%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:45:07 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : Refutation 0.09s
% 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(f12,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(f13,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,[],[f12]) ).
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(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X0)
& in(sK0(X0,X1,X2),X1) )
| in(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f16]) ).
fof(f20,plain,
( ~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7)))
& in(sK3,cartesian_product2(sK4,sK5))
& in(sK3,cartesian_product2(sK6,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7)],[f13]) ).
fof(f25,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,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(f33,plain,
in(sK3,cartesian_product2(sK6,sK7)),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
in(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7))),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f25]) ).
fof(f532,plain,
~ in(sK3,set_intersection2(cartesian_product2(sK4,sK5),cartesian_product2(sK6,sK7))),
inference(superposition,[],[f35,f32]) ).
fof(f533,plain,
( ~ in(sK3,cartesian_product2(sK4,sK5))
| ~ in(sK3,cartesian_product2(sK6,sK7)) ),
inference(resolution,[],[f532,f36]) ).
fof(f534,plain,
~ in(sK3,cartesian_product2(sK6,sK7)),
inference(forward_subsumption_resolution,[],[f533,f34]) ).
fof(f535,plain,
$false,
inference(forward_subsumption_resolution,[],[f534,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:22:48 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % (3227298)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (3227305)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1600804751:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (3227303)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2402189353_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (3227306)dis+10_1_sil=32000:sp=arity:random_seed=3765601330:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (3227308)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1006175829:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (3227309)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3329685235:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % (3227306) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3227298-3227306"...
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % (3227309) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3227298-3227309"...
% 0.09/0.45 % (3227306)...printing done.
% 0.09/0.45 % (3227308) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3227298-3227308"...
% 0.09/0.45 % (3227309)...printing done.
% 0.09/0.45 % (3227305) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3227298-3227305"...
% 0.09/0.45 % (3227308)...printing done.
% 0.09/0.45 % (3227305)...printing done.
% 0.09/0.45 % (3227307)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3124492091:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (3227304)% WARNING: option uhcvi not known.
% 0.09/0.45 % (3227305)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (3227305)------------------------------
% 0.09/0.45 % (3227305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (3227305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (3227305)CaDiCaL version: 2.1.3
% 0.09/0.45 % (3227305)Termination reason: Refutation
% 0.09/0.45 % (3227305)Time elapsed: 0.013 s
% 0.09/0.45 % (3227305)Peak memory usage: 12 MB
% 0.09/0.45 % (3227305)Instructions burned: 44 (million)
% 0.09/0.45 % (3227298)Success in time 0.038 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------