%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO664-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 02:28:33 PM UTC 2026
% Result : Unsatisfiable 3.13s 1.12s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 8 unt; 5 def)
% Number of atoms : 219 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 296 ( 145 ~; 146 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37) ).
fof(f2,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_70) ).
fof(f3,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s('0')))
| 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X0),suc(X4))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).
fof(f5,axiom,
! [X0] : 'LE'(f(X0),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_58) ).
fof(f6,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s('0'))
| 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_117) ).
fof(f8,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_94) ).
fof(f9,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50) ).
fof(f10,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).
fof(f11,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f3,f5]) ).
fof(f12,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f11,f8]) ).
fof(f13,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f11,f7]) ).
fof(f14,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f12,f2]) ).
fof(f16,definition,
( spl0_1
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f17,plain,
( 'E'(s('0'),f(z))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f19,definition,
( spl0_2
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f20,plain,
( 'E'('0',f(z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f21,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f19,f16]) ).
fof(f22,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f10,f5]) ).
fof(f23,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f22,f8]) ).
fof(f24,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f22,f7]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f4]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X2)) ),
inference(duplicate_literal_removal,[],[f38]) ).
fof(f53,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f23,f2]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1))) ),
inference(factoring,[],[f1]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f82,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f13,f2]) ).
fof(f84,definition,
( spl0_3
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f85,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl0_4
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f88,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f82,f87,f84]) ).
fof(f95,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f39]) ).
fof(f98,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f104,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f98,f6]) ).
fof(f105,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f116,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f24,f2]) ).
fof(f118,definition,
( spl0_5
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f119,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f116,f87,f118]) ).
fof(f121,plain,
( ~ 'E'('0',f(z))
| ~ spl0_4 ),
inference(resolution,[],[f88,f105]) ).
fof(f122,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f121,f20]) ).
fof(f123,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f127,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(factoring,[],[f68]) ).
fof(f130,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f127]) ).
fof(f134,plain,
! [X0] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f130,f9]) ).
fof(f136,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f134]) ).
fof(f137,plain,
( ~ 'E'(s('0'),f(z))
| ~ spl0_3 ),
inference(resolution,[],[f136,f85]) ).
fof(f138,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_5 ),
inference(resolution,[],[f136,f119]) ).
fof(f139,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f138,f85]) ).
fof(f140,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f141,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f53,f19,f84]) ).
fof(f143,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f137,f17]) ).
fof(f144,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f143]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f89]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f120]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f123]) ).
cnf(s5,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f140]) ).
cnf(s6,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f141]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f144]) ).
cnf(s8,plain,
spl0_4,
inference(rat,[],[s5,s2,s3]) ).
cnf(s9,plain,
~ spl0_2,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
spl0_3,
inference(rat,[],[s6,s9]) ).
cnf(s11,plain,
spl0_1,
inference(rat,[],[s1,s9]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s7,s10,s11]) ).
fof(f145,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO664-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 18:07:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/1.12 % (581506)Input is clausal, will run a generic CNF schedule.
% 3.13/1.12 % (581512)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3062832556:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.13/1.12 % (581514)lrs+10_1_sil=8000:sp=occurrence:random_seed=4176850091:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.13/1.12 % (581513)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1802721785:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.13/1.12 % (581517)dis-21_1_sil=8000:lcm=predicate:random_seed=1820368569: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)
% 3.13/1.12 % (581516)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3053681836:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.13/1.12 % (581511)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=2867305706:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.13/1.12 % (581515)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=20315516:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.13/1.12 % (581515)Refutation not found, incomplete strategy
% 3.13/1.12 % (581515)------------------------------
% 3.13/1.12 % (581515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.12 % (581514)Refutation not found, incomplete strategy
% 3.13/1.12 % (581514)------------------------------
% 3.13/1.12 % (581514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.12 % (581514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.12 % (581515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.12 % (581514)CaDiCaL version: 2.1.3
% 3.13/1.12 % (581515)CaDiCaL version: 2.1.3
% 3.13/1.12 % (581514)Termination reason: Refutation not found, incomplete strategy
% 3.13/1.12 % (581514)Time elapsed: 0.001 s
% 3.13/1.12 % (581515)Termination reason: Refutation not found, incomplete strategy
% 3.13/1.12 % (581515)Time elapsed: 0.001 s
% 3.13/1.12 % (581515)Peak memory usage: 86 MB
% 3.13/1.12 % (581514)Peak memory usage: 86 MB
% 3.13/1.12 % (581517)First to succeed.
% 3.13/1.12 % (581517)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-581506"
% 3.13/1.12 % (581516)Also succeeded, but the first one will report.
% 3.13/1.12 % (581514)------------------------------
% 3.13/1.12 % (581514)------------------------------
% 3.13/1.12 % (581515)------------------------------
% 3.13/1.12 % (581515)------------------------------
% 3.13/1.12 % (581517)Refutation found. Thanks to Tanya!
% 3.13/1.12 % SZS status Unsatisfiable for theBenchmark
% 3.13/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.21 % (581517)------------------------------
% 3.68/1.21 % (581517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.21 % (581517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.21 % (581517)CaDiCaL version: 2.1.3
% 3.68/1.21 % (581517)Termination reason: Refutation
% 3.68/1.21 % (581517)Time elapsed: 0.006 s
% 3.68/1.21 % (581517)Peak memory usage: 88 MB
% 3.68/1.21 % (581517)Instructions burned: 7 (million)
% 3.68/1.21 % (581517)------------------------------
% 3.68/1.21 % (581517)------------------------------
% 3.68/1.21 % (581506)Success in time 0.437 s
% 3.68/1.21 % Vampire exiting
%------------------------------------------------------------------------------