%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET075-6 : 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 : 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 12:42:59 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 62 ( 20 unt; 4 def)
% Number of atoms : 116 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 109 ( 55 ~; 50 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f102,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f103,plain,
null_class = unordered_pair(x,y),
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(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(definition_unfolding,[],[f101,f108]) ).
fof(f171,plain,
( member(y,null_class)
| ~ member(y,universal_class) ),
inference(superposition,[],[f10,f103]) ).
fof(f173,definition,
( spl0_3
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f175,plain,
( ~ member(y,universal_class)
| spl0_3 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f177,definition,
( spl0_4
<=> member(y,null_class) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f179,plain,
( member(y,null_class)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f171,f177,f173]) ).
fof(f183,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f199,plain,
( ! [X0] : ~ member(y,X0)
| spl0_3 ),
inference(resolution,[],[f183,f175]) ).
fof(f218,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f301,plain,
member(x,u),
inference(resolution,[],[f114,f152]) ).
fof(f307,plain,
member(y,v),
inference(resolution,[],[f115,f152]) ).
fof(f311,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f307,f199]) ).
fof(f312,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f350,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))))),unordered_pair(first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),unordered_pair(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))))))),
inference(resolution,[],[f117,f152]) ).
fof(f354,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(X0,X1))
| member(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),X1) ),
inference(superposition,[],[f115,f350]) ).
fof(f382,plain,
member(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),v),
inference(resolution,[],[f354,f152]) ).
fof(f383,plain,
! [X0,X1] :
( member(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),X0)
| ~ member(y,X0)
| ~ member(x,X1) ),
inference(resolution,[],[f354,f116]) ).
fof(f403,definition,
( spl0_19
<=> ! [X1] : ~ member(x,X1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f404,plain,
( ! [X1] : ~ member(x,X1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f406,definition,
( spl0_20
<=> ! [X0] :
( member(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),X0)
| ~ member(y,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f407,plain,
( ! [X0] :
( member(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),X0)
| ~ member(y,X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f408,plain,
( spl0_19
| spl0_20 ),
inference(avatar_split_clause,[],[f383,f406,f403]) ).
fof(f420,plain,
( $false
| ~ spl0_19 ),
inference(resolution,[],[f404,f301]) ).
fof(f432,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f596,plain,
( ! [X0] :
( ~ member(second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),X0)
| ~ member(y,complement(X0)) )
| ~ spl0_20 ),
inference(resolution,[],[f407,f24]) ).
fof(f624,plain,
( ~ member(y,complement(v))
| ~ spl0_20 ),
inference(resolution,[],[f596,f382]) ).
fof(f1000,plain,
( ~ member(y,null_class)
| null_class = complement(v)
| ~ spl0_20 ),
inference(resolution,[],[f624,f218]) ).
fof(f1001,plain,
( null_class = complement(v)
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1000,f179]) ).
fof(f1340,plain,
( ~ member(y,null_class)
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f624,f1001]) ).
fof(f1355,plain,
( $false
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1340,f179]) ).
fof(f1356,plain,
( ~ spl0_4
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f1355]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f180]) ).
cnf(s8,plain,
spl0_3,
inference(sat_conversion,[],[f312]) ).
cnf(s14,plain,
( spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f408]) ).
cnf(s15,plain,
~ spl0_19,
inference(sat_conversion,[],[f432]) ).
cnf(s67,plain,
( ~ spl0_4
| ~ spl0_20 ),
inference(sat_conversion,[],[f1356]) ).
cnf(s69,plain,
spl0_20,
inference(rat,[],[s14,s15]) ).
cnf(s70,plain,
~ spl0_4,
inference(rat,[],[s67,s69]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s2,s70,s8]) ).
fof(f1366,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n019.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 00:31:18 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 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
% 0.15/0.51 % (3551349)Will run a generic schedule for satisfiability detection.
% 0.15/0.51 % (3551358)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=171182863:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.51 % (3551355)% WARNING: option uhcvi not known.
% 0.15/0.51 % (3551354)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4223554717_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.51 % (3551356)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2384895865:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.51 % (3551355)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=542051149:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.51 % (3551357)dis+10_1_sil=32000:sp=arity:random_seed=3789732348:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.51 % (3551359)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2968754597:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.51 % (3551360)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4226593561:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.51 % (3551358) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3551349-3551358"...
% 0.15/0.51 % (3551358)...printing done.
% 0.15/0.51 % (3551358)Refutation found. Thanks to Tanya!
% 0.15/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.51 % (3551358)------------------------------
% 0.15/0.51 % (3551358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.51 % (3551358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.51 % (3551358)CaDiCaL version: 2.1.3
% 0.15/0.51 % (3551358)Termination reason: Refutation
% 0.15/0.51 % (3551358)Time elapsed: 0.028 s
% 0.15/0.51 % (3551358)Peak memory usage: 13 MB
% 0.15/0.51 % (3551358)Instructions burned: 82 (million)
% 0.15/0.51 % (3551349)Success in time 0.06 s
% 0.15/0.51 % Vampire exiting
%------------------------------------------------------------------------------