%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET912+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 : n003.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 12:44:58 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 42 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 13 ~; 8 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f9,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X2,X1) )
=> set_intersection2(unordered_pair(X0,X2),X1) = unordered_pair(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
( ( in(X0,X1)
& in(X2,X1) )
=> set_intersection2(unordered_pair(X0,X2),X1) = unordered_pair(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f16,plain,
? [X0,X1,X2] :
( unordered_pair(X0,X2) != set_intersection2(unordered_pair(X0,X2),X1)
& in(X0,X1)
& in(X2,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
? [X0,X1,X2] :
( unordered_pair(X0,X2) != set_intersection2(unordered_pair(X0,X2),X1)
& in(X0,X1)
& in(X2,X1) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f29,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
unordered_pair(sK2,sK4) != set_intersection2(unordered_pair(sK2,sK4),sK3),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
unordered_pair(sK2,sK4) != set_intersection2(sK3,unordered_pair(sK2,sK4)),
inference(superposition,[],[f31,f20]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ in(X2,X1)
| ~ in(X0,X1)
| unordered_pair(X0,X2) = set_intersection2(unordered_pair(X0,X2),X1) ),
inference(resolution,[],[f28,f25]) ).
fof(f59,plain,
! [X0] :
( ~ in(X0,sK3)
| unordered_pair(X0,sK2) = set_intersection2(unordered_pair(X0,sK2),sK3) ),
inference(resolution,[],[f47,f30]) ).
fof(f62,plain,
! [X0] :
( ~ in(X0,sK3)
| unordered_pair(X0,sK2) = set_intersection2(sK3,unordered_pair(X0,sK2)) ),
inference(forward_demodulation,[],[f59,f20]) ).
fof(f64,plain,
unordered_pair(sK4,sK2) = set_intersection2(sK3,unordered_pair(sK4,sK2)),
inference(resolution,[],[f62,f29]) ).
fof(f66,plain,
unordered_pair(sK2,sK4) = set_intersection2(sK3,unordered_pair(sK2,sK4)),
inference(forward_demodulation,[],[f64,f19]) ).
fof(f67,plain,
$false,
inference(forward_subsumption_resolution,[],[f66,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n003.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 03:11:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.44 % (1148766)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (1148772)% WARNING: option uhcvi not known.
% 0.11/0.44 % (1148772)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=990750645:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % (1148772) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1148766-1148772"...
% 0.11/0.44 % (1148772)...printing done.
% 0.11/0.44 % (1148772)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (1148772)------------------------------
% 0.11/0.45 % (1148772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (1148772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (1148772)CaDiCaL version: 2.1.3
% 0.11/0.45 % (1148772)Termination reason: Refutation
% 0.11/0.45 % (1148772)Time elapsed: 0.002 s
% 0.11/0.45 % (1148772)Peak memory usage: 12 MB
% 0.11/0.45 % (1148772)Instructions burned: 3 (million)
% 0.11/0.45 % (1148766)Success in time 0.027 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------