%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET114-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:43:10 PM UTC 2026
% Result : Unsatisfiable 0.04s 0.41s
% Output : Refutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f176,axiom,
! [X0] :
( member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class))
| second(X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
fof(f181,negated_conjecture,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets2_1) ).
fof(f182,negated_conjecture,
second(x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_2nd_in_pair_of_non_sets) ).
fof(f183,plain,
x != second(x),
inference(reorient_equations,[],[f182]) ).
fof(f188,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(f276,plain,
! [X0] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| second(X0) = X0 ),
inference(definition_unfolding,[],[f176,f188]) ).
fof(f281,plain,
~ member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f181,f188]) ).
fof(f1189,plain,
x = second(x),
inference(resolution,[],[f276,f281]) ).
fof(f1201,plain,
$false,
inference(forward_subsumption_resolution,[],[f1189,f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET114-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.33 % Computer : n012.cluster.edu
% 0.04/0.33 % Model : x86_64 x86_64
% 0.04/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.33 % Memory : 8046.5625MB
% 0.04/0.33 % OS : Linux 6.8.0-71-generic
% 0.04/0.33 % CPULimit : 300
% 0.04/0.33 % WCLimit : 300
% 0.04/0.33 % DateTime : Mon Sep 28 00:46:50 UTC 2026
% 0.04/0.33 % CPUTime :
% 0.04/0.33 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.35 Running first-order model finding
% 0.04/0.35 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
% 0.04/0.41 % (2910289)Will run a generic schedule for satisfiability detection.
% 0.04/0.41 % (2910295)% WARNING: option uhcvi not known.
% 0.04/0.41 % (2910294)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1071964139_2999 on theBenchmark for (2999ds/0Mi)
% 0.04/0.41 % (2910295)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=817271771:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.04/0.41 % (2910297)dis+10_1_sil=32000:sp=arity:random_seed=2008983009:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.04/0.41 % (2910296)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1983005152:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.04/0.41 % (2910298)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4271133338:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.04/0.41 % (2910299)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3933197622:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.04/0.41 % (2910300)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1154676758:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.04/0.41 % (2910295) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2910289-2910295"...
% 0.04/0.41 % (2910295)...printing done.
% 0.04/0.41 % (2910295)Refutation found. Thanks to Tanya!
% 0.04/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.04/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.04/0.41 % (2910295)------------------------------
% 0.04/0.41 % (2910295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/0.41 % (2910295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/0.41 % (2910295)CaDiCaL version: 2.1.3
% 0.04/0.41 % (2910295)Termination reason: Refutation
% 0.04/0.41 % (2910295)Time elapsed: 0.018 s
% 0.04/0.41 % (2910295)Peak memory usage: 12 MB
% 0.04/0.41 % (2910295)Instructions burned: 47 (million)
% 0.04/0.41 % (2910289)Success in time 0.05 s
% 0.04/0.41 % Vampire exiting
%------------------------------------------------------------------------------