%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:39:32 PM UTC 2026
% Result : Unsatisfiable 3.52s 1.37s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 53 ( 18 unt; 5 def)
% Number of atoms : 98 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 87 ( 42 ~; 40 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f8,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f9,axiom,
! [X0,X1] :
( ~ little_set(X0)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f10,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
fof(f14,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(f17(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
fof(f15,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(f17(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
fof(f16,axiom,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
fof(f17,axiom,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
fof(f18,negated_conjecture,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
fof(f19,plain,
~ subset(complement(intersection(complement(as),complement(bs))),cs),
inference(definition_unfolding,[],[f18,f10]) ).
fof(f27,plain,
member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(intersection(complement(as),complement(bs)))),
inference(resolution,[],[f14,f19]) ).
fof(f28,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(as),complement(bs))),
inference(resolution,[],[f27,f8]) ).
fof(f29,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),cs),
inference(resolution,[],[f15,f19]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X0,complement(X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(resolution,[],[f9,f1]) ).
fof(f31,plain,
! [X0] :
( ~ member(X0,as)
| member(X0,cs) ),
inference(resolution,[],[f13,f16]) ).
fof(f32,plain,
! [X0] :
( ~ member(X0,bs)
| member(X0,cs) ),
inference(resolution,[],[f13,f17]) ).
fof(f37,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
inference(resolution,[],[f7,f28]) ).
fof(f39,definition,
( spl1_1
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f40,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs))
| spl1_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl1_2
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f43,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as))
| spl1_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f37,f42,f39]) ).
fof(f48,definition,
( spl1_3
<=> ! [X0] : ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f49,plain,
( ! [X0] : ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl1_4
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),bs) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f52,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),bs)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( ! [X0] :
( member(f17(complement(intersection(complement(as),complement(bs))),cs),as)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) )
| spl1_2 ),
inference(resolution,[],[f43,f30]) ).
fof(f56,definition,
( spl1_5
<=> member(f17(complement(intersection(complement(as),complement(bs))),cs),as) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f57,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),as)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( spl1_3
| spl1_5
| spl1_2 ),
inference(avatar_split_clause,[],[f54,f42,f56,f48]) ).
fof(f59,plain,
( $false
| ~ spl1_3 ),
inference(resolution,[],[f49,f27]) ).
fof(f63,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f59]) ).
fof(f64,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| ~ spl1_5 ),
inference(resolution,[],[f57,f31]) ).
fof(f65,plain,
( $false
| ~ spl1_5 ),
inference(resolution,[],[f64,f29]) ).
fof(f66,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f67,plain,
( ! [X0] :
( member(f17(complement(intersection(complement(as),complement(bs))),cs),bs)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) )
| spl1_1 ),
inference(resolution,[],[f40,f30]) ).
fof(f68,plain,
( spl1_3
| spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f67,f39,f51,f48]) ).
fof(f69,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| ~ spl1_4 ),
inference(resolution,[],[f52,f32]) ).
fof(f70,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f69,f29]) ).
fof(f71,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f70]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
( spl1_2
| spl1_3
| spl1_5 ),
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
~ spl1_3,
inference(sat_conversion,[],[f63]) ).
cnf(s5,plain,
~ spl1_5,
inference(sat_conversion,[],[f66]) ).
cnf(s6,plain,
( spl1_1
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f68]) ).
cnf(s7,plain,
~ spl1_4,
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
( spl1_1
| spl1_3 ),
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s8,s4]) ).
cnf(s10,plain,
spl1_2,
inference(rat,[],[s3,s5,s4]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s9]) ).
fof(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:03:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.52/1.37 % (2553209)Input is clausal, will run a generic CNF schedule.
% 3.52/1.37 % (2553215)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2253276506:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.52/1.37 % (2553216)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3570786214:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.52/1.37 % (2553220)dis-21_1_sil=8000:lcm=predicate:random_seed=639630785: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)
% 3.52/1.37 % (2553214)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=3151558606:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.52/1.37 % (2553217)lrs+10_1_sil=8000:sp=occurrence:random_seed=3659505988:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.52/1.37 % (2553218)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1279668447:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.52/1.37 % (2553219)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3476509067:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.52/1.37 % (2553220)First to succeed.
% 3.52/1.37 % (2553220)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2553209"
% 3.52/1.37 % (2553217)Instruction limit reached!
% 3.52/1.37 % (2553217)------------------------------
% 3.52/1.37 % (2553217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (2553217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (2553217)CaDiCaL version: 2.1.3
% 3.52/1.37 % (2553217)Termination reason: Instruction limit
% 3.52/1.37 % (2553217)Termination phase: Saturation
% 3.52/1.37 % (2553217)Time elapsed: 0.070 s
% 3.52/1.37 % (2553217)Peak memory usage: 89 MB
% 3.52/1.37 % (2553217)Instructions burned: 108 (million)
% 3.52/1.37 % (2553218)Instruction limit reached!
% 3.52/1.37 % (2553218)------------------------------
% 3.52/1.37 % (2553218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (2553218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (2553218)CaDiCaL version: 2.1.3
% 3.52/1.37 % (2553218)Termination reason: Instruction limit
% 3.52/1.37 % (2553218)Termination phase: Saturation
% 3.52/1.37 % (2553218)Time elapsed: 0.078 s
% 3.52/1.37 % (2553218)Peak memory usage: 89 MB
% 3.52/1.37 % (2553218)Instructions burned: 114 (million)
% 3.52/1.37 % (2553219)Instruction limit reached!
% 3.52/1.37 % (2553219)------------------------------
% 3.52/1.37 % (2553219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (2553219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (2553219)CaDiCaL version: 2.1.3
% 3.52/1.37 % (2553219)Termination reason: Instruction limit
% 3.52/1.37 % (2553219)Termination phase: Saturation
% 3.52/1.37 % (2553219)Time elapsed: 0.121 s
% 3.52/1.37 % (2553219)Peak memory usage: 89 MB
% 3.52/1.37 % (2553219)Instructions burned: 181 (million)
% 3.52/1.37 % (2553229)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2230683217: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)
% 3.52/1.37 % (2553228)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=1144609012:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.52/1.37 % (2553228)Refutation not found, incomplete strategy
% 3.52/1.37 % (2553228)------------------------------
% 3.52/1.37 % (2553228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (2553228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (2553228)CaDiCaL version: 2.1.3
% 3.52/1.37 % (2553228)Termination reason: Refutation not found, incomplete strategy
% 3.52/1.37 % (2553228)Time elapsed: 0.003 s
% 3.52/1.37 % (2553228)Peak memory usage: 88 MB
% 3.52/1.37 % (2553228)Instructions burned: 2 (million)
% 3.52/1.37 % (2553229)Also succeeded, but the first one will report.
% 3.52/1.37 % (2553220)Refutation found. Thanks to Tanya!
% 3.52/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.52/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.37 % (2553220)------------------------------
% 3.52/1.37 % (2553220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (2553220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (2553220)CaDiCaL version: 2.1.3
% 3.52/1.37 % (2553220)Termination reason: Refutation
% 3.52/1.37 % (2553220)Time elapsed: 0.003 s
% 3.52/1.37 % (2553220)Peak memory usage: 89 MB
% 3.52/1.37 % (2553220)Instructions burned: 2 (million)
% 3.52/1.37 % (2553220)------------------------------
% 3.52/1.37 % (2553220)------------------------------
% 3.52/1.37 % (2553209)Success in time 0.431 s
% 3.52/1.37 % Vampire exiting
%------------------------------------------------------------------------------