%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET018-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:42:38 PM UTC 2026
% Result : Unsatisfiable 1.14s 0.63s
% Output : Refutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 20 unt; 3 def)
% Number of atoms : 142 ( 54 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 136 ( 63 ~; 70 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,non_ordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
fof(f162,axiom,
! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ordered_pair(X0,X2) != ordered_pair(X1,X3)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ordered_pair(X1,X3) != ordered_pair(X0,X2)
| X0 = X1 ),
inference(reorient_equations,[],[f162]) ).
fof(f165,axiom,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
fof(f166,axiom,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_little_set) ).
fof(f167,axiom,
little_set(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_little_set) ).
fof(f168,axiom,
little_set(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_little_set) ).
fof(f169,axiom,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pair) ).
fof(f170,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f172,plain,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),
inference(definition_unfolding,[],[f10,f9]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)) != non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))
| ~ little_set(X1)
| ~ little_set(X0)
| X0 = X1 ),
inference(definition_unfolding,[],[f163,f172,f172]) ).
fof(f200,plain,
non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)) = non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)),
inference(definition_unfolding,[],[f169,f172,f172]) ).
fof(f202,plain,
! [X2,X1] :
( member(X2,non_ordered_pair(X1,X2))
| ~ little_set(X2) ),
inference(equality_resolution,[],[f7]) ).
fof(f220,plain,
! [X0,X1] :
( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))
| ~ little_set(X0)
| ~ little_set(c)
| c = X0 ),
inference(superposition,[],[f199,f200]) ).
fof(f223,plain,
! [X0,X1] :
( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))
| ~ little_set(X0)
| c = X0 ),
inference(forward_subsumption_resolution,[],[f220,f167]) ).
fof(f228,plain,
( ~ little_set(a)
| a = c ),
inference(equality_resolution,[],[f223]) ).
fof(f229,plain,
a = c,
inference(forward_subsumption_resolution,[],[f228,f165]) ).
fof(f412,plain,
( member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| ~ little_set(non_ordered_pair(c,d)) ),
inference(superposition,[],[f202,f200]) ).
fof(f418,plain,
member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(forward_subsumption_resolution,[],[f412,f8]) ).
fof(f2115,plain,
! [X0] :
( ~ member(X0,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| non_ordered_pair(c,c) = X0
| non_ordered_pair(c,d) = X0 ),
inference(superposition,[],[f5,f200]) ).
fof(f2124,definition,
( spl0_57
<=> non_ordered_pair(a,b) = non_ordered_pair(a,d) ),
introduced(definition,[new_symbols(definition,[spl0_57])],[avatar_definition]) ).
fof(f2126,plain,
( non_ordered_pair(a,b) = non_ordered_pair(a,d)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f2124]) ).
fof(f3047,plain,
member(non_ordered_pair(a,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(forward_demodulation,[],[f418,f229]) ).
fof(f3048,plain,
! [X0] :
( non_ordered_pair(a,a) = X0
| ~ member(X0,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| non_ordered_pair(c,d) = X0 ),
inference(forward_demodulation,[],[f2115,f229]) ).
fof(f3060,plain,
! [X0] :
( ~ member(X0,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| non_ordered_pair(a,a) = X0
| non_ordered_pair(a,d) = X0 ),
inference(forward_demodulation,[],[f3048,f229]) ).
fof(f3537,plain,
( non_ordered_pair(a,a) = non_ordered_pair(a,d)
| non_ordered_pair(a,b) = non_ordered_pair(a,d) ),
inference(resolution,[],[f3047,f5]) ).
fof(f3548,definition,
( spl0_100
<=> non_ordered_pair(a,a) = non_ordered_pair(a,d) ),
introduced(definition,[new_symbols(definition,[spl0_100])],[avatar_definition]) ).
fof(f3550,plain,
( non_ordered_pair(a,a) = non_ordered_pair(a,d)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f3548]) ).
fof(f3551,plain,
( spl0_57
| spl0_100 ),
inference(avatar_split_clause,[],[f3537,f3548,f2124]) ).
fof(f3649,plain,
( non_ordered_pair(a,a) = non_ordered_pair(a,b)
| non_ordered_pair(a,b) = non_ordered_pair(a,d)
| ~ little_set(non_ordered_pair(a,b)) ),
inference(resolution,[],[f3060,f202]) ).
fof(f3731,plain,
( non_ordered_pair(a,a) = non_ordered_pair(a,b)
| non_ordered_pair(a,b) = non_ordered_pair(a,d) ),
inference(forward_subsumption_resolution,[],[f3649,f8]) ).
fof(f3742,definition,
( spl0_118
<=> non_ordered_pair(a,a) = non_ordered_pair(a,b) ),
introduced(definition,[new_symbols(definition,[spl0_118])],[avatar_definition]) ).
fof(f3744,plain,
( non_ordered_pair(a,a) = non_ordered_pair(a,b)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f3742]) ).
fof(f3745,plain,
( spl0_57
| spl0_118 ),
inference(avatar_split_clause,[],[f3731,f3742,f2124]) ).
fof(f4169,plain,
( member(d,non_ordered_pair(a,a))
| ~ little_set(d)
| ~ spl0_100 ),
inference(superposition,[],[f202,f3550]) ).
fof(f4179,plain,
( member(d,non_ordered_pair(a,a))
| ~ spl0_100 ),
inference(forward_subsumption_resolution,[],[f4169,f168]) ).
fof(f4304,plain,
( a = d
| a = d
| ~ spl0_100 ),
inference(resolution,[],[f4179,f5]) ).
fof(f4313,plain,
( a = d
| ~ spl0_100 ),
inference(duplicate_literal_removal,[],[f4304]) ).
fof(f4316,plain,
( a != b
| ~ spl0_100 ),
inference(superposition,[],[f170,f4313]) ).
fof(f4559,plain,
( member(b,non_ordered_pair(a,a))
| ~ little_set(b)
| ~ spl0_118 ),
inference(superposition,[],[f202,f3744]) ).
fof(f4575,plain,
( member(b,non_ordered_pair(a,a))
| ~ spl0_118 ),
inference(forward_subsumption_resolution,[],[f4559,f166]) ).
fof(f4582,plain,
( a = b
| a = b
| ~ spl0_118 ),
inference(resolution,[],[f4575,f5]) ).
fof(f4591,plain,
( a = b
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f4582]) ).
fof(f4593,plain,
( $false
| ~ spl0_100
| ~ spl0_118 ),
inference(forward_subsumption_resolution,[],[f4591,f4316]) ).
fof(f4594,plain,
( ~ spl0_100
| ~ spl0_118 ),
inference(avatar_contradiction_clause,[],[f4593]) ).
fof(f4929,plain,
( member(d,non_ordered_pair(a,b))
| ~ little_set(d)
| ~ spl0_57 ),
inference(superposition,[],[f202,f2126]) ).
fof(f4944,plain,
( member(d,non_ordered_pair(a,b))
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[],[f4929,f168]) ).
fof(f4950,plain,
( a = d
| b = d
| ~ spl0_57 ),
inference(resolution,[],[f4944,f5]) ).
fof(f4960,plain,
( a = d
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[],[f4950,f170]) ).
fof(f4962,plain,
( a != b
| ~ spl0_57 ),
inference(superposition,[],[f170,f4960]) ).
fof(f4965,plain,
( non_ordered_pair(a,a) = non_ordered_pair(a,b)
| ~ spl0_57 ),
inference(superposition,[],[f2126,f4960]) ).
fof(f5008,plain,
( member(b,non_ordered_pair(a,a))
| ~ little_set(b)
| ~ spl0_57 ),
inference(superposition,[],[f202,f4965]) ).
fof(f5024,plain,
( member(b,non_ordered_pair(a,a))
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[],[f5008,f166]) ).
fof(f5044,plain,
( a = b
| a = b
| ~ spl0_57 ),
inference(resolution,[],[f5024,f5]) ).
fof(f5053,plain,
( a = b
| ~ spl0_57 ),
inference(duplicate_literal_removal,[],[f5044]) ).
fof(f5055,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[],[f5053,f4962]) ).
fof(f5056,plain,
~ spl0_57,
inference(avatar_contradiction_clause,[],[f5055]) ).
cnf(s155,plain,
( spl0_57
| spl0_100 ),
inference(sat_conversion,[],[f3551]) ).
cnf(s164,plain,
( spl0_57
| spl0_118 ),
inference(sat_conversion,[],[f3745]) ).
cnf(s191,plain,
( ~ spl0_100
| ~ spl0_118 ),
inference(sat_conversion,[],[f4594]) ).
cnf(s230,plain,
~ spl0_57,
inference(sat_conversion,[],[f5056]) ).
cnf(s232,plain,
spl0_118,
inference(rat,[],[s164,s230]) ).
cnf(s233,plain,
~ spl0_100,
inference(rat,[],[s191,s232]) ).
cnf(s234,plain,
$false,
inference(rat,[],[s155,s233,s230]) ).
fof(f5057,plain,
$false,
inference(avatar_sat_refutation,[],[s234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:08:32 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.38 Running first-order model finding
% 0.14/0.38 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.14/0.63 % (1310381)Will run a generic schedule for satisfiability detection.
% 1.14/0.63 % (1310388)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=392187971:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.14/0.63 % (1310387)% WARNING: option uhcvi not known.
% 1.14/0.63 % (1310386)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1480764169_2999 on theBenchmark for (2999ds/0Mi)
% 1.14/0.63 % (1310391)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1883154205:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.14/0.63 % (1310389)dis+10_1_sil=32000:sp=arity:random_seed=93624057:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.14/0.63 % (1310390)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3418587717:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.14/0.63 % (1310392)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3949911870:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.14/0.63 % (1310387)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3103954107:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.14/0.63 % TRYING [1]
% 1.14/0.63 % TRYING [2]
% 1.14/0.63 % TRYING [3]
% 1.14/0.63 % (1310389)Instruction limit reached!
% 1.14/0.63 % (1310389)------------------------------
% 1.14/0.63 % (1310389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.14/0.63 % (1310389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/0.63 % (1310389)CaDiCaL version: 2.1.3
% 1.14/0.63 % (1310389)Termination reason: Instruction limit
% 1.14/0.63 % (1310389)Termination phase: Saturation
% 1.14/0.63 % (1310389)Time elapsed: 0.063 s
% 1.14/0.63 % (1310389)Peak memory usage: 12 MB
% 1.14/0.63 % (1310389)Instructions burned: 103 (million)
% 1.14/0.63 % (1310390)Instruction limit reached!
% 1.14/0.63 % (1310390)------------------------------
% 1.14/0.63 % (1310390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.14/0.63 % (1310390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/0.63 % (1310390)CaDiCaL version: 2.1.3
% 1.14/0.63 % (1310390)Termination reason: Instruction limit
% 1.14/0.63 % (1310390)Termination phase: Saturation
% 1.14/0.63 % (1310390)Time elapsed: 0.068 s
% 1.14/0.63 % (1310390)Peak memory usage: 13 MB
% 1.14/0.63 % (1310390)Instructions burned: 116 (million)
% 1.14/0.63 % (1310391)Instruction limit reached!
% 1.14/0.63 % (1310391)------------------------------
% 1.14/0.63 % (1310391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.14/0.63 % (1310391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/0.63 % (1310391)CaDiCaL version: 2.1.3
% 1.14/0.63 % (1310391)Termination reason: Instruction limit
% 1.14/0.63 % (1310391)Termination phase: Saturation
% 1.14/0.63 % (1310391)Time elapsed: 0.073 s
% 1.14/0.63 % (1310391)Peak memory usage: 13 MB
% 1.14/0.63 % (1310391)Instructions burned: 132 (million)
% 1.14/0.63 % (1310400)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1176872621:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.14/0.63 % (1310401)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1343992906:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.14/0.63 % (1310402)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3969741595:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.14/0.63 % TRYING [1]
% 1.14/0.63 % TRYING [2]
% 1.14/0.63 % (1310392)Instruction limit reached!
% 1.14/0.63 % (1310392)------------------------------
% 1.14/0.63 % (1310392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.14/0.63 % (1310392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/0.63 % (1310392)CaDiCaL version: 2.1.3
% 1.14/0.63 % (1310392)Termination reason: Instruction limit
% 1.14/0.63 % (1310392)Termination phase: Saturation
% 1.14/0.63 % (1310392)Time elapsed: 0.105 s
% 1.14/0.63 % (1310392)Peak memory usage: 14 MB
% 1.14/0.63 % (1310392)Instructions burned: 162 (million)
% 1.14/0.63 % TRYING [3]
% 1.14/0.63 % (1310406)ott-21_1_sil=16000:fs=off:random_seed=441574798:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.14/0.63 % (1310401)Instruction limit reached!
% 1.14/0.63 % (1310401)------------------------------
% 1.14/0.63 % (1310401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.14/0.63 % (1310401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/0.63 % (1310401)CaDiCaL version: 2.1.3
% 1.14/0.63 % (1310401)Termination reason: Instruction limit
% 1.14/0.63 % (1310401)Termination phase: Saturation
% 1.14/0.63 % (1310401)Time elapsed: 0.084 s
% 1.14/0.63 % (1310401)Peak memory usage: 13 MB
% 1.14/0.63 % (1310401)Instructions burned: 132 (million)
% 1.14/0.63 % (1310402) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1310381-1310402"...
% 1.14/0.63 % (1310402)...printing done.
% 1.14/0.63 % (1310402)Refutation found. Thanks to Tanya!
% 1.14/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.14/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.14/0.63 % (1310402)------------------------------
% 1.14/0.63 % (1310402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.14/0.63 % (1310402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/0.63 % (1310402)CaDiCaL version: 2.1.3
% 1.14/0.63 % (1310402)Termination reason: Refutation
% 1.14/0.63 % (1310402)Time elapsed: 0.094 s
% 1.14/0.63 % (1310402)Peak memory usage: 14 MB
% 1.14/0.63 % (1310402)Instructions burned: 140 (million)
% 1.14/0.63 % (1310381)Success in time 0.235 s
% 1.14/0.63 % Vampire exiting
%------------------------------------------------------------------------------