%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:45:06 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 35 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 2 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) = cartesian_product2(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) = cartesian_product2(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
& subset(X0,X1)
& subset(X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
& subset(X0,X1)
& subset(X2,X3) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
( cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4))
& subset(sK2,sK3)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f13]) ).
fof(f18,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
sK4 = set_intersection2(sK4,sK5),
inference(resolution,[],[f27,f24]) ).
fof(f29,plain,
sK2 = set_intersection2(sK2,sK3),
inference(resolution,[],[f27,f25]) ).
fof(f35,plain,
! [X0,X1] : set_intersection2(cartesian_product2(sK2,X0),cartesian_product2(sK3,X1)) = cartesian_product2(sK2,set_intersection2(X0,X1)),
inference(superposition,[],[f23,f29]) ).
fof(f58,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,set_intersection2(sK5,sK4)),
inference(superposition,[],[f26,f35]) ).
fof(f65,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,set_intersection2(sK4,sK5)),
inference(superposition,[],[f58,f18]) ).
fof(f66,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,sK4),
inference(superposition,[],[f65,f28]) ).
fof(f67,plain,
$false,
inference(trivial_inequality_removal,[],[f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:16:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (2631839)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2631844)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=43937563_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % (2631845)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2631846)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2004493674:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2631849)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3765958932:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2631847)dis+10_1_sil=32000:sp=arity:random_seed=3164971333:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2631848)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3526303640:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2631850)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2151863370:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2631845)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3336707711:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (2631850) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2631839-2631850"...
% 0.10/0.45 % (2631846) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2631839-2631846"...
% 0.10/0.45 % (2631846)...printing done.
% 0.10/0.45 % (2631850)...printing done.
% 0.10/0.45 % (2631847) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2631839-2631847"...
% 0.10/0.45 % (2631848) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2631839-2631848"...
% 0.10/0.45 % (2631850)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2631850)------------------------------
% 0.10/0.45 % (2631850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2631850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2631850)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2631850)Termination reason: Refutation
% 0.10/0.45 % (2631850)Time elapsed: 0.003 s
% 0.10/0.45 % (2631850)Peak memory usage: 11 MB
% 0.10/0.45 % (2631850)Instructions burned: 4 (million)
% 0.10/0.45 % (2631839)Success in time 0.042 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------