%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:42:28 PM UTC 2026
% Result : Theorem 2.05s 0.90s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 92 ( 12 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 113 ( 42 ~; 38 |; 29 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 58 ( 45 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,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/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X1,X2))
& in(X0,cartesian_product2(X3,X4)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X1,X2))
& in(X0,cartesian_product2(X3,X4)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X1,X2))
& in(X0,cartesian_product2(X3,X4)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X1,X2))
& in(X0,cartesian_product2(X3,X4)) ),
inference(flattening,[],[f10]) ).
fof(f13,plain,
( ~ in(sK0,cartesian_product2(set_intersection2(sK1,sK3),set_intersection2(sK2,sK4)))
& in(sK0,cartesian_product2(sK1,sK2))
& in(sK0,cartesian_product2(sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f16]) ).
fof(f18,plain,
in(sK0,cartesian_product2(sK3,sK4)),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
in(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
~ in(sK0,cartesian_product2(set_intersection2(sK1,sK3),set_intersection2(sK2,sK4))),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,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,[],[f7]) ).
fof(f29,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f23]) ).
fof(f32,plain,
~ in(sK0,set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),
inference(forward_demodulation,[],[f20,f28]) ).
fof(f35,plain,
( ~ in(sK0,cartesian_product2(sK1,sK2))
| ~ in(sK0,cartesian_product2(sK3,sK4)) ),
inference(resolution,[],[f32,f29]) ).
fof(f36,plain,
~ in(sK0,cartesian_product2(sK3,sK4)),
inference(forward_subsumption_resolution,[],[f35,f19]) ).
fof(f37,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 03:17:49 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.05/0.90 % (2984528)Detected formulas, will run a generic FOF schedule.
% 2.05/0.90 % (2984533)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=1159777028:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.05/0.90 % (2984538)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3441065930:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.05/0.90 % (2984537)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2175858174:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.05/0.90 % (2984535)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=1551342067:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.05/0.90 % (2984534)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=44137447:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.05/0.90 % (2984539)dis-21_1_sil=8000:lcm=predicate:random_seed=2016676651: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)
% 2.05/0.90 % (2984536)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2160286785:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.05/0.90 % (2984536)First to succeed.
% 2.05/0.90 % (2984536)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2984528"
% 2.05/0.90 % (2984538)Also succeeded, but the first one will report.
% 2.05/0.90 % (2984537)Also succeeded, but the first one will report.
% 2.05/0.90 % (2984539)Instruction limit reached!
% 2.05/0.90 % (2984539)------------------------------
% 2.05/0.90 % (2984539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.90 % (2984539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.90 % (2984539)CaDiCaL version: 2.1.3
% 2.05/0.90 % (2984539)Termination reason: Instruction limit
% 2.05/0.90 % (2984539)Termination phase: Saturation
% 2.05/0.90 % (2984539)Time elapsed: 0.036 s
% 2.05/0.90 % (2984539)Peak memory usage: 88 MB
% 2.05/0.90 % (2984539)Instructions burned: 129 (million)
% 2.05/0.90 % (2984547)lrs+10_1_sil=8000:sp=occurrence:random_seed=2722171741:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.05/0.90 % (2984547)Also succeeded, but the first one will report.
% 2.05/0.90 % (2984536)Refutation found. Thanks to Tanya!
% 2.05/0.90 % SZS status Theorem for theBenchmark
% 2.05/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 2.05/0.90 % (2984536)------------------------------
% 2.05/0.90 % (2984536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.90 % (2984536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.90 % (2984536)CaDiCaL version: 2.1.3
% 2.05/0.90 % (2984536)Termination reason: Refutation
% 2.05/0.90 % (2984536)Time elapsed: 0.001 s
% 2.05/0.90 % (2984536)Peak memory usage: 88 MB
% 2.05/0.90 % (2984536)Instructions burned: 1 (million)
% 2.05/0.90 % (2984536)------------------------------
% 2.05/0.90 % (2984536)------------------------------
% 2.05/0.90 % (2984528)Success in time 0.266 s
% 2.05/0.90 % Vampire exiting
%------------------------------------------------------------------------------