%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET619+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 : n008.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 12:41:24 PM UTC 2026
% Result : Theorem 3.77s 1.52s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 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 : 46 ( 44 !; 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] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f3,axiom,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection) ).
fof(f4,axiom,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(f8,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f14,conjecture,
! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th95) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
? [X0,X1] : union(X0,X1) != union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f30,plain,
union(sK2,sK3) != union(symmetric_difference(sK2,sK3),intersection(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f31,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f55,plain,
union(sK2,sK3) != union(symmetric_difference(sK2,sK3),intersection(sK2,sK3)),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
union(sK2,sK3) != union(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(superposition,[],[f55,f44]) ).
fof(f70,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X1,X0)) = X1,
inference(superposition,[],[f34,f45]) ).
fof(f79,plain,
! [X2,X0,X1] : union(X0,union(intersection(X0,X1),X2)) = union(X0,X2),
inference(superposition,[],[f32,f33]) ).
fof(f85,plain,
! [X2,X0,X1] : union(X0,X2) = union(intersection(X0,X1),union(difference(X0,X1),X2)),
inference(superposition,[],[f32,f34]) ).
fof(f129,plain,
! [X0,X1] : union(X1,X0) = union(X1,difference(X0,X1)),
inference(superposition,[],[f79,f70]) ).
fof(f368,plain,
! [X0,X1] : union(X0,difference(X1,X0)) = union(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(superposition,[],[f85,f31]) ).
fof(f404,plain,
! [X0,X1] : union(X0,X1) = union(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(forward_demodulation,[],[f368,f129]) ).
fof(f1760,plain,
union(sK2,sK3) != union(sK2,sK3),
inference(superposition,[],[f60,f404]) ).
fof(f1775,plain,
$false,
inference(trivial_inequality_removal,[],[f1760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n008.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Mon Sep 28 02:22:55 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 3.77/1.52 % (1808020)Detected formulas, will run a generic FOF schedule.
% 3.77/1.52 % (1808025)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=929691193:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.77/1.52 % (1808030)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=141497657:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.77/1.52 % (1808029)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4216995315:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.77/1.52 % (1808028)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3730325416:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.77/1.52 % (1808027)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=2597292984:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.77/1.52 % (1808026)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=945104926:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.77/1.52 % (1808028)Refutation not found, incomplete strategy
% 3.77/1.52 % (1808028)------------------------------
% 3.77/1.52 % (1808028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (1808028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (1808028)CaDiCaL version: 2.1.3
% 3.77/1.52 % (1808028)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.52 % (1808028)Time elapsed: 0.001 s
% 3.77/1.52 % (1808028)Peak memory usage: 88 MB
% 3.77/1.52 % (1808031)dis-21_1_sil=8000:lcm=predicate:random_seed=653318705: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)
% 3.77/1.52 % (1808030)First to succeed.
% 3.77/1.52 % (1808030)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1808020"
% 3.77/1.52 % (1808029)Instruction limit reached!
% 3.77/1.52 % (1808029)------------------------------
% 3.77/1.52 % (1808029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (1808029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (1808029)CaDiCaL version: 2.1.3
% 3.77/1.52 % (1808029)Termination reason: Instruction limit
% 3.77/1.52 % (1808029)Termination phase: Saturation
% 3.77/1.52 % (1808029)Time elapsed: 0.062 s
% 3.77/1.52 % (1808029)Peak memory usage: 88 MB
% 3.77/1.52 % (1808029)Instructions burned: 119 (million)
% 3.77/1.52 % (1808031)Instruction limit reached!
% 3.77/1.52 % (1808031)------------------------------
% 3.77/1.52 % (1808031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (1808031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (1808031)CaDiCaL version: 2.1.3
% 3.77/1.52 % (1808031)Termination reason: Instruction limit
% 3.77/1.52 % (1808031)Termination phase: Saturation
% 3.77/1.52 % (1808031)Time elapsed: 0.078 s
% 3.77/1.52 % (1808031)Peak memory usage: 89 MB
% 3.77/1.52 % (1808031)Instructions burned: 129 (million)
% 3.77/1.52 % (1808039)lrs+10_1_sil=8000:sp=occurrence:random_seed=747670275:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.77/1.52 % (1808040)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3581122028:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.77/1.52 % (1808040)Also succeeded, but the first one will report.
% 3.77/1.52 % (1808028)------------------------------
% 3.77/1.52 % (1808028)------------------------------
% 3.77/1.52 % (1808039)Also succeeded, but the first one will report.
% 3.77/1.52 % (1808030)Refutation found. Thanks to Tanya!
% 3.77/1.52 % SZS status Theorem for theBenchmark
% 3.77/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.52 % (1808030)------------------------------
% 3.77/1.52 % (1808030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (1808030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (1808030)CaDiCaL version: 2.1.3
% 3.77/1.52 % (1808030)Termination reason: Refutation
% 3.77/1.52 % (1808030)Time elapsed: 0.041 s
% 3.77/1.52 % (1808030)Peak memory usage: 89 MB
% 3.77/1.52 % (1808030)Instructions burned: 70 (million)
% 3.77/1.52 % (1808030)------------------------------
% 3.77/1.52 % (1808030)------------------------------
% 3.77/1.52 % (1808020)Success in time 0.441 s
% 3.77/1.52 % Vampire exiting
%------------------------------------------------------------------------------