%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:39:30 PM UTC 2026
% Result : Unsatisfiable 3.38s 1.58s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 30 ( 13 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
fof(f15,axiom,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_sets(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
fof(f22,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(member_of_1_not_of_2(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f11,f3]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(member_of_1_not_of_2(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f12,f3]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X2)
| ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[],[f10,f4]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0))
| subset(intersection(X0,X1),intersection(X2,X0)) ),
inference(resolution,[],[f33,f28]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0)) ),
inference(duplicate_literal_removal,[],[f47]) ).
fof(f129,plain,
! [X0,X1] :
( subset(intersection(X0,X1),intersection(X1,X0))
| subset(intersection(X0,X1),intersection(X1,X0)) ),
inference(resolution,[],[f51,f29]) ).
fof(f137,plain,
! [X0,X1] : subset(intersection(X0,X1),intersection(X1,X0)),
inference(duplicate_literal_removal,[],[f129]) ).
fof(f160,plain,
! [X0,X1] :
( ~ subset(intersection(X0,X1),intersection(X1,X0))
| equal_sets(intersection(X1,X0),intersection(X0,X1)) ),
inference(resolution,[],[f137,f15]) ).
fof(f162,plain,
! [X0,X1] : equal_sets(intersection(X1,X0),intersection(X0,X1)),
inference(forward_subsumption_resolution,[],[f160,f137]) ).
fof(f168,plain,
$false,
inference(resolution,[],[f162,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.60 % Computer : n010.cluster.edu
% 0.11/0.60 % Model : x86_64 x86_64
% 0.11/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.60 % Memory : 8046.5625MB
% 0.11/0.60 % OS : Linux 6.8.0-71-generic
% 0.11/0.60 % CPULimit : 300
% 0.11/0.60 % WCLimit : 300
% 0.11/0.60 % DateTime : Mon Sep 28 00:03:51 UTC 2026
% 0.11/0.60 % CPUTime :
% 0.11/0.60 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.63 Running first-order theorem proving
% 0.15/0.63 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.38/1.58 % (1445801)Input is clausal, will run a generic CNF schedule.
% 3.38/1.58 % (1445806)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=3589214517:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.38/1.58 % (1445810)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1572869490:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.38/1.58 % (1445807)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2277232334:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.38/1.58 % (1445809)lrs+10_1_sil=8000:sp=occurrence:random_seed=1540535955:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.38/1.58 % (1445808)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3187766813:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.38/1.58 % (1445809)First to succeed.
% 3.38/1.58 % (1445809)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1445801"
% 3.38/1.58 % (1445811)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=528409711:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.38/1.58 % (1445812)dis-21_1_sil=8000:lcm=predicate:random_seed=3687704360:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.38/1.58 % (1445812)Also succeeded, but the first one will report.
% 3.38/1.58 % (1445811)Also succeeded, but the first one will report.
% 3.38/1.58 % (1445810)Instruction limit reached!
% 3.38/1.58 % (1445810)------------------------------
% 3.38/1.58 % (1445810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.58 % (1445810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.58 % (1445810)CaDiCaL version: 2.1.3
% 3.38/1.58 % (1445810)Termination reason: Instruction limit
% 3.38/1.58 % (1445810)Termination phase: Saturation
% 3.38/1.58 % (1445810)Time elapsed: 0.060 s
% 3.38/1.58 % (1445810)Peak memory usage: 88 MB
% 3.38/1.58 % (1445810)Instructions burned: 114 (million)
% 3.38/1.58 % (1445820)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3689743967:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.38/1.58 % (1445820)Refutation not found, incomplete strategy
% 3.38/1.58 % (1445820)------------------------------
% 3.38/1.58 % (1445820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.58 % (1445820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.58 % (1445820)CaDiCaL version: 2.1.3
% 3.38/1.58 % (1445820)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.58 % (1445820)Time elapsed: 0.001 s
% 3.38/1.58 % (1445820)Peak memory usage: 87 MB
% 3.38/1.58 % (1445809)Refutation found. Thanks to Tanya!
% 3.38/1.58 % SZS status Unsatisfiable for theBenchmark
% 3.38/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.58 % (1445809)------------------------------
% 3.38/1.58 % (1445809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.58 % (1445809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.58 % (1445809)CaDiCaL version: 2.1.3
% 3.38/1.58 % (1445809)Termination reason: Refutation
% 3.38/1.58 % (1445809)Time elapsed: 0.004 s
% 3.38/1.58 % (1445809)Peak memory usage: 88 MB
% 3.38/1.58 % (1445809)Instructions burned: 4 (million)
% 3.38/1.58 % (1445809)------------------------------
% 3.38/1.58 % (1445809)------------------------------
% 3.38/1.58 % (1445801)Success in time 0.412 s
% 3.38/1.58 % Vampire exiting
%------------------------------------------------------------------------------