%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET622+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 : 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 12:44:12 PM UTC 2026
% Result : Theorem 0.03s 0.39s
% Output : Refutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(f2,axiom,
! [X0,X1,X2] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
fof(f3,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
fof(f15,conjecture,
! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f18,plain,
? [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) != union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
inference(ennf_transformation,[],[f16]) ).
fof(f33,plain,
difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f18]) ).
fof(f34,plain,
! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X2,X0,X1] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
fof(f61,plain,
difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),
inference(cnf_transformation,[],[f33]) ).
fof(f64,plain,
union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)) != difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),
inference(definition_unfolding,[],[f61,f36]) ).
fof(f83,plain,
difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))) != union(difference(sK2,union(sK3,sK4)),intersection(sK2,intersection(sK3,sK4))),
inference(superposition,[],[f64,f34]) ).
fof(f88,plain,
$false,
inference(forward_subsumption_resolution,[],[f83,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.34 % Computer : n012.cluster.edu
% 0.03/0.34 % Model : x86_64 x86_64
% 0.03/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.34 % Memory : 8046.5625MB
% 0.03/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/0.34 % CPULimit : 300
% 0.03/0.34 % WCLimit : 300
% 0.03/0.34 % DateTime : Mon Sep 28 02:19:50 UTC 2026
% 0.03/0.35 % CPUTime :
% 0.03/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.36 Running first-order model finding
% 0.03/0.36 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
% 0.03/0.39 % (2948398)Will run a generic schedule for satisfiability detection.
% 0.03/0.39 % (2948404)% WARNING: option uhcvi not known.
% 0.03/0.39 % (2948406)dis+10_1_sil=32000:sp=arity:random_seed=1704066530:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.03/0.39 % (2948403)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3965428174_2999 on theBenchmark for (2999ds/0Mi)
% 0.03/0.39 % (2948405)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1868677539:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.03/0.39 % (2948404)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2465438781:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.03/0.39 % (2948407)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2754207608:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.03/0.39 % (2948408)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=861827803:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.03/0.39 % (2948409)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=873377557:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.03/0.39 % TRYING [1]
% 0.03/0.39 % TRYING [2]
% 0.03/0.39 % (2948408) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2948398-2948408"...
% 0.03/0.39 % (2948407) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2948398-2948407"...
% 0.03/0.39 % TRYING [3]
% 0.03/0.39 % (2948408)...printing done.
% 0.03/0.39 % (2948407)...printing done.
% 0.03/0.39 % (2948408)Refutation found. Thanks to Tanya!
% 0.03/0.39 % SZS status Theorem for theBenchmark
% 0.03/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.03/0.39 % (2948408)------------------------------
% 0.03/0.39 % (2948408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.03/0.39 % (2948408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.03/0.39 % (2948408)CaDiCaL version: 2.1.3
% 0.03/0.39 % (2948408)Termination reason: Refutation
% 0.03/0.39 % (2948408)Time elapsed: 0.001 s
% 0.03/0.39 % (2948408)Peak memory usage: 11 MB
% 0.03/0.39 % (2948408)Instructions burned: 3 (million)
% 0.03/0.39 % (2948398)Success in time 0.025 s
% 0.03/0.39 % Vampire exiting
%------------------------------------------------------------------------------