%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:44:11 PM UTC 2026
% Result : Theorem 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_into_intersection) ).
fof(f3,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f14,conjecture,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th96) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
? [X0,X1] : symmetric_difference(X0,X1) != difference(union(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f32,plain,
symmetric_difference(sK2,sK3) != difference(union(sK2,sK3),intersection(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f33,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X2,X0,X1] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f49,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f59,plain,
symmetric_difference(sK2,sK3) != difference(union(sK2,sK3),intersection(sK2,sK3)),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
difference(union(sK2,sK3),intersection(sK2,sK3)) != union(difference(sK2,sK3),difference(sK3,sK2)),
inference(definition_unfolding,[],[f59,f33]) ).
fof(f97,plain,
! [X0,X1] : difference(X1,X0) = difference(X1,intersection(X0,X1)),
inference(superposition,[],[f34,f49]) ).
fof(f144,plain,
! [X2,X0,X1] : difference(union(X0,X2),intersection(X0,X1)) = union(difference(X0,X1),difference(X2,intersection(X0,X1))),
inference(superposition,[],[f35,f34]) ).
fof(f299,plain,
! [X0,X1] : union(difference(X1,X0),difference(X0,X1)) = difference(union(X1,X0),intersection(X1,X0)),
inference(superposition,[],[f144,f97]) ).
fof(f730,plain,
union(difference(sK2,sK3),difference(sK3,sK2)) != union(difference(sK2,sK3),difference(sK3,sK2)),
inference(superposition,[],[f61,f299]) ).
fof(f763,plain,
$false,
inference(trivial_inequality_removal,[],[f730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:21:52 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.16/0.49 % (4089862)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (4089869)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=359794864:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (4089868)% WARNING: option uhcvi not known.
% 0.16/0.49 % (4089867)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=701440548_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (4089868)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=588925073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (4089870)dis+10_1_sil=32000:sp=arity:random_seed=2152533371:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (4089871)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1838071999:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (4089873)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3654525078:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (4089872)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1526731674:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % (4089873) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4089862-4089873"...
% 0.16/0.49 % (4089873)...printing done.
% 0.16/0.49 % (4089873)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (4089873)------------------------------
% 0.16/0.49 % (4089873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (4089873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (4089873)CaDiCaL version: 2.1.3
% 0.16/0.49 % (4089873)Termination reason: Refutation
% 0.16/0.49 % (4089873)Time elapsed: 0.025 s
% 0.16/0.49 % (4089873)Peak memory usage: 12 MB
% 0.16/0.49 % (4089873)Instructions burned: 39 (million)
% 0.16/0.49 % (4089862)Success in time 0.058 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------