%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n016.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 12:42:26 PM UTC 2026
% Result : Theorem 4.77s 1.88s
% Output : Refutation 4.77s
% 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(f40,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(f140,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,set_intersection2(sK5,sK4)),
inference(superposition,[],[f26,f40]) ).
fof(f152,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,set_intersection2(sK4,sK5)),
inference(forward_demodulation,[],[f140,f18]) ).
fof(f155,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,sK4),
inference(forward_demodulation,[],[f152,f28]) ).
fof(f156,plain,
$false,
inference(trivial_inequality_removal,[],[f155]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:21:33 UTC 2026
% 0.16/0.39 % CPUTime :
% 0.16/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.77/1.88 % (3224782)Detected formulas, will run a generic FOF schedule.
% 4.77/1.88 % (3224802)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1715285218:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.77/1.88 % (3224807)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3523014205:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.77/1.88 % (3224805)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2166376619:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.77/1.88 % (3224805)Refutation not found, incomplete strategy
% 4.77/1.88 % (3224805)------------------------------
% 4.77/1.88 % (3224805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.88 % (3224805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.88 % (3224805)CaDiCaL version: 2.1.3
% 4.77/1.88 % (3224805)Termination reason: Refutation not found, incomplete strategy
% 4.77/1.88 % (3224805)Time elapsed: 0.002 s
% 4.77/1.88 % (3224805)Peak memory usage: 88 MB
% 4.77/1.88 % (3224803)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3046969564:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.77/1.88 % (3224807)First to succeed.
% 4.77/1.88 % (3224807)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3224782"
% 4.77/1.88 % (3224806)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2422725491:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.77/1.88 % (3224808)dis-21_1_sil=8000:lcm=predicate:random_seed=2991803679:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.77/1.88 % (3224804)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4094626215:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.77/1.88 % (3224808)Refutation not found, incomplete strategy
% 4.77/1.88 % (3224808)------------------------------
% 4.77/1.88 % (3224808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.88 % (3224808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.88 % (3224808)CaDiCaL version: 2.1.3
% 4.77/1.88 % (3224808)Termination reason: Refutation not found, incomplete strategy
% 4.77/1.88 % (3224808)Time elapsed: 0.002 s
% 4.77/1.88 % (3224808)Peak memory usage: 88 MB
% 4.77/1.88 % (3224806)Also succeeded, but the first one will report.
% 4.77/1.88 % (3224805)------------------------------
% 4.77/1.88 % (3224805)------------------------------
% 4.77/1.88 % (3224808)------------------------------
% 4.77/1.88 % (3224808)------------------------------
% 4.77/1.88 % (3224807)Refutation found. Thanks to Tanya!
% 4.77/1.88 % SZS status Theorem for theBenchmark
% 4.77/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 4.77/1.88 % (3224807)------------------------------
% 4.77/1.88 % (3224807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.88 % (3224807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.88 % (3224807)CaDiCaL version: 2.1.3
% 4.77/1.88 % (3224807)Termination reason: Refutation
% 4.77/1.88 % (3224807)Time elapsed: 0.008 s
% 4.77/1.88 % (3224807)Peak memory usage: 89 MB
% 4.77/1.88 % (3224807)Instructions burned: 8 (million)
% 4.77/1.88 % (3224807)------------------------------
% 4.77/1.88 % (3224807)------------------------------
% 4.77/1.88 % (3224782)Success in time 0.55 s
% 4.77/1.88 % Vampire exiting
%------------------------------------------------------------------------------