%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:42:40 PM UTC 2026
% Result : Unsatisfiable 1.33s 0.64s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 18 unt; 2 def)
% Number of atoms : 83 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 42 ~; 35 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f101,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
fof(f102,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
fof(f103,plain,
u != first(ordered_pair(u,v)),
inference(reorient_equations,[],[f102]) ).
fof(f108,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f108]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f108]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f108]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f108]) ).
fof(f152,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f101,f108]) ).
fof(f153,plain,
u != first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),
inference(definition_unfolding,[],[f103,f108]) ).
fof(f161,plain,
unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))),
inference(resolution,[],[f117,f152]) ).
fof(f163,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X0,X1))
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0) ),
inference(superposition,[],[f116,f161]) ).
fof(f164,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X0,X1))
| member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(superposition,[],[f115,f161]) ).
fof(f165,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X0,X1))
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0) ),
inference(superposition,[],[f114,f161]) ).
fof(f166,plain,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(resolution,[],[f164,f152]) ).
fof(f186,plain,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(resolution,[],[f165,f152]) ).
fof(f215,definition,
( spl0_9
<=> ! [X1] :
( ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| member(u,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f216,plain,
( ! [X1] :
( ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| member(u,X1) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,definition,
( spl0_10
<=> ! [X0] : ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f219,plain,
( ! [X0] : ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f317,plain,
( ! [X0] :
( ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class)
| member(u,unordered_pair(X0,first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))))) )
| ~ spl0_9 ),
inference(resolution,[],[f10,f216]) ).
fof(f342,plain,
( ! [X0] : member(u,unordered_pair(X0,first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f317,f186]) ).
fof(f862,plain,
( $false
| ~ spl0_10 ),
inference(resolution,[],[f219,f166]) ).
fof(f867,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f862]) ).
fof(f914,plain,
! [X0,X1] :
( ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| member(u,X1) ),
inference(resolution,[],[f163,f114]) ).
fof(f925,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f914,f218,f215]) ).
fof(f3432,plain,
( ! [X0] :
( u = X0
| u = first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) )
| ~ spl0_9 ),
inference(resolution,[],[f8,f342]) ).
fof(f3453,plain,
( ! [X0] : u = X0
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f3432,f153]) ).
fof(f3501,plain,
( ! [X0] : first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(v,v)))) != X0
| ~ spl0_9 ),
inference(superposition,[],[f153,f3453]) ).
fof(f4698,plain,
( ! [X0] : u != X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3501,f3453]) ).
fof(f4991,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f4698,f3453]) ).
fof(f4992,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f4991]) ).
cnf(s57,plain,
~ spl0_10,
inference(sat_conversion,[],[f867]) ).
cnf(s62,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f925]) ).
cnf(s332,plain,
~ spl0_9,
inference(sat_conversion,[],[f4992]) ).
cnf(s484,plain,
spl0_10,
inference(rat,[],[s62,s332]) ).
cnf(s487,plain,
$false,
inference(rat,[],[s57,s484]) ).
fof(f5199,plain,
$false,
inference(avatar_sat_refutation,[],[s487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:11:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.33/0.64 % (2872845)Will run a generic schedule for satisfiability detection.
% 1.33/0.64 % (2872853)dis+10_1_sil=32000:sp=arity:random_seed=185428590:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.33/0.64 % (2872851)% WARNING: option uhcvi not known.
% 1.33/0.64 % (2872850)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3927782897_2999 on theBenchmark for (2999ds/0Mi)
% 1.33/0.64 % (2872854)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3778683214:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.33/0.64 % (2872851)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=89982090:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.33/0.64 % (2872852)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1851700730:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.33/0.64 % (2872856)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1934164597:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.33/0.64 % (2872855)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=908511404:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.33/0.64 % (2872853)Instruction limit reached!
% 1.33/0.64 % (2872853)------------------------------
% 1.33/0.64 % (2872853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.64 % (2872853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.64 % (2872853)CaDiCaL version: 2.1.3
% 1.33/0.64 % (2872853)Termination reason: Instruction limit
% 1.33/0.64 % (2872853)Termination phase: Saturation
% 1.33/0.64 % (2872853)Time elapsed: 0.038 s
% 1.33/0.64 % (2872853)Peak memory usage: 12 MB
% 1.33/0.64 % (2872853)Instructions burned: 105 (million)
% 1.33/0.64 % (2872864)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2054204915:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.33/0.64 % (2872854)Instruction limit reached!
% 1.33/0.64 % (2872854)------------------------------
% 1.33/0.64 % (2872854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.64 % (2872854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.64 % (2872854)CaDiCaL version: 2.1.3
% 1.33/0.64 % (2872854)Termination reason: Instruction limit
% 1.33/0.64 % (2872854)Termination phase: Saturation
% 1.33/0.64 % (2872854)Time elapsed: 0.073 s
% 1.33/0.64 % (2872854)Peak memory usage: 13 MB
% 1.33/0.64 % (2872854)Instructions burned: 116 (million)
% 1.33/0.64 % (2872855)Instruction limit reached!
% 1.33/0.64 % (2872855)------------------------------
% 1.33/0.64 % (2872855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.64 % (2872855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.64 % (2872855)CaDiCaL version: 2.1.3
% 1.33/0.64 % (2872855)Termination reason: Instruction limit
% 1.33/0.64 % (2872855)Termination phase: Saturation
% 1.33/0.64 % (2872855)Time elapsed: 0.079 s
% 1.33/0.64 % (2872855)Peak memory usage: 13 MB
% 1.33/0.64 % (2872855)Instructions burned: 133 (million)
% 1.33/0.64 % (2872866)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1140359330:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.33/0.64 % (2872867)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=3922445633:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.33/0.64 % (2872856)Instruction limit reached!
% 1.33/0.64 % (2872856)------------------------------
% 1.33/0.64 % (2872856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.64 % (2872856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.64 % (2872856)CaDiCaL version: 2.1.3
% 1.33/0.64 % (2872856)Termination reason: Instruction limit
% 1.33/0.64 % (2872856)Termination phase: Saturation
% 1.33/0.64 % (2872856)Time elapsed: 0.110 s
% 1.33/0.64 % (2872856)Peak memory usage: 13 MB
% 1.33/0.64 % (2872856)Instructions burned: 159 (million)
% 1.33/0.64 % (2872870)ott-21_1_sil=16000:fs=off:random_seed=714661227:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.33/0.64 % TRYING [1]
% 1.33/0.64 % TRYING [2]
% 1.33/0.64 % TRYING [3]
% 1.33/0.64 % (2872867) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2872845-2872867"...
% 1.33/0.64 % (2872867)...printing done.
% 1.33/0.64 % (2872867)Refutation found. Thanks to Tanya!
% 1.33/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.33/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.64 % (2872867)------------------------------
% 1.33/0.64 % (2872867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.64 % (2872867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.64 % (2872867)CaDiCaL version: 2.1.3
% 1.33/0.64 % (2872867)Termination reason: Refutation
% 1.33/0.64 % (2872867)Time elapsed: 0.075 s
% 1.33/0.64 % (2872867)Peak memory usage: 14 MB
% 1.33/0.64 % (2872867)Instructions burned: 124 (million)
% 1.33/0.64 % (2872845)Success in time 0.218 s
% 1.33/0.64 % Vampire exiting
%------------------------------------------------------------------------------