%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET978+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 : n014.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 12:42:27 PM UTC 2026
% Result : Theorem 3.34s 1.35s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 36 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 39 ( 20 ~; 10 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 2 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 : 34 ( 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( disjoint(X0,X1)
| disjoint(X2,X3) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f5,conjecture,
! [X0,X1,X2,X3] :
( X0 != X1
=> ( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
& disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( X0 != X1
=> ( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
& disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f8,plain,
? [X0,X1,X2,X3] :
( ( ~ disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
| ~ disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) )
& X0 != X1 ),
inference(ennf_transformation,[],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ( ~ disjoint(X0,X1)
& ~ disjoint(X2,X3) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f12,plain,
( ( ~ disjoint(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK3))
| ~ disjoint(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK3,singleton(sK1))) )
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f8]) ).
fof(f13,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f12]) ).
fof(f14,plain,
( ~ disjoint(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK3,singleton(sK1)))
| ~ disjoint(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK3)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X2,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
( ~ disjoint(singleton(sK0),singleton(sK1))
| ~ disjoint(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK3)) ),
inference(resolution,[],[f16,f14]) ).
fof(f27,plain,
~ disjoint(singleton(sK0),singleton(sK1)),
inference(forward_subsumption_resolution,[],[f21,f17]) ).
fof(f29,plain,
sK0 = sK1,
inference(resolution,[],[f27,f15]) ).
fof(f31,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:17:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 3.34/1.35 % (1405153)Detected formulas, will run a generic FOF schedule.
% 3.34/1.35 % (1405160)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=4099747937:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.35 % (1405161)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2431270466:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.35 % (1405162)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=144914369:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.35 % (1405162)First to succeed.
% 3.34/1.35 % (1405161)Also succeeded, but the first one will report.
% 3.34/1.35 % (1405162)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1405153"
% 3.34/1.35 % (1405158)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=1750747523:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.35 % (1405159)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=2150746652:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.35 % (1405163)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3135760362:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.35 % (1405163)Also succeeded, but the first one will report.
% 3.34/1.35 % (1405164)dis-21_1_sil=8000:lcm=predicate:random_seed=1355446348: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)
% 3.34/1.35 % (1405164)Also succeeded, but the first one will report.
% 3.34/1.35 % (1405162)Refutation found. Thanks to Tanya!
% 3.34/1.35 % SZS status Theorem for theBenchmark
% 3.34/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/1.35 % (1405162)------------------------------
% 3.34/1.35 % (1405162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.35 % (1405162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.35 % (1405162)CaDiCaL version: 2.1.3
% 3.34/1.35 % (1405162)Termination reason: Refutation
% 3.34/1.35 % (1405162)Time elapsed: 0.002 s
% 3.34/1.35 % (1405162)Peak memory usage: 88 MB
% 3.34/1.35 % (1405162)Instructions burned: 1 (million)
% 3.34/1.35 % (1405162)------------------------------
% 3.34/1.35 % (1405162)------------------------------
% 3.34/1.35 % (1405153)Success in time 0.403 s
% 3.34/1.35 % Vampire exiting
%------------------------------------------------------------------------------