%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET071-6 : 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 : n013.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 12:42:57 PM UTC 2026
% Result : Unsatisfiable 1.35s 0.65s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 15 unt; 2 def)
% Number of atoms : 133 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 131 ( 56 ~; 73 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 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 : 78 ( 0 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| 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(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(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(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(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f101,negated_conjecture,
unordered_pair(x,y) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_1) ).
fof(f102,plain,
null_class != unordered_pair(x,y),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_2) ).
fof(f104,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_3) ).
fof(f109,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(f116,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,f109]) ).
fof(f117,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,f109]) ).
fof(f263,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f68,f8]) ).
fof(f532,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| null_class = X0 ),
inference(resolution,[],[f1,f68]) ).
fof(f2122,plain,
! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(equality_factoring,[],[f263]) ).
fof(f2128,plain,
! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = null_class ),
inference(equality_resolution,[],[f2122]) ).
fof(f2129,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class
| unordered_pair(X0,X0) = null_class ),
inference(superposition,[],[f68,f2128]) ).
fof(f2132,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class ),
inference(duplicate_literal_removal,[],[f2129]) ).
fof(f2134,plain,
! [X0,X1] :
( ~ subclass(unordered_pair(X0,X0),X1)
| unordered_pair(X0,X0) = null_class
| member(X0,X1) ),
inference(resolution,[],[f2132,f1]) ).
fof(f2165,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(resolution,[],[f2134,f4]) ).
fof(f2171,plain,
null_class = unordered_pair(x,x),
inference(resolution,[],[f2165,f103]) ).
fof(f2172,plain,
null_class = unordered_pair(y,y),
inference(resolution,[],[f2165,f104]) ).
fof(f2201,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(null_class,unordered_pair(x,unordered_pair(X0,X0))),cross_product(X1,X2))
| member(X0,X2) ),
inference(superposition,[],[f116,f2171]) ).
fof(f2203,plain,
! [X2,X0,X1] :
( member(unordered_pair(null_class,unordered_pair(x,unordered_pair(X0,X0))),cross_product(X1,X2))
| ~ member(X0,X2)
| ~ member(x,X1) ),
inference(superposition,[],[f117,f2171]) ).
fof(f2255,plain,
! [X0] :
( member(regular(X0),universal_class)
| null_class = X0 ),
inference(resolution,[],[f532,f4]) ).
fof(f2297,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(superposition,[],[f2255,f263]) ).
fof(f2300,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 ),
inference(duplicate_literal_removal,[],[f2297]) ).
fof(f2425,plain,
! [X0,X1] :
( ~ member(unordered_pair(null_class,unordered_pair(x,null_class)),cross_product(X0,X1))
| member(y,X1) ),
inference(superposition,[],[f2201,f2172]) ).
fof(f2461,plain,
! [X0,X1] :
( member(unordered_pair(null_class,unordered_pair(x,null_class)),cross_product(X0,X1))
| ~ member(x,X1)
| ~ member(x,X0) ),
inference(superposition,[],[f2203,f2171]) ).
fof(f2463,plain,
! [X0,X1] :
( ~ member(x,X0)
| ~ member(x,X1)
| member(y,X0) ),
inference(resolution,[],[f2461,f2425]) ).
fof(f2468,definition,
( spl0_123
<=> ! [X1] : ~ member(x,X1) ),
introduced(definition,[new_symbols(definition,[spl0_123])],[avatar_definition]) ).
fof(f2469,plain,
( ! [X1] : ~ member(x,X1)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f2471,definition,
( spl0_124
<=> ! [X0] :
( ~ member(x,X0)
| member(y,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_124])],[avatar_definition]) ).
fof(f2472,plain,
( ! [X0] :
( ~ member(x,X0)
| member(y,X0) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f2471]) ).
fof(f2473,plain,
( spl0_123
| spl0_124 ),
inference(avatar_split_clause,[],[f2463,f2471,f2468]) ).
fof(f2479,plain,
( ! [X0,X1] :
( member(y,intersection(X0,X1))
| ~ member(x,X1)
| ~ member(x,X0) )
| ~ spl0_124 ),
inference(resolution,[],[f2472,f23]) ).
fof(f2494,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X1,X0),X2)
| ~ member(x,X1)
| ~ member(x,X0)
| member(y,X2) )
| ~ spl0_124 ),
inference(resolution,[],[f2479,f1]) ).
fof(f2675,plain,
( ! [X0,X1] :
( ~ member(x,X0)
| ~ member(x,X1)
| member(y,universal_class) )
| ~ spl0_124 ),
inference(resolution,[],[f2494,f4]) ).
fof(f2691,plain,
( ! [X0,X1] :
( ~ member(x,X0)
| ~ member(x,X1) )
| ~ spl0_124 ),
inference(forward_subsumption_resolution,[],[f2675,f104]) ).
fof(f2692,plain,
( spl0_123
| spl0_123
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f2691,f2471,f2468,f2468]) ).
fof(f3407,plain,
( ! [X0] :
( regular(unordered_pair(x,X0)) = X0
| null_class = unordered_pair(x,X0) )
| ~ spl0_123 ),
inference(resolution,[],[f2300,f2469]) ).
fof(f3415,plain,
( ! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(x,X0)
| null_class = unordered_pair(x,X0) )
| ~ spl0_123 ),
inference(superposition,[],[f2255,f3407]) ).
fof(f3420,plain,
( ! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(x,X0) )
| ~ spl0_123 ),
inference(duplicate_literal_removal,[],[f3415]) ).
fof(f3525,plain,
( null_class = unordered_pair(x,y)
| ~ spl0_123 ),
inference(resolution,[],[f104,f3420]) ).
fof(f3528,plain,
( $false
| ~ spl0_123 ),
inference(forward_subsumption_resolution,[],[f3525,f102]) ).
fof(f3529,plain,
~ spl0_123,
inference(avatar_contradiction_clause,[],[f3528]) ).
cnf(s168,plain,
( spl0_123
| spl0_124 ),
inference(sat_conversion,[],[f2473]) ).
cnf(s184,plain,
( spl0_123
| spl0_123
| ~ spl0_124 ),
inference(sat_conversion,[],[f2692]) ).
cnf(s185,plain,
( spl0_123
| ~ spl0_124 ),
inference(rat,[],[s184]) ).
cnf(s252,plain,
~ spl0_123,
inference(sat_conversion,[],[f3529]) ).
cnf(s253,plain,
~ spl0_124,
inference(rat,[],[s185,s252]) ).
cnf(s258,plain,
$false,
inference(rat,[],[s168,s253,s252]) ).
fof(f3530,plain,
$false,
inference(avatar_sat_refutation,[],[s258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:29:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 1.35/0.65 % (700093)Will run a generic schedule for satisfiability detection.
% 1.35/0.65 % (700103)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2639282481:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.35/0.65 % (700099)% WARNING: option uhcvi not known.
% 1.35/0.65 % (700099)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2152937313:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.35/0.65 % (700098)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1384222373_2999 on theBenchmark for (2999ds/0Mi)
% 1.35/0.65 % (700100)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=623431829:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.35/0.65 % (700101)dis+10_1_sil=32000:sp=arity:random_seed=3865780920:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.35/0.65 % (700102)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4087222858:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.35/0.65 % (700104)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1030997077:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.35/0.65 % (700103)Instruction limit reached!
% 1.35/0.65 % (700103)------------------------------
% 1.35/0.65 % (700103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.65 % (700103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.65 % (700103)CaDiCaL version: 2.1.3
% 1.35/0.65 % (700103)Termination reason: Instruction limit
% 1.35/0.65 % (700103)Termination phase: Saturation
% 1.35/0.65 % (700103)Time elapsed: 0.043 s
% 1.35/0.65 % (700103)Peak memory usage: 13 MB
% 1.35/0.65 % (700103)Instructions burned: 131 (million)
% 1.35/0.65 % (700112)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=902002910:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.35/0.65 % (700101)Instruction limit reached!
% 1.35/0.65 % (700101)------------------------------
% 1.35/0.65 % (700101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.65 % (700101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.65 % (700101)CaDiCaL version: 2.1.3
% 1.35/0.65 % (700101)Termination reason: Instruction limit
% 1.35/0.65 % (700101)Termination phase: Saturation
% 1.35/0.65 % (700101)Time elapsed: 0.068 s
% 1.35/0.65 % (700101)Peak memory usage: 12 MB
% 1.35/0.65 % (700101)Instructions burned: 104 (million)
% 1.35/0.65 % (700102)Instruction limit reached!
% 1.35/0.65 % (700102)------------------------------
% 1.35/0.65 % (700102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.65 % (700102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.65 % (700102)CaDiCaL version: 2.1.3
% 1.35/0.65 % (700102)Termination reason: Instruction limit
% 1.35/0.65 % (700102)Termination phase: Saturation
% 1.35/0.65 % (700102)Time elapsed: 0.072 s
% 1.35/0.65 % (700102)Peak memory usage: 12 MB
% 1.35/0.65 % (700102)Instructions burned: 117 (million)
% 1.35/0.65 % (700114)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2978977652:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.35/0.65 % (700115)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=329462176:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.35/0.65 % (700104)Instruction limit reached!
% 1.35/0.65 % (700104)------------------------------
% 1.35/0.65 % (700104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.65 % (700104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.65 % (700104)CaDiCaL version: 2.1.3
% 1.35/0.65 % (700104)Termination reason: Instruction limit
% 1.35/0.65 % (700104)Termination phase: Saturation
% 1.35/0.65 % (700104)Time elapsed: 0.101 s
% 1.35/0.65 % (700104)Peak memory usage: 12 MB
% 1.35/0.65 % (700104)Instructions burned: 160 (million)
% 1.35/0.65 % (700118)ott-21_1_sil=16000:fs=off:random_seed=3649231928:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.35/0.65 % TRYING [1]
% 1.35/0.65 % TRYING [2]
% 1.35/0.65 % TRYING [3]
% 1.35/0.65 % (700114)Instruction limit reached!
% 1.35/0.65 % (700114)------------------------------
% 1.35/0.65 % (700114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.65 % (700114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.65 % (700114)CaDiCaL version: 2.1.3
% 1.35/0.65 % (700114)Termination reason: Instruction limit
% 1.35/0.65 % (700114)Termination phase: Saturation
% 1.35/0.65 % (700114)Time elapsed: 0.089 s
% 1.35/0.65 % (700114)Peak memory usage: 13 MB
% 1.35/0.65 % (700114)Instructions burned: 131 (million)
% 1.35/0.65 % TRYING [1]
% 1.35/0.65 % (700115) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-700093-700115"...
% 1.35/0.65 % TRYING [2]
% 1.35/0.65 % (700115)...printing done.
% 1.35/0.65 % (700115)Refutation found. Thanks to Tanya!
% 1.35/0.65 % SZS status Unsatisfiable for theBenchmark
% 1.35/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.35/0.65 % (700115)------------------------------
% 1.35/0.65 % (700115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.65 % (700115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.65 % (700115)CaDiCaL version: 2.1.3
% 1.35/0.65 % (700115)Termination reason: Refutation
% 1.35/0.65 % (700115)Time elapsed: 0.087 s
% 1.35/0.65 % (700115)Peak memory usage: 13 MB
% 1.35/0.65 % (700115)Instructions burned: 124 (million)
% 1.35/0.65 % (700093)Success in time 0.236 s
% 1.35/0.65 % Vampire exiting
%------------------------------------------------------------------------------