%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET103-6 : 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 : n006.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 12:43:08 PM UTC 2026
% Result : Unsatisfiable 0.34s 0.56s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 62 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 15 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 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(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).
fof(f71,axiom,
! [X0,X1] : sum_class(image(X0,singleton(X1))) = apply(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',apply) ).
fof(f73,axiom,
! [X0] :
( ~ member(X0,universal_class)
| X0 = null_class
| member(apply(choice,X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',choice2) ).
fof(f74,plain,
! [X0] :
( ~ member(X0,universal_class)
| null_class = X0
| member(apply(choice,X0),X0) ),
inference(reorient_equations,[],[f73]) ).
fof(f101,negated_conjecture,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_1) ).
fof(f102,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_2) ).
fof(f103,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f104,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f105,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f104,f28]) ).
fof(f106,plain,
! [X0,X1] : apply(X0,X1) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f71,f103,f105,f12]) ).
fof(f107,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(f139,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X0)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f74,f106]) ).
fof(f151,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f101,f12,f107]) ).
fof(f160,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ),
inference(resolution,[],[f139,f8]) ).
fof(f162,plain,
! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = null_class ),
inference(forward_subsumption_resolution,[],[f160,f11]) ).
fof(f175,plain,
! [X0,X1] :
( X0 != X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = null_class ),
inference(equality_factoring,[],[f162]) ).
fof(f181,plain,
! [X0] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X0) = null_class ),
inference(equality_resolution,[],[f175]) ).
fof(f182,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class
| ~ member(unordered_pair(X0,X0),universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(superposition,[],[f139,f181]) ).
fof(f185,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class
| ~ member(unordered_pair(X0,X0),universal_class) ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f186,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class ),
inference(forward_subsumption_resolution,[],[f185,f11]) ).
fof(f587,plain,
! [X0,X1] :
( ~ subclass(unordered_pair(X0,X0),X1)
| member(X0,X1)
| unordered_pair(X0,X0) = null_class ),
inference(resolution,[],[f1,f186]) ).
fof(f1496,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(resolution,[],[f587,f4]) ).
fof(f1505,plain,
null_class = unordered_pair(y,y),
inference(resolution,[],[f1496,f102]) ).
fof(f1515,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),
inference(superposition,[],[f151,f1505]) ).
fof(f1555,plain,
$false,
inference(trivial_inequality_removal,[],[f1515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET103-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.37 % Computer : n006.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 28 00:43:25 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 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
% 0.34/0.56 % (3485987)Will run a generic schedule for satisfiability detection.
% 0.34/0.56 % (3485996)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2833679109:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.34/0.56 % (3485992)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=307990354_2999 on theBenchmark for (2999ds/0Mi)
% 0.34/0.56 % (3485994)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=613591440:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.34/0.56 % (3485995)dis+10_1_sil=32000:sp=arity:random_seed=1083202352:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.34/0.56 % (3485997)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2242084418:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.34/0.56 % (3485998)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=402811559:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.34/0.56 % (3485993)% WARNING: option uhcvi not known.
% 0.34/0.56 % (3485993)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1051496319:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.34/0.56 % (3485996)Instruction limit reached!
% 0.34/0.56 % (3485996)------------------------------
% 0.34/0.56 % (3485996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.56 % (3485996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.56 % (3485996)CaDiCaL version: 2.1.3
% 0.34/0.56 % (3485996)Termination reason: Instruction limit
% 0.34/0.56 % (3485996)Termination phase: Saturation
% 0.34/0.56 % (3485996)Time elapsed: 0.039 s
% 0.34/0.56 % (3485996)Peak memory usage: 12 MB
% 0.34/0.56 % (3485996)Instructions burned: 117 (million)
% 0.34/0.56 % (3486006)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4264484207:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.34/0.56 % (3485995)Instruction limit reached!
% 0.34/0.56 % (3485995)------------------------------
% 0.34/0.56 % (3485995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.56 % (3485995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.56 % (3485995)CaDiCaL version: 2.1.3
% 0.34/0.56 % (3485995)Termination reason: Instruction limit
% 0.34/0.56 % (3485995)Termination phase: Saturation
% 0.34/0.56 % (3485995)Time elapsed: 0.066 s
% 0.34/0.56 % (3485995)Peak memory usage: 12 MB
% 0.34/0.56 % (3485995)Instructions burned: 103 (million)
% 0.34/0.56 % (3485997)Instruction limit reached!
% 0.34/0.56 % (3485997)------------------------------
% 0.34/0.56 % (3485997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.56 % (3485997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.56 % (3485997)CaDiCaL version: 2.1.3
% 0.34/0.56 % (3485997)Termination reason: Instruction limit
% 0.34/0.56 % (3485997)Termination phase: Saturation
% 0.34/0.56 % (3485997)Time elapsed: 0.078 s
% 0.34/0.56 % (3485997)Peak memory usage: 12 MB
% 0.34/0.56 % (3485997)Instructions burned: 132 (million)
% 0.34/0.56 % (3486008)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=194269793:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.34/0.56 % (3486009)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=639200466:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.34/0.56 % (3485998)Instruction limit reached!
% 0.34/0.56 % (3485998)------------------------------
% 0.34/0.56 % (3485998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.56 % (3485998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.56 % (3486009) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3485987-3486009"...
% 0.34/0.56 % (3485998)CaDiCaL version: 2.1.3
% 0.34/0.56 % (3485998)Termination reason: Instruction limit
% 0.34/0.56 % (3485998)Termination phase: Saturation
% 0.34/0.56 % (3485998)Time elapsed: 0.108 s
% 0.34/0.56 % (3485998)Peak memory usage: 13 MB
% 0.34/0.56 % (3485998)Instructions burned: 159 (million)
% 0.34/0.56 % (3486009)...printing done.
% 0.34/0.56 % (3486009)Refutation found. Thanks to Tanya!
% 0.34/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.34/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.34/0.56 % (3486009)------------------------------
% 0.34/0.56 % (3486009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.56 % (3486009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.56 % (3486009)CaDiCaL version: 2.1.3
% 0.34/0.56 % (3486009)Termination reason: Refutation
% 0.34/0.56 % (3486009)Time elapsed: 0.020 s
% 0.34/0.56 % (3486009)Peak memory usage: 13 MB
% 0.34/0.56 % (3486009)Instructions burned: 51 (million)
% 0.34/0.56 % (3485987)Success in time 0.148 s
% 0.34/0.56 % Vampire exiting
%------------------------------------------------------------------------------