%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET021-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 0.15s 0.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 18 unt; 2 def)
% Number of atoms : 89 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 46 ~; 40 |; 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f101,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_1) ).
fof(f102,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
fof(f103,plain,
v != second(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,
v != second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),
inference(definition_unfolding,[],[f103,f108]) ).
fof(f297,plain,
member(u,universal_class),
inference(resolution,[],[f114,f152]) ).
fof(f298,plain,
member(v,universal_class),
inference(resolution,[],[f115,f152]) ).
fof(f377,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(f402,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,f377]) ).
fof(f430,plain,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(resolution,[],[f402,f152]) ).
fof(f431,plain,
! [X0,X1] :
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ member(v,X0)
| ~ member(u,X1) ),
inference(resolution,[],[f402,f116]) ).
fof(f433,definition,
( spl0_27
<=> ! [X1] : ~ member(u,X1) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f434,plain,
( ! [X1] : ~ member(u,X1)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f436,definition,
( spl0_28
<=> ! [X0] :
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ member(v,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f437,plain,
( ! [X0] :
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ member(v,X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f438,plain,
( spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f431,f436,f433]) ).
fof(f464,plain,
( $false
| ~ spl0_27 ),
inference(backward_subsumption_resolution,[],[f297,f434]) ).
fof(f472,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f493,plain,
( ! [X0] :
( ~ member(v,complement(X0))
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0) )
| ~ spl0_28 ),
inference(resolution,[],[f437,f24]) ).
fof(f746,plain,
( ! [X0] :
( ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ member(v,universal_class)
| member(v,X0) )
| ~ spl0_28 ),
inference(resolution,[],[f493,f25]) ).
fof(f747,plain,
( ! [X0] :
( ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| member(v,X0) )
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f746,f298]) ).
fof(f751,plain,
( ! [X0] :
( member(v,unordered_pair(X0,second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class) )
| ~ spl0_28 ),
inference(resolution,[],[f747,f10]) ).
fof(f778,plain,
( ! [X0] : member(v,unordered_pair(X0,second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f751,f430]) ).
fof(f783,plain,
( ! [X0] :
( v = X0
| v = second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) )
| ~ spl0_28 ),
inference(resolution,[],[f778,f8]) ).
fof(f785,plain,
( ! [X0] : v = X0
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f783,f153]) ).
fof(f808,plain,
( $false
| ~ spl0_28 ),
inference(backward_subsumption_resolution,[],[f153,f785]) ).
fof(f1142,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f808]) ).
cnf(s16,plain,
( spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f438]) ).
cnf(s18,plain,
~ spl0_27,
inference(sat_conversion,[],[f472]) ).
cnf(s45,plain,
~ spl0_28,
inference(sat_conversion,[],[f1142]) ).
cnf(s169,plain,
$false,
inference(rat,[],[s16,s45,s18]) ).
fof(f1845,plain,
$false,
inference(avatar_sat_refutation,[],[s169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET021-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:15:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.15/0.50 % (3143501)Will run a generic schedule for satisfiability detection.
% 0.15/0.50 % (3143511)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3032959473:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.50 % (3143507)% WARNING: option uhcvi not known.
% 0.15/0.50 % (3143507)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3343900792:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.50 % (3143506)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=506151749_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.50 % (3143508)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1262959482:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.50 % (3143509)dis+10_1_sil=32000:sp=arity:random_seed=105440121:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.50 % (3143510)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1069760327:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.50 % (3143512)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=312297316:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.50 % (3143511)Instruction limit reached!
% 0.15/0.50 % (3143511)------------------------------
% 0.15/0.50 % (3143511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (3143511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (3143511)CaDiCaL version: 2.1.3
% 0.15/0.50 % (3143511)Termination reason: Instruction limit
% 0.15/0.50 % (3143511)Termination phase: Saturation
% 0.15/0.50 % (3143511)Time elapsed: 0.044 s
% 0.15/0.50 % (3143511)Peak memory usage: 13 MB
% 0.15/0.50 % (3143511)Instructions burned: 133 (million)
% 0.15/0.50 % (3143507) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3143501-3143507"...
% 0.15/0.50 % (3143507)...printing done.
% 0.15/0.50 % (3143507)Refutation found. Thanks to Tanya!
% 0.15/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.50 % (3143507)------------------------------
% 0.15/0.50 % (3143507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (3143507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (3143507)CaDiCaL version: 2.1.3
% 0.15/0.50 % (3143507)Termination reason: Refutation
% 0.15/0.50 % (3143507)Time elapsed: 0.039 s
% 0.15/0.50 % (3143507)Peak memory usage: 13 MB
% 0.15/0.50 % (3143507)Instructions burned: 56 (million)
% 0.15/0.50 % (3143501)Success in time 0.074 s
% 0.15/0.50 % Vampire exiting
%------------------------------------------------------------------------------