%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET954+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 12:42:24 PM UTC 2026
% Result : Theorem 3.01s 1.09s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 38 ( 17 ~; 11 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
& in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
( ~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,sK2))
& in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,sK2)),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
in(sK1,sK3),
inference(resolution,[],[f15,f18]) ).
fof(f22,plain,
in(sK0,sK2),
inference(resolution,[],[f15,f19]) ).
fof(f24,plain,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(resolution,[],[f16,f20]) ).
fof(f25,plain,
~ in(sK0,sK2),
inference(forward_subsumption_resolution,[],[f24,f21]) ).
fof(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:15:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.01/1.09 % (1403424)Detected formulas, will run a generic FOF schedule.
% 3.01/1.09 % (1403431)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=505024871:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.01/1.09 % (1403429)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=1132857028:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.01/1.09 % (1403435)dis-21_1_sil=8000:lcm=predicate:random_seed=2866019958: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)
% 3.01/1.09 % (1403432)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=814602548:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.01/1.09 % (1403433)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2863787320:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.01/1.09 % (1403430)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=2675360315:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.01/1.09 % (1403434)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4137300934:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.01/1.09 % (1403433)Also succeeded, but the first one will report.
% 3.01/1.09 % (1403432)First to succeed.
% 3.01/1.09 % (1403432)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1403424"
% 3.01/1.09 % (1403435)Also succeeded, but the first one will report.
% 3.01/1.09 % (1403434)Also succeeded, but the first one will report.
% 3.01/1.09 % (1403432)Refutation found. Thanks to Tanya!
% 3.01/1.09 % SZS status Theorem for theBenchmark
% 3.01/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.01/1.09 % (1403432)------------------------------
% 3.01/1.09 % (1403432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.09 % (1403432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.09 % (1403432)CaDiCaL version: 2.1.3
% 3.01/1.09 % (1403432)Termination reason: Refutation
% 3.01/1.09 % (1403432)Time elapsed: 0.002 s
% 3.01/1.09 % (1403432)Peak memory usage: 88 MB
% 3.01/1.09 % (1403432)Instructions burned: 1 (million)
% 3.01/1.09 % (1403432)------------------------------
% 3.01/1.09 % (1403432)------------------------------
% 3.01/1.09 % (1403424)Success in time 0.387 s
% 3.01/1.09 % Vampire exiting
%------------------------------------------------------------------------------