%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 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 : Tue Sep 29 10:13:23 AM UTC 2026
% Result : Unsatisfiable 2.57s 1.38s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 35
% Syntax : Number of formulae : 174 ( 19 unt; 15 def)
% Number of atoms : 432 ( 163 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 469 ( 211 ~; 243 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f21,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| multiply(sk_c7,X1) != sk_c6
| multiply(X2,sk_c7) != X1
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != multiply(sk_c7,X1)
| multiply(X2,sk_c7) != X1
| sk_c7 != inverse(X2)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X3,X0,X4] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(equality_resolution,[],[f46]) ).
fof(f49,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_2
<=> ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f53,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,definition,
( spl0_3
<=> ! [X2] :
( sk_c6 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( ! [X2] :
( sk_c6 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f47,f52,f55,f52,f49]) ).
fof(f59,definition,
( spl0_4
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f61,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_5
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f63,f59]) ).
fof(f68,definition,
( spl0_6
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f70,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f63,f68]) ).
fof(f73,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f75,plain,
( sk_c7 = multiply(sk_c4,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f63,f73]) ).
fof(f78,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f80,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f38,f63,f78]) ).
fof(f83,definition,
( spl0_9
<=> sk_c3 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f85,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f36,f83,f59]) ).
fof(f87,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f83,f68]) ).
fof(f88,plain,
( spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f32,f83,f73]) ).
fof(f89,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f30,f83,f78]) ).
fof(f91,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c7,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f93,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f28,f91,f59]) ).
fof(f95,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f26,f91,f68]) ).
fof(f96,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f24,f91,f73]) ).
fof(f97,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f22,f91,f78]) ).
fof(f99,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f104,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f16,f99,f73]) ).
fof(f105,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f14,f99,f78]) ).
fof(f107,definition,
( spl0_12
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f109,plain,
( inverse(sk_c1) = sk_c7
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f112,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f8,f107,f73]) ).
fof(f113,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f6,f107,f78]) ).
fof(f115,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f53,f80]) ).
fof(f116,plain,
( sk_c7 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f115]) ).
fof(f120,plain,
( ~ spl0_7
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f116,f78,f52,f73]) ).
fof(f123,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f53,f109]) ).
fof(f124,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f123]) ).
fof(f125,plain,
( ~ spl0_11
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f124,f107,f52,f99]) ).
fof(f126,plain,
( sk_c6 != multiply(sk_c7,sk_c3)
| sk_c7 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f56,f85]) ).
fof(f127,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f126,f93]) ).
fof(f130,plain,
( ~ spl0_5
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f127,f91,f83,f55,f63]) ).
fof(f137,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c7,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f138,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f142,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f3,f80]) ).
fof(f155,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f75]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f155,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f142]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c4,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f191,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f168,f75]) ).
fof(f192,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f56,f168]) ).
fof(f196,plain,
( spl0_14
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f191,f78,f73,f137]) ).
fof(f218,definition,
( spl0_20
<=> sk_c6 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f219,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f271,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_9 ),
inference(superposition,[],[f165,f85]) ).
fof(f274,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f165,f70]) ).
fof(f283,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f274,f61]) ).
fof(f287,plain,
( spl0_20
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f283,f68,f59,f218]) ).
fof(f290,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f160,f219]) ).
fof(f296,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f290,f138]) ).
fof(f303,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f296,f75]) ).
fof(f308,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f50,f109]) ).
fof(f309,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f50,f80]) ).
fof(f314,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f309,f75]) ).
fof(f316,definition,
( spl0_23
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f318,plain,
( sk_c7 != sk_c6
| spl0_23 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f319,plain,
( ~ spl0_11
| ~ spl0_23
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f308,f107,f49,f316,f99]) ).
fof(f320,plain,
( ~ spl0_23
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f314,f78,f73,f49,f316]) ).
fof(f355,plain,
( sk_c7 = multiply(sk_c7,sk_c3)
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f271,f65]) ).
fof(f356,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f355,f93]) ).
fof(f365,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f356,f318]) ).
fof(f366,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f367,plain,
( sk_c6 != multiply(sk_c7,sk_c3)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f126,f65]) ).
fof(f368,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f192,f80]) ).
fof(f373,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f303,f218,f137,f73,f316]) ).
fof(f374,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f367,f355]) ).
fof(f375,plain,
( ~ spl0_23
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f368,f78,f55,f316]) ).
fof(f378,plain,
( ~ spl0_23
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f374,f83,f63,f55,f316]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f87]) ).
cnf(s9,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s11,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f94]) ).
cnf(s12,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s14,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s17,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s18,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s21,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s22,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s24,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f120]) ).
cnf(s25,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f125]) ).
cnf(s27,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f130]) ).
cnf(s30,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f196]) ).
cnf(s34,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_20 ),
inference(sat_conversion,[],[f287]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(sat_conversion,[],[f319]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_23 ),
inference(sat_conversion,[],[f320]) ).
cnf(s45,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_23 ),
inference(sat_conversion,[],[f366]) ).
cnf(s49,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_20
| spl0_23 ),
inference(sat_conversion,[],[f373]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_23 ),
inference(sat_conversion,[],[f375]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_23 ),
inference(sat_conversion,[],[f378]) ).
cnf(s53,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s27,s3,s7,s11]) ).
cnf(s54,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s49,s34,s30,s12,s13,s14,s52,s27,s53]) ).
cnf(s55,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s49,s34,s30,s50,s8,s9,s10,s53]) ).
cnf(s56,plain,
~ spl0_3,
inference(rat,[],[s49,s34,s30,s50,s4,s5,s6,s54,s55,s53]) ).
cnf(s57,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s25,s18,s22]) ).
cnf(s58,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s25,s17,s21,s24]) ).
cnf(s59,plain,
~ spl0_2,
inference(rat,[],[s58,s57]) ).
cnf(s60,plain,
spl0_1,
inference(rat,[],[s2,s56,s59]) ).
cnf(s61,plain,
spl0_8,
inference(rat,[],[s45,s39,s6,s10,s14,s18,s22,s60]) ).
cnf(s62,plain,
( spl0_6
| spl0_23 ),
inference(rat,[],[s45,s4,s8,s12]) ).
cnf(s63,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_14 ),
inference(rat,[],[s45,s3,s7,s11,s34,s62,s49]) ).
cnf(s64,plain,
~ spl0_7,
inference(rat,[],[s63,s40,s30,s61,s60]) ).
cnf(s65,plain,
spl0_12,
inference(rat,[],[s21,s64]) ).
cnf(s66,plain,
spl0_11,
inference(rat,[],[s17,s64]) ).
cnf(s67,plain,
spl0_10,
inference(rat,[],[s13,s64]) ).
cnf(s68,plain,
spl0_9,
inference(rat,[],[s9,s64]) ).
cnf(s69,plain,
spl0_5,
inference(rat,[],[s5,s64]) ).
cnf(s70,plain,
~ spl0_23,
inference(rat,[],[s39,s65,s60,s66]) ).
cnf(s71,plain,
$false,
inference(rat,[],[s45,s70,s68,s69,s67]) ).
fof(f379,plain,
$false,
inference(avatar_sat_refutation,[],[s71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:38:34 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.57/1.38 % (2839431)Input is clausal, will run a generic CNF schedule.
% 2.57/1.38 % (2839457)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1673695919:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.57/1.38 % (2839460)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4098718572:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.57/1.38 % (2839456)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1782399331:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.57/1.38 % (2839462)dis-21_1_sil=8000:lcm=predicate:random_seed=1995553297:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.57/1.38 % (2839458)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4137382056:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.57/1.38 % (2839459)lrs+10_1_sil=8000:sp=occurrence:random_seed=3452912540:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.57/1.38 % (2839461)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2686125980:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.57/1.38 % (2839462)Refutation not found, incomplete strategy
% 2.57/1.38 % (2839462)------------------------------
% 2.57/1.38 % (2839462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.38 % (2839462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.38 % (2839462)CaDiCaL version: 2.1.3
% 2.57/1.38 % (2839462)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.38 % (2839462)Time elapsed: 0.002 s
% 2.57/1.38 % (2839462)Peak memory usage: 88 MB
% 2.57/1.38 % (2839462)Instructions burned: 2 (million)
% 2.57/1.38 % (2839461)First to succeed.
% 2.57/1.38 % (2839461)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2839431"
% 2.57/1.38 % (2839459)Instruction limit reached!
% 2.57/1.38 % (2839459)------------------------------
% 2.57/1.38 % (2839459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.38 % (2839459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.38 % (2839459)CaDiCaL version: 2.1.3
% 2.57/1.38 % (2839459)Termination reason: Instruction limit
% 2.57/1.38 % (2839459)Termination phase: Saturation
% 2.57/1.38 % (2839459)Time elapsed: 0.054 s
% 2.57/1.38 % (2839459)Peak memory usage: 89 MB
% 2.57/1.38 % (2839459)Instructions burned: 108 (million)
% 2.57/1.38 % (2839460)Instruction limit reached!
% 2.57/1.38 % (2839460)------------------------------
% 2.57/1.38 % (2839460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.38 % (2839460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.38 % (2839460)CaDiCaL version: 2.1.3
% 2.57/1.38 % (2839460)Termination reason: Instruction limit
% 2.57/1.38 % (2839460)Termination phase: Saturation
% 2.57/1.38 % (2839460)Time elapsed: 0.065 s
% 2.57/1.38 % (2839460)Peak memory usage: 89 MB
% 2.57/1.38 % (2839460)Instructions burned: 114 (million)
% 2.57/1.38 % (2839477)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2978647991:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.57/1.38 % (2839477)Also succeeded, but the first one will report.
% 2.57/1.38 % (2839482)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2289315485:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 2.57/1.38 % (2839462)------------------------------
% 2.57/1.38 % (2839462)------------------------------
% 2.57/1.38 % (2839461)Refutation found. Thanks to Tanya!
% 2.57/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.57/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.56 % (2839461)------------------------------
% 3.52/1.56 % (2839461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.56 % (2839461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.56 % (2839461)CaDiCaL version: 2.1.3
% 3.52/1.56 % (2839461)Termination reason: Refutation
% 3.52/1.56 % (2839461)Time elapsed: 0.010 s
% 3.52/1.56 % (2839461)Peak memory usage: 89 MB
% 3.52/1.56 % (2839461)Instructions burned: 15 (million)
% 3.52/1.56 % (2839461)------------------------------
% 3.52/1.56 % (2839461)------------------------------
% 3.52/1.56 % (2839431)Success in time 0.388 s
% 3.52/1.56 % Vampire exiting
%------------------------------------------------------------------------------