%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET204-6 : 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 : n003.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 12:43:27 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 27 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f122,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property2_1) ).
fof(f123,negated_conjecture,
~ member(ordered_pair(v,u),cross_product(y,x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property2_2) ).
fof(f128,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(f137,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,f128]) ).
fof(f138,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,f128]) ).
fof(f139,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,f128]) ).
fof(f186,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(x,y)),
inference(definition_unfolding,[],[f122,f128]) ).
fof(f187,plain,
~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(u,u))),cross_product(y,x)),
inference(definition_unfolding,[],[f123,f128]) ).
fof(f398,plain,
member(u,x),
inference(resolution,[],[f137,f186]) ).
fof(f400,plain,
member(v,y),
inference(resolution,[],[f138,f186]) ).
fof(f457,plain,
( ~ member(u,x)
| ~ member(v,y) ),
inference(resolution,[],[f139,f187]) ).
fof(f462,plain,
~ member(v,y),
inference(forward_subsumption_resolution,[],[f457,f398]) ).
fof(f463,plain,
$false,
inference(forward_subsumption_resolution,[],[f462,f400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 01:08:11 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.44 % (1097500)Will run a generic schedule for satisfiability detection.
% 0.12/0.44 % (1097506)% WARNING: option uhcvi not known.
% 0.12/0.44 % (1097506)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3939088089:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.44 % (1097505)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1477556462_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.44 % (1097511)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=122535188:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.44 % (1097507)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1540262636:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.44 % (1097508)dis+10_1_sil=32000:sp=arity:random_seed=2299851236:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.44 % (1097509)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=428329952:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.44 % (1097510)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1893770130:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.44 % (1097506) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1097500-1097506"...
% 0.12/0.44 % (1097506)...printing done.
% 0.12/0.44 % (1097506)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.44 % (1097506)------------------------------
% 0.12/0.44 % (1097506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.44 % (1097506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.44 % (1097506)CaDiCaL version: 2.1.3
% 0.12/0.44 % (1097506)Termination reason: Refutation
% 0.12/0.44 % (1097506)Time elapsed: 0.007 s
% 0.12/0.44 % (1097506)Peak memory usage: 12 MB
% 0.12/0.44 % (1097506)Instructions burned: 16 (million)
% 0.12/0.44 % (1097500)Success in time 0.038 s
% 0.12/0.44 % Vampire exiting
%------------------------------------------------------------------------------