%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 12:45:04 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 35 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 9 |; 2 &)
% ( 1 <=>; 2 =>; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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(f11,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(f14,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f21,plain,
in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4)),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f18,f14]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f17,f14]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f16,f14]) ).
fof(f27,plain,
~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
inference(definition_unfolding,[],[f22,f14]) ).
fof(f28,plain,
in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
inference(definition_unfolding,[],[f21,f14]) ).
fof(f51,plain,
in(sK2,sK4),
inference(resolution,[],[f25,f28]) ).
fof(f58,plain,
in(sK3,sK5),
inference(resolution,[],[f26,f28]) ).
fof(f65,plain,
( ~ in(sK3,sK5)
| ~ in(sK2,sK4) ),
inference(resolution,[],[f24,f27]) ).
fof(f78,plain,
~ in(sK2,sK4),
inference(forward_subsumption_resolution,[],[f65,f58]) ).
fof(f79,plain,
$false,
inference(forward_subsumption_resolution,[],[f78,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 SAT
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:17:05 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.43 % (3993023)Will run a generic schedule for satisfiability detection.
% 0.13/0.43 % (3993032)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1823218397:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.43 % (3993032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3993023-3993032"...
% 0.13/0.43 % (3993032)...printing done.
% 0.13/0.43 % (3993032)Refutation found. Thanks to Tanya!
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.43 % (3993032)------------------------------
% 0.13/0.43 % (3993032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.43 % (3993032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.43 % (3993032)CaDiCaL version: 2.1.3
% 0.13/0.43 % (3993032)Termination reason: Refutation
% 0.13/0.43 % (3993032)Time elapsed: 0.002 s
% 0.13/0.43 % (3993032)Peak memory usage: 12 MB
% 0.13/0.43 % (3993032)Instructions burned: 3 (million)
% 0.13/0.43 % (3993023)Success in time 0.034 s
% 0.13/0.43 % Vampire exiting
%------------------------------------------------------------------------------