%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET013-2 : 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 : n007.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 12:39:31 PM UTC 2026
% Result : Unsatisfiable 5.27s 1.71s
% Output : Refutation 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 11 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 27 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ member(X0,X1)
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
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(f13,axiom,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
fof(f14,axiom,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
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,axiom,
equal_sets(intersection(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_a_and_b_is_c) ).
fof(f23,axiom,
equal_sets(intersection(bs,as),ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_b_and_a_is_d) ).
fof(f24,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f25,plain,
subset(intersection(as,bs),cs),
inference(resolution,[],[f22,f13]) ).
fof(f26,plain,
subset(cs,intersection(as,bs)),
inference(resolution,[],[f22,f14]) ).
fof(f29,plain,
subset(intersection(bs,as),ds),
inference(resolution,[],[f23,f13]) ).
fof(f30,plain,
subset(ds,intersection(bs,as)),
inference(resolution,[],[f23,f14]) ).
fof(f33,plain,
! [X0] :
( ~ member(X0,intersection(as,bs))
| member(X0,cs) ),
inference(resolution,[],[f25,f2]) ).
fof(f35,plain,
! [X0] :
( member(X0,intersection(as,bs))
| ~ member(X0,cs) ),
inference(resolution,[],[f26,f2]) ).
fof(f42,plain,
! [X0] :
( ~ member(X0,intersection(bs,as))
| member(X0,ds) ),
inference(resolution,[],[f29,f2]) ).
fof(f44,plain,
! [X0] :
( member(X0,intersection(bs,as))
| ~ member(X0,ds) ),
inference(resolution,[],[f30,f2]) ).
fof(f55,plain,
! [X0] :
( ~ member(X0,bs)
| member(X0,cs)
| ~ member(X0,as) ),
inference(resolution,[],[f33,f10]) ).
fof(f60,plain,
! [X0] :
( ~ member(X0,cs)
| member(X0,as) ),
inference(resolution,[],[f35,f11]) ).
fof(f61,plain,
! [X0] :
( ~ member(X0,cs)
| member(X0,bs) ),
inference(resolution,[],[f35,f12]) ).
fof(f64,plain,
! [X0] :
( member(member_of_1_not_of_2(cs,X0),as)
| subset(cs,X0) ),
inference(resolution,[],[f60,f3]) ).
fof(f66,plain,
! [X0] :
( member(member_of_1_not_of_2(cs,X0),bs)
| subset(cs,X0) ),
inference(resolution,[],[f61,f3]) ).
fof(f83,plain,
! [X0] :
( ~ member(X0,bs)
| ~ member(X0,as)
| member(X0,ds) ),
inference(resolution,[],[f42,f10]) ).
fof(f88,plain,
! [X0] :
( ~ member(X0,ds)
| member(X0,bs) ),
inference(resolution,[],[f44,f11]) ).
fof(f89,plain,
! [X0] :
( ~ member(X0,ds)
| member(X0,as) ),
inference(resolution,[],[f44,f12]) ).
fof(f100,plain,
! [X0] :
( member(member_of_1_not_of_2(ds,X0),bs)
| subset(ds,X0) ),
inference(resolution,[],[f88,f3]) ).
fof(f121,plain,
! [X0] :
( member(member_of_1_not_of_2(ds,X0),as)
| subset(ds,X0) ),
inference(resolution,[],[f89,f3]) ).
fof(f200,plain,
! [X0] :
( member(member_of_1_not_of_2(ds,X0),cs)
| ~ member(member_of_1_not_of_2(ds,X0),as)
| subset(ds,X0) ),
inference(resolution,[],[f55,f100]) ).
fof(f204,plain,
! [X0] :
( member(member_of_1_not_of_2(ds,X0),cs)
| subset(ds,X0) ),
inference(forward_subsumption_resolution,[],[f200,f121]) ).
fof(f217,plain,
( subset(ds,cs)
| subset(ds,cs) ),
inference(resolution,[],[f204,f4]) ).
fof(f220,plain,
subset(ds,cs),
inference(duplicate_literal_removal,[],[f217]) ).
fof(f221,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(cs,X0),as)
| member(member_of_1_not_of_2(cs,X0),ds)
| subset(cs,X0) ),
inference(resolution,[],[f83,f66]) ).
fof(f227,plain,
! [X0] :
( member(member_of_1_not_of_2(cs,X0),ds)
| subset(cs,X0) ),
inference(forward_subsumption_resolution,[],[f221,f64]) ).
fof(f232,plain,
( subset(cs,ds)
| subset(cs,ds) ),
inference(resolution,[],[f227,f4]) ).
fof(f235,plain,
subset(cs,ds),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f254,plain,
( ~ subset(ds,cs)
| equal_sets(cs,ds) ),
inference(resolution,[],[f235,f15]) ).
fof(f255,plain,
equal_sets(cs,ds),
inference(forward_subsumption_resolution,[],[f254,f220]) ).
fof(f256,plain,
$false,
inference(forward_subsumption_resolution,[],[f255,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n007.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 00:01:40 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 5.27/1.71 % (1911230)Input is clausal, will run a generic CNF schedule.
% 5.27/1.71 % (1911236)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=799763352:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.27/1.71 % (1911238)lrs+10_1_sil=8000:sp=occurrence:random_seed=1985472380:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.27/1.71 % (1911239)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=804808827:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.27/1.71 % (1911235)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=4224102954:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.27/1.71 % (1911241)dis-21_1_sil=8000:lcm=predicate:random_seed=3797934003: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)
% 5.27/1.71 % (1911237)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=585364267:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.27/1.71 % (1911240)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3418991499:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.27/1.71 % (1911238)Refutation not found, incomplete strategy
% 5.27/1.71 % (1911238)------------------------------
% 5.27/1.71 % (1911238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.71 % (1911238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.71 % (1911238)CaDiCaL version: 2.1.3
% 5.27/1.71 % (1911238)Termination reason: Refutation not found, incomplete strategy
% 5.27/1.71 % (1911238)Time elapsed: 0.002 s
% 5.27/1.71 % (1911238)Peak memory usage: 88 MB
% 5.27/1.71 % (1911238)Instructions burned: 2 (million)
% 5.27/1.71 % (1911239)Instruction limit reached!
% 5.27/1.71 % (1911239)------------------------------
% 5.27/1.71 % (1911239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.71 % (1911239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.71 % (1911239)CaDiCaL version: 2.1.3
% 5.27/1.71 % (1911239)Termination reason: Instruction limit
% 5.27/1.71 % (1911239)Termination phase: Saturation
% 5.27/1.71 % (1911239)Time elapsed: 0.067 s
% 5.27/1.71 % (1911239)Peak memory usage: 87 MB
% 5.27/1.71 % (1911239)Instructions burned: 115 (million)
% 5.27/1.71 % (1911241)Instruction limit reached!
% 5.27/1.71 % (1911241)------------------------------
% 5.27/1.71 % (1911241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.71 % (1911241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.71 % (1911241)CaDiCaL version: 2.1.3
% 5.27/1.71 % (1911241)Termination reason: Instruction limit
% 5.27/1.71 % (1911241)Termination phase: Saturation
% 5.27/1.71 % (1911241)Time elapsed: 0.073 s
% 5.27/1.71 % (1911241)Peak memory usage: 88 MB
% 5.27/1.71 % (1911241)Instructions burned: 117 (million)
% 5.27/1.71 % (1911240)Instruction limit reached!
% 5.27/1.71 % (1911240)------------------------------
% 5.27/1.71 % (1911240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.71 % (1911240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.71 % (1911240)CaDiCaL version: 2.1.3
% 5.27/1.71 % (1911240)Termination reason: Instruction limit
% 5.27/1.71 % (1911240)Termination phase: Saturation
% 5.27/1.71 % (1911240)Time elapsed: 0.122 s
% 5.27/1.71 % (1911240)Peak memory usage: 90 MB
% 5.27/1.71 % (1911240)Instructions burned: 180 (million)
% 5.27/1.71 % (1911249)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=22522781:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.27/1.71 % (1911249)First to succeed.
% 5.27/1.71 % (1911249)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1911230"
% 5.27/1.71 % (1911250)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2987829386:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.27/1.71 % (1911250)Refutation not found, incomplete strategy
% 5.27/1.71 % (1911250)------------------------------
% 5.27/1.71 % (1911250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.71 % (1911250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.71 % (1911250)CaDiCaL version: 2.1.3
% 5.27/1.71 % (1911250)Termination reason: Refutation not found, incomplete strategy
% 5.27/1.71 % (1911250)Time elapsed: 0.002 s
% 5.27/1.71 % (1911250)Peak memory usage: 87 MB
% 5.27/1.71 % (1911250)Instructions burned: 2 (million)
% 5.27/1.71 % (1911238)------------------------------
% 5.27/1.71 % (1911238)------------------------------
% 5.27/1.71 % (1911251)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3858769861:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.27/1.71 % (1911251)Also succeeded, but the first one will report.
% 5.27/1.71 % (1911254)lrs+10_64_to=lpo:sil=8000:random_seed=2722987305:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.27/1.71 % (1911254)Also succeeded, but the first one will report.
% 5.27/1.71 % (1911250)------------------------------
% 5.27/1.71 % (1911250)------------------------------
% 5.27/1.71 % (1911249)Refutation found. Thanks to Tanya!
% 5.27/1.71 % SZS status Unsatisfiable for theBenchmark
% 5.27/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 5.27/1.71 % (1911249)------------------------------
% 5.27/1.71 % (1911249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.71 % (1911249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.71 % (1911249)CaDiCaL version: 2.1.3
% 5.27/1.71 % (1911249)Termination reason: Refutation
% 5.27/1.71 % (1911249)Time elapsed: 0.005 s
% 5.27/1.71 % (1911249)Peak memory usage: 88 MB
% 5.27/1.71 % (1911249)Instructions burned: 5 (million)
% 5.27/1.71 % (1911249)------------------------------
% 5.27/1.71 % (1911249)------------------------------
% 5.27/1.71 % (1911230)Success in time 0.65 s
% 5.27/1.71 % Vampire exiting
%------------------------------------------------------------------------------