%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET123-6 : 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 : 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 12:43:12 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 38 ( 17 unt; 2 def)
% Number of atoms : 66 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 22 ~; 26 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(x,set_builder(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_1) ).
fof(f103,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_2) ).
fof(f104,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_3) ).
fof(f110,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f154,plain,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(definition_unfolding,[],[f102,f110]) ).
fof(f160,plain,
~ member(x,intersection(complement(unordered_pair(y,y)),complement(z))),
inference(resolution,[],[f24,f154]) ).
fof(f165,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f193,plain,
member(x,universal_class),
inference(resolution,[],[f165,f154]) ).
fof(f208,plain,
( ~ member(x,complement(z))
| ~ member(x,complement(unordered_pair(y,y))) ),
inference(resolution,[],[f23,f160]) ).
fof(f215,definition,
( spl0_1
<=> member(x,complement(unordered_pair(y,y))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f217,plain,
( ~ member(x,complement(unordered_pair(y,y)))
| spl0_1 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f219,definition,
( spl0_2
<=> member(x,complement(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f221,plain,
( ~ member(x,complement(z))
| spl0_2 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f208,f219,f215]) ).
fof(f223,plain,
( ~ member(x,universal_class)
| member(x,unordered_pair(y,y))
| spl0_1 ),
inference(resolution,[],[f217,f25]) ).
fof(f224,plain,
( member(x,unordered_pair(y,y))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f223,f193]) ).
fof(f231,plain,
( x = y
| x = y
| spl0_1 ),
inference(resolution,[],[f224,f8]) ).
fof(f233,plain,
( x = y
| spl0_1 ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f234,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f233,f103]) ).
fof(f235,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f236,plain,
( ~ member(x,universal_class)
| member(x,z)
| spl0_2 ),
inference(resolution,[],[f221,f25]) ).
fof(f237,plain,
( member(x,z)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f236,f193]) ).
fof(f238,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f237,f104]) ).
fof(f239,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f238]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f222]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f235]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f239]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f240,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:56:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.18/0.47 % (4119831)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (4119840)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3700649436:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (4119837)% WARNING: option uhcvi not known.
% 0.18/0.47 % (4119840) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4119831-4119840"...
% 0.18/0.47 % (4119840)...printing done.
% 0.18/0.47 % (4119836)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2534468641_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (4119840)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (4119840)------------------------------
% 0.18/0.47 % (4119840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (4119840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (4119840)CaDiCaL version: 2.1.3
% 0.18/0.47 % (4119840)Termination reason: Refutation
% 0.18/0.47 % (4119840)Time elapsed: 0.005 s
% 0.18/0.47 % (4119840)Peak memory usage: 12 MB
% 0.18/0.47 % (4119840)Instructions burned: 12 (million)
% 0.18/0.47 % (4119831)Success in time 0.041 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------