plain,
identity = inverse(identity),
inference(superposition,[],[f594,f2]) ).
fof(f818,plain,
! [X0] : multiply(inverse(inverse(inverse(identity))),X0) = X0,
inference(superposition,[],[f55,f594]) ).
fof(f817,plain,
identity = inverse(identity),
inference(superposition,[],[f2,f594]) ).
fof(f594,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[],[f55,f361]) ).
fof(f814,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(forward_demodulation,[],[f808,f1]) ).
fof(f808,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),multiply(identity,X1)),
inference(superposition,[],[f3,f362]) ).
fof(f362,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f55,f2]) ).
fof(f649,plain,
( identity = sk_c5
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f647,plain,
( spl0_7
<=> identity = sk_c5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f12,axiom,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f11,axiom,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f14,axiom,
( sk_c5 = multiply(sk_c3,sk_c4)
| sk_c5 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f10,axiom,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f15,axiom,
( sk_c4 = inverse(sk_c3)
| sk_c5 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f361,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f55,f1]) ).
fof(f13,axiom,
( sk_c4 = inverse(sk_c6)
| sk_c5 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f25,axiom,
( sk_c4 = inverse(sk_c6)
| sk_c5 = multiply(sk_c4,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f27,axiom,
( sk_c4 = inverse(sk_c3)
| sk_c5 = multiply(sk_c4,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f22,axiom,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f26,axiom,
( sk_c5 = multiply(sk_c3,sk_c4)
| sk_c5 = multiply(sk_c4,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f23,axiom,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f365,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f55,f3]) ).
fof(f55,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f47,f1]) ).
fof(f47,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f3,f2]) ).
fof(f7,axiom,
( sk_c4 = inverse(sk_c6)
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f19,axiom,
( sk_c4 = inverse(sk_c6)
| sk_c6 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f21,axiom,
( sk_c4 = inverse(sk_c3)
| sk_c6 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f9,axiom,
( sk_c4 = inverse(sk_c3)
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,axiom,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f17,axiom,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c2,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f20,axiom,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c3,sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f4,axiom,
( sk_c6 = multiply(sk_c5,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f5,axiom,
( sk_c5 = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,axiom,
( sk_c5 = multiply(sk_c3,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f28,axiom,
! [X3,X4,X5] :
( sk_c4 != inverse(sk_c6)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c4,sk_c6)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4)
| multiply(sk_c6,sk_c5) != sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f18,axiom,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f24,axiom,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f1047,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f1046]) ).
fof(f1046,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f1045,f36]) ).
fof(f36,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f34,plain,
( spl0_2
<=> sk_c6 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1045,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f1016,f523]) ).
fof(f523,plain,
( identity = multiply(sk_c4,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f2,f154]) ).
fof(f154,plain,
( sk_c4 = inverse(sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f152,plain,
( spl0_5
<=> sk_c4 = inverse(sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1016,plain,
( identity != multiply(sk_c4,sk_c6)
| sk_c6 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f140,f634]) ).
fof(f634,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c2,X0)
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f633,f1]) ).
fof(f633,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c4,multiply(identity,X0))
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f3,f623]) ).
fof(f623,plain,
( sk_c2 = multiply(sk_c4,identity)
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f621,f154]) ).
fof(f621,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_2 ),
inference(superposition,[],[f55,f620]) ).
fof(f620,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f2,f36]) ).
fof(f140,plain,
( ! [X3] :
( identity != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f139,plain,
( spl0_3
<=> ! [X3] :
( sk_c6 != inverse(X3)
| identity != multiply(X3,sk_c6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1044,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1043]) ).
fof(f1043,plain,
( $false
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f1042,f898]) ).
fof(f1042,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3 ),
inference(forward_demodulation,[],[f1019,f898]) ).
fof(f1019,plain,
( sk_c6 != inverse(inverse(inverse(inverse(sk_c6))))
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f1015]) ).
fof(f1015,plain,
( identity != identity
| sk_c6 != inverse(inverse(inverse(inverse(sk_c6))))
| ~ spl0_3 ),
inference(superposition,[],[f140,f807]) ).
fof(f1036,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1035]) ).
fof(f1035,plain,
( $false
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f1020,f898]) ).
fof(f1020,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f1012]) ).
fof(f1012,plain,
( identity != identity
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3 ),
inference(superposition,[],[f140,f2]) ).
fof(f1032,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1031]) ).
fof(f1031,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f1021,f747]) ).
fof(f747,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f36,f742]) ).
fof(f742,plain,
( sk_c6 = sk_c2
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f714,f731]) ).
fof(f731,plain,
( sk_c6 = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f706,f708]) ).
fof(f708,plain,
( sk_c6 = sk_c4
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f707,f532]) ).
fof(f532,plain,
( sk_c6 = multiply(inverse(sk_c4),identity)
| ~ spl0_5 ),
inference(superposition,[],[f55,f523]) ).
fof(f707,plain,
( sk_c4 = multiply(inverse(sk_c4),identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f628,f649]) ).
fof(f628,plain,
( sk_c4 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f55,f608]) ).
fof(f608,plain,
( sk_c5 = multiply(sk_c4,sk_c4)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f385,f154]) ).
fof(f385,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c4)
| ~ spl0_4 ),
inference(superposition,[],[f55,f150]) ).
fof(f150,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f706,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f150,f649]) ).
fof(f714,plain,
( sk_c2 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f623,f708]) ).
fof(f1021,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f1010]) ).
fof(f1010,plain,
( identity != identity
| sk_c6 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f140,f710]) ).
fof(f710,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f523,f708]) ).
fof(f1030,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1029]) ).
fof(f1029,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f1028,f747]) ).
fof(f1028,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1027,f708]) ).
fof(f1027,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1022,f898]) ).
fof(f1022,plain,
( sk_c6 != inverse(inverse(inverse(sk_c4)))
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f1009]) ).
fof(f1009,plain,
( identity != identity
| sk_c6 != inverse(inverse(inverse(sk_c4)))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f140,f638]) ).
fof(f638,plain,
( identity = multiply(inverse(inverse(sk_c4)),sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f55,f532]) ).
fof(f1026,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1025]) ).
fof(f1025,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f1024,f747]) ).
fof(f1024,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1023,f708]) ).
fof(f1023,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f1008]) ).
fof(f1008,plain,
( identity != identity
| sk_c6 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f140,f523]) ).
fof(f1007,plain,
( spl0_3
| spl0_3
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f839,f647,f152,f148,f139,f139,f139]) ).
fof(f839,plain,
( ! [X3,X4,X5] :
( identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f838,f1]) ).
fof(f838,plain,
( ! [X3,X4,X5] :
( sk_c6 != multiply(identity,sk_c6)
| identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f837,f708]) ).
fof(f837,plain,
( ! [X3,X4,X5] :
( identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c6 != multiply(identity,sk_c4) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f836,f708]) ).
fof(f836,plain,
( ! [X3,X4,X5] :
( sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X5,sk_c4)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c6 != multiply(identity,sk_c4) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f835,f708]) ).
fof(f835,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X5,sk_c4)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c6 != multiply(identity,sk_c4) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f618,f649]) ).
fof(f618,plain,
( ! [X3,X4,X5] :
( identity != sk_c5
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X5,sk_c4)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c6 != multiply(identity,sk_c4) )
| ~ spl0_4
| ~ spl0_5 ),
inference(inner_rewriting,[],[f617]) ).
fof(f617,plain,
( ! [X3,X4,X5] :
( identity != sk_c5
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f616,f523]) ).
fof(f616,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c4,sk_c6)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| ~ spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f508,f154]) ).
fof(f508,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(sk_c6)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c4,sk_c6)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f28,f150]) ).
fof(f704,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f703]) ).
fof(f703,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(subsumption_resolution,[],[f702,f648]) ).
fof(f648,plain,
( identity != sk_c5
| spl0_7 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f702,plain,
( identity = sk_c5
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(forward_demodulation,[],[f700,f2]) ).
fof(f700,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(superposition,[],[f55,f699]) ).
fof(f699,plain,
( sk_c4 = multiply(sk_c4,sk_c5)
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(forward_demodulation,[],[f697,f154]) ).
fof(f697,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(superposition,[],[f55,f695]) ).
fof(f695,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(forward_demodulation,[],[f694,f655]) ).
fof(f655,plain,
( sk_c6 = sk_c3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f653,f532]) ).
fof(f653,plain,
( sk_c3 = multiply(inverse(sk_c4),identity)
| ~ spl0_6 ),
inference(superposition,[],[f55,f652]) ).
fof(f652,plain,
( identity = multiply(sk_c4,sk_c3)
| ~ spl0_6 ),
inference(superposition,[],[f2,f645]) ).
fof(f645,plain,
( sk_c4 = inverse(sk_c3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f643,plain,
( spl0_6
<=> sk_c4 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f694,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| ~ spl0_5
| spl0_7 ),
inference(subsumption_resolution,[],[f611,f648]) ).
fof(f611,plain,
( identity = sk_c5
| sk_c5 = multiply(sk_c3,sk_c4)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f26,f523]) ).
fof(f650,plain,
( spl0_6
| spl0_7
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f609,f152,f647,f643]) ).
fof(f609,plain,
( identity = sk_c5
| sk_c4 = inverse(sk_c3)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f27,f523]) ).
fof(f607,plain,
( spl0_3
| spl0_3
| spl0_3
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f579,f152,f148,f34,f30,f139,f139,f139]) ).
fof(f30,plain,
( spl0_1
<=> sk_c6 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f579,plain,
( ! [X3,X4,X5] :
( sk_c6 != inverse(X5)
| identity != multiply(X5,sk_c6)
| identity != multiply(X3,sk_c6)
| identity != multiply(X4,sk_c6)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f578,f545]) ).
fof(f545,plain,
( sk_c6 = sk_c4
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f535,f536]) ).
fof(f536,plain,
( sk_c6 = multiply(sk_c6,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f527,f530]) ).
fof(f530,plain,
( identity = sk_c5
| spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f523,f511]) ).
fof(f511,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| spl0_2 ),
inference(subsumption_resolution,[],[f24,f35]) ).
fof(f35,plain,
( sk_c6 != inverse(sk_c2)
| spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f527,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[],[f525,f32]) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f525,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c5)
| spl0_2 ),
inference(superposition,[],[f55,f510]) ).
fof(f510,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| spl0_2 ),
inference(subsumption_resolution,[],[f12,f35]) ).
fof(f535,plain,
( sk_c4 = multiply(sk_c6,identity)
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f150,f530]) ).
fof(f578,plain,
( ! [X3,X4,X5] :
( identity != multiply(X5,sk_c6)
| identity != multiply(X3,sk_c6)
| identity != multiply(X4,sk_c6)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f577,f545]) ).
fof(f577,plain,
( ! [X3,X4,X5] :
( identity != multiply(X3,sk_c6)
| identity != multiply(X4,sk_c6)
| identity != multiply(X5,sk_c4)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f576,f1]) ).
fof(f576,plain,
( ! [X3,X4,X5] :
( sk_c6 != multiply(identity,sk_c6)
| identity != multiply(X3,sk_c6)
| identity != multiply(X4,sk_c6)
| identity != multiply(X5,sk_c4)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f544,f545]) ).
fof(f544,plain,
( ! [X3,X4,X5] :
( sk_c6 != multiply(identity,sk_c4)
| identity != multiply(X3,sk_c6)
| identity != multiply(X4,sk_c6)
| identity != multiply(X5,sk_c4)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3) )
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f543,f530]) ).
fof(f543,plain,
( ! [X3,X4,X5] :
( identity != multiply(X3,sk_c6)
| identity != multiply(X4,sk_c6)
| identity != multiply(X5,sk_c4)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(sk_c5,sk_c4) )
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f542,f530]) ).
fof(f542,plain,
( ! [X3,X4,X5] :
( identity != multiply(X4,sk_c6)
| identity != multiply(X5,sk_c4)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f541,f530]) ).
fof(f541,plain,
( ! [X3,X4,X5] :
( identity != multiply(X5,sk_c4)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f540,f530]) ).
fof(f540,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f509,f154]) ).
fof(f509,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(sk_c6)
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4) )
| spl0_2
| ~ spl0_4 ),
inference(global_subsumption,[],[f12,f24,f6,f1,f2,f18,f3,f28,f26,f23,f22,f14,f11,f10,f8,f5,f4,f27,f25,f20,f17,f16,f15,f13,f9,f21,f19,f7,f150,f156,f55,f361,f362,f365,f376,f35,f508]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_4 ),
inference(superposition,[],[f3,f150]) ).
fof(f507,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f506,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(subsumption_resolution,[],[f503,f160]) ).
fof(f160,plain,
( sk_c6 = sk_c4
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f158,f150]) ).
fof(f158,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_1
| spl0_5 ),
inference(superposition,[],[f144,f157]) ).
fof(f157,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| spl0_5 ),
inference(subsumption_resolution,[],[f13,f153]) ).
fof(f153,plain,
( sk_c4 != inverse(sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c1,X0)) = X0
| ~ spl0_1 ),
inference(forward_demodulation,[],[f143,f1]) ).
fof(f143,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c1,X0))
| ~ spl0_1 ),
inference(superposition,[],[f3,f142]) ).
fof(f142,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_1 ),
inference(superposition,[],[f2,f32]) ).
fof(f503,plain,
( sk_c6 != sk_c4
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f153,f494]) ).
fof(f494,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f32,f493]) ).
fof(f493,plain,
( sk_c6 = sk_c1
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f447,f438]) ).
fof(f438,plain,
( sk_c6 = multiply(sk_c6,identity)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f425,f160]) ).
fof(f425,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f150,f413]) ).
fof(f413,plain,
( identity = sk_c5
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f412,f2]) ).
fof(f412,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f385,f160]) ).
fof(f447,plain,
( sk_c1 = multiply(sk_c6,identity)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f433,f1]) ).
fof(f433,plain,
( multiply(sk_c6,identity) = multiply(identity,sk_c1)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f212,f413]) ).
fof(f212,plain,
( multiply(sk_c6,identity) = multiply(sk_c5,sk_c1)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f165,f142]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c6,X0))
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f3,f164]) ).
fof(f164,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f163,f160]) ).
fof(f163,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| spl0_5 ),
inference(subsumption_resolution,[],[f25,f153]) ).
fof(f465,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f464,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(subsumption_resolution,[],[f461,f160]) ).
fof(f461,plain,
( sk_c6 != sk_c4
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f153,f449]) ).
fof(f449,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f36,f441]) ).
fof(f441,plain,
( sk_c6 = sk_c2
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f440,f1]) ).
fof(f440,plain,
( sk_c2 = multiply(identity,sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f439,f330]) ).
fof(f330,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f266,f38]) ).
fof(f38,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f2,f36]) ).
fof(f266,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = X0
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f262,f246]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f245,f1]) ).
fof(f245,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(identity,X0))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f3,f236]) ).
fof(f236,plain,
( identity = multiply(sk_c5,identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f226,f165]) ).
fof(f226,plain,
( identity = multiply(sk_c6,multiply(sk_c6,identity))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f187,f211]) ).
fof(f211,plain,
( multiply(sk_c6,identity) = multiply(sk_c5,sk_c2)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f165,f38]) ).
fof(f187,plain,
( identity = multiply(sk_c6,multiply(sk_c5,sk_c2))
| ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(superposition,[],[f144,f174]) ).
fof(f174,plain,
( multiply(sk_c5,sk_c2) = multiply(sk_c1,identity)
| ~ spl0_2
| spl0_5 ),
inference(superposition,[],[f159,f38]) ).
fof(f159,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| spl0_5 ),
inference(superposition,[],[f3,f157]) ).
fof(f262,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c5,X0)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f159,f256]) ).
fof(f256,plain,
( sk_c2 = sk_c1
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f249,f246]) ).
fof(f249,plain,
( sk_c1 = multiply(sk_c5,sk_c2)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f246,f191]) ).
fof(f191,plain,
( multiply(sk_c5,sk_c2) = multiply(sk_c5,sk_c1)
| ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(forward_demodulation,[],[f175,f174]) ).
fof(f175,plain,
( multiply(sk_c1,identity) = multiply(sk_c5,sk_c1)
| ~ spl0_1
| spl0_5 ),
inference(superposition,[],[f159,f142]) ).
fof(f439,plain,
( multiply(identity,sk_c6) = multiply(sk_c2,identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f427,f256]) ).
fof(f427,plain,
( multiply(identity,sk_c6) = multiply(sk_c1,identity)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f171,f413]) ).
fof(f171,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c1,sk_c5)
| ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(superposition,[],[f159,f164]) ).
fof(f155,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f7,f152,f148]) ).
fof(f141,plain,
( spl0_3
| spl0_3
| spl0_3
| spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f106,f34,f30,f139,f139,f139]) ).
fof(f106,plain,
( ! [X3,X4,X5] :
( identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6) )
| spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f105,f81]) ).
fof(f81,plain,
( sk_c6 = sk_c4
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f78,f1]) ).
fof(f78,plain,
( sk_c6 = multiply(identity,sk_c4)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f43,f76]) ).
fof(f76,plain,
( identity = sk_c5
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f74,f40]) ).
fof(f40,plain,
( identity = multiply(sk_c4,sk_c6)
| spl0_1 ),
inference(superposition,[],[f2,f39]) ).
fof(f39,plain,
( sk_c4 = inverse(sk_c6)
| spl0_1 ),
inference(subsumption_resolution,[],[f19,f31]) ).
fof(f31,plain,
( sk_c6 != inverse(sk_c1)
| spl0_1 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f74,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f58,f70]) ).
fof(f70,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f59,f44]) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| spl0_1 ),
inference(subsumption_resolution,[],[f17,f31]) ).
fof(f59,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f53,f1]) ).
fof(f53,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f38]) ).
fof(f58,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c6,X0)) = X0
| spl0_1 ),
inference(forward_demodulation,[],[f49,f1]) ).
fof(f49,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c4,multiply(sk_c6,X0))
| spl0_1 ),
inference(superposition,[],[f3,f40]) ).
fof(f43,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| spl0_1 ),
inference(subsumption_resolution,[],[f16,f31]) ).
fof(f105,plain,
( ! [X3,X4,X5] :
( sk_c6 != sk_c4
| identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6) )
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f104,f77]) ).
fof(f77,plain,
( sk_c6 = multiply(sk_c6,identity)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f70,f76]) ).
fof(f104,plain,
( ! [X3,X4,X5] :
( identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c4 != multiply(sk_c6,identity) )
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f103,f81]) ).
fof(f103,plain,
( ! [X3,X4,X5] :
( sk_c6 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X5,sk_c4)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c4 != multiply(sk_c6,identity) )
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f102,f81]) ).
fof(f102,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X5,sk_c4)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c4 != multiply(sk_c6,identity) )
| spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f64,f76]) ).
fof(f64,plain,
( ! [X3,X4,X5] :
( identity != sk_c5
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| identity != multiply(X5,sk_c4)
| identity != multiply(X4,sk_c6)
| identity != multiply(X3,sk_c6)
| sk_c4 != multiply(sk_c6,identity) )
| spl0_1 ),
inference(inner_rewriting,[],[f63]) ).
fof(f63,plain,
( ! [X3,X4,X5] :
( identity != sk_c5
| sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| multiply(sk_c6,sk_c5) != sk_c4 )
| spl0_1 ),
inference(forward_demodulation,[],[f62,f40]) ).
fof(f62,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c4,sk_c6)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| multiply(sk_c6,sk_c5) != sk_c4 )
| spl0_1 ),
inference(subsumption_resolution,[],[f61,f43]) ).
fof(f61,plain,
( ! [X3,X4,X5] :
( sk_c4 != inverse(X5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c4,sk_c6)
| sk_c5 != multiply(X5,sk_c4)
| sk_c5 != multiply(X4,sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4)
| multiply(sk_c6,sk_c5) != sk_c4 )
| spl0_1 ),
inference(subsumption_resolution,[],[f28,f39]) ).
fof(f37,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f18,f34,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP300-1 : TPTP v8.1.2. Released v2.5.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 04:25:44 EDT 2024
% 0.22/0.35 % CPUTime :
% 0.22/0.36 % (24711)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37 % (24714)WARNING: value z3 for option sas not known
% 0.22/0.38 % (24712)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (24715)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (24716)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.38 % (24717)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.38 % (24718)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38 % (24714)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (24713)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [4]
% 0.22/0.40 TRYING [4]
% 0.22/0.40 TRYING [5]
% 0.22/0.40 % (24714)First to succeed.
% 0.22/0.41 % (24714)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (24714)------------------------------
% 0.22/0.41 % (24714)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41 % (24714)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (24714)Memory used [KB]: 1067
% 0.22/0.41 % (24714)Time elapsed: 0.033 s
% 0.22/0.41 % (24714)Instructions burned: 57 (million)
% 0.22/0.41 % (24714)------------------------------
% 0.22/0.41 % (24714)------------------------------
% 0.22/0.41 % (24711)Success in time 0.05 s
%------------------------------------------------------------------------------