%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:44:14 PM UTC 2026
% Result : Theorem 0.04s 0.39s
% Output : Refutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 47 ( 4 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 14 |; 5 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X1)
| intersect(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_with_union) ).
fof(f3,axiom,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f8,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f12,conjecture,
! [X0,X1] : disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0,X1] : ~ disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( intersect(X0,union(X1,X2))
| ( ~ intersect(X0,X1)
& ~ intersect(X0,X2) ) )
& ( intersect(X0,X1)
| intersect(X0,X2)
| ~ intersect(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( intersect(X0,union(X1,X2))
| ( ~ intersect(X0,X1)
& ~ intersect(X0,X2) ) )
& ( intersect(X0,X1)
| intersect(X0,X2)
| ~ intersect(X0,union(X1,X2)) ) ),
inference(flattening,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| intersect(X0,X1) )
& ( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f27,plain,
~ disjoint(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f28,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f49,plain,
~ disjoint(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
~ disjoint(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))),
inference(definition_unfolding,[],[f49,f28]) ).
fof(f54,plain,
intersect(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))),
inference(resolution,[],[f40,f51]) ).
fof(f57,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),difference(X0,X1)),
inference(resolution,[],[f32,f39]) ).
fof(f64,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),difference(X1,X0)),
inference(superposition,[],[f57,f42]) ).
fof(f87,plain,
( intersect(intersection(sK2,sK3),difference(sK3,sK2))
| intersect(intersection(sK2,sK3),difference(sK2,sK3)) ),
inference(resolution,[],[f29,f54]) ).
fof(f93,plain,
intersect(intersection(sK2,sK3),difference(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f87,f64]) ).
fof(f94,plain,
$false,
inference(forward_subsumption_resolution,[],[f93,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.34 % Computer : n012.cluster.edu
% 0.04/0.34 % Model : x86_64 x86_64
% 0.04/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.34 % Memory : 8046.5625MB
% 0.04/0.34 % OS : Linux 6.8.0-71-generic
% 0.04/0.34 % CPULimit : 300
% 0.04/0.34 % WCLimit : 300
% 0.04/0.34 % DateTime : Mon Sep 28 02:22:34 UTC 2026
% 0.04/0.34 % CPUTime :
% 0.04/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.35 Running first-order model finding
% 0.04/0.35 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
% 0.04/0.39 % (2951562)Will run a generic schedule for satisfiability detection.
% 0.04/0.39 % (2951568)% WARNING: option uhcvi not known.
% 0.04/0.39 % (2951567)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2150406069_2999 on theBenchmark for (2999ds/0Mi)
% 0.04/0.39 % (2951570)dis+10_1_sil=32000:sp=arity:random_seed=2171953672:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.04/0.39 % (2951571)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2315056081:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.04/0.39 % (2951569)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2185560947:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.04/0.39 % (2951568)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2399483023:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.04/0.39 % (2951572)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3386890323:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.04/0.39 % (2951573)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4075123605:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.04/0.39 % TRYING [1]
% 0.04/0.39 % TRYING [2]
% 0.04/0.39 % (2951570) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2951562-2951570"...
% 0.04/0.39 % (2951571) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2951562-2951571"...
% 0.04/0.39 % TRYING [3]
% 0.04/0.39 % (2951568) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2951562-2951568"...
% 0.04/0.39 % (2951573) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2951562-2951573"...
% 0.04/0.39 % (2951570)...printing done.
% 0.04/0.39 % (2951571)...printing done.
% 0.04/0.39 % (2951568)...printing done.
% 0.04/0.39 % (2951570)Refutation found. Thanks to Tanya!
% 0.04/0.39 % SZS status Theorem for theBenchmark
% 0.04/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.04/0.39 % (2951570)------------------------------
% 0.04/0.39 % (2951570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/0.39 % (2951570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/0.39 % (2951570)CaDiCaL version: 2.1.3
% 0.04/0.39 % (2951570)Termination reason: Refutation
% 0.04/0.39 % (2951570)Time elapsed: 0.002 s
% 0.04/0.39 % (2951570)Peak memory usage: 11 MB
% 0.04/0.39 % (2951570)Instructions burned: 3 (million)
% 0.04/0.39 % (2951562)Success in time 0.026 s
% 0.04/0.39 % Vampire exiting
%------------------------------------------------------------------------------