%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:41:25 PM UTC 2026
% Result : Theorem 3.33s 1.34s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 22 unt; 1 def)
% Number of atoms : 22 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 26 !; 3 ?)
% 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] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union) ).
fof(f3,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f7,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f12,conjecture,
! [X0,X1,X2] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th97) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] : difference(symmetric_difference(X0,X1),X2) != union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
difference(symmetric_difference(sK0,sK1),sK2) != union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
fof(f16,plain,
difference(symmetric_difference(sK0,sK1),sK2) != union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))),
inference(cnf_transformation,[],[f15]) ).
fof(f18,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f22,plain,
union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))) != difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(definition_unfolding,[],[f16,f18]) ).
fof(f24,definition,
~ sP3(union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2)))),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f25,plain,
sP3(difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2)),
inference(inequality_splitting,[],[f22,f24]) ).
fof(f26,plain,
~ sP3(union(difference(sK1,union(sK0,sK2)),difference(sK0,union(sK1,sK2)))),
inference(forward_demodulation,[],[f24,f21]) ).
fof(f27,plain,
~ sP3(union(difference(sK1,union(sK0,sK2)),difference(difference(sK0,sK1),sK2))),
inference(forward_demodulation,[],[f26,f20]) ).
fof(f28,plain,
~ sP3(union(difference(difference(sK0,sK1),sK2),difference(sK1,union(sK0,sK2)))),
inference(forward_demodulation,[],[f27,f21]) ).
fof(f29,plain,
~ sP3(union(difference(difference(sK0,sK1),sK2),difference(difference(sK1,sK0),sK2))),
inference(forward_demodulation,[],[f28,f20]) ).
fof(f30,plain,
~ sP3(difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2)),
inference(forward_demodulation,[],[f29,f19]) ).
fof(f31,plain,
$false,
inference(forward_subsumption_resolution,[],[f30,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n006.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 02:21:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/1.34 % (3527809)Detected formulas, will run a generic FOF schedule.
% 3.33/1.34 % (3527814)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1861034995:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.34 % (3527817)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1076125568:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.34 % (3527820)dis-21_1_sil=8000:lcm=predicate:random_seed=3984352128:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.33/1.34 % (3527816)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4124752772:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.34 % (3527818)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2642902413:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.34 % (3527815)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1236822065:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.34 % (3527817)First to succeed.
% 3.33/1.34 % (3527817)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3527809"
% 3.33/1.34 % (3527820)Also succeeded, but the first one will report.
% 3.33/1.34 % (3527819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2870262102:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.34 % (3527818)Also succeeded, but the first one will report.
% 3.33/1.34 % (3527819)Instruction limit reached!
% 3.33/1.34 % (3527819)------------------------------
% 3.33/1.34 % (3527819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.34 % (3527819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.34 % (3527819)CaDiCaL version: 2.1.3
% 3.33/1.34 % (3527819)Termination reason: Instruction limit
% 3.33/1.34 % (3527819)Termination phase: Saturation
% 3.33/1.34 % (3527819)Time elapsed: 0.087 s
% 3.33/1.34 % (3527819)Peak memory usage: 89 MB
% 3.33/1.34 % (3527819)Instructions burned: 140 (million)
% 3.33/1.34 % (3527828)lrs+10_1_sil=8000:sp=occurrence:random_seed=3575916618:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.33/1.34 % (3527817)Refutation found. Thanks to Tanya!
% 3.33/1.34 % SZS status Theorem for theBenchmark
% 3.33/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.34 % (3527817)------------------------------
% 3.33/1.34 % (3527817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.34 % (3527817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.34 % (3527817)CaDiCaL version: 2.1.3
% 3.33/1.34 % (3527817)Termination reason: Refutation
% 3.33/1.34 % (3527817)Time elapsed: 0.002 s
% 3.33/1.34 % (3527817)Peak memory usage: 88 MB
% 3.33/1.34 % (3527817)Instructions burned: 1 (million)
% 3.33/1.34 % (3527817)------------------------------
% 3.33/1.34 % (3527817)------------------------------
% 3.33/1.34 % (3527809)Success in time 0.403 s
% 3.33/1.34 % Vampire exiting
%------------------------------------------------------------------------------