%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n016.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 12:42:34 PM UTC 2026
% Result : Unsatisfiable 0.33s 15.74s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 8 unt; 6 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 105 ( 44 ~; 55 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',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/Axioms/SET002-0.ax',subsets_axiom2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',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/Axioms/SET002-0.ax',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/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
fof(f15,axiom,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_sets(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',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(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f26,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f33,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f34,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f37,plain,
! [X0,X1] :
( ~ equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f41,plain,
equal_sets(intersection(as,bs),intersection(bs,as)),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f51,plain,
( ~ subset(intersection(as,bs),intersection(bs,as))
| ~ subset(intersection(bs,as),intersection(as,bs)) ),
inference(resolution,[],[f37,f41]) ).
fof(f56,definition,
( spl0_1
<=> subset(intersection(bs,as),intersection(as,bs)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ~ subset(intersection(bs,as),intersection(as,bs))
| spl0_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl0_2
<=> subset(intersection(as,bs),intersection(bs,as)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( ~ subset(intersection(as,bs),intersection(bs,as))
| spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f51,f60,f56]) ).
fof(f64,plain,
( ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),intersection(bs,as))
| spl0_1 ),
inference(resolution,[],[f58,f25]) ).
fof(f66,plain,
( ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),as)
| spl0_1 ),
inference(resolution,[],[f64,f34]) ).
fof(f67,plain,
( ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),bs)
| spl0_1 ),
inference(resolution,[],[f64,f33]) ).
fof(f77,plain,
! [X2,X0,X1] :
( subset(X0,intersection(X1,X2))
| member(member_of_1_not_of_2(X0,intersection(X1,X2)),X1)
| member(member_of_1_not_of_2(X0,intersection(X1,X2)),X2) ),
inference(resolution,[],[f32,f26]) ).
fof(f357,plain,
( member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),as)
| member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),bs)
| spl0_1 ),
inference(resolution,[],[f77,f58]) ).
fof(f358,plain,
( member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),bs)
| member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),as)
| spl0_2 ),
inference(resolution,[],[f77,f62]) ).
fof(f360,definition,
( spl0_14
<=> member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),as) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f364,definition,
( spl0_15
<=> member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),bs) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f367,plain,
( spl0_14
| spl0_15
| spl0_2 ),
inference(avatar_split_clause,[],[f358,f60,f364,f360]) ).
fof(f369,definition,
( spl0_16
<=> member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),bs) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f371,plain,
( member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),bs)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f373,definition,
( spl0_17
<=> member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),as) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f375,plain,
( member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),as)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f376,plain,
( spl0_16
| spl0_17
| spl0_1 ),
inference(avatar_split_clause,[],[f357,f56,f373,f369]) ).
fof(f380,plain,
( $false
| spl0_1
| ~ spl0_16 ),
inference(resolution,[],[f371,f67]) ).
fof(f383,plain,
( spl0_1
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f384,plain,
( $false
| spl0_1
| ~ spl0_17 ),
inference(resolution,[],[f375,f66]) ).
fof(f387,plain,
( spl0_1
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f394,plain,
( ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),intersection(as,bs))
| spl0_2 ),
inference(resolution,[],[f62,f25]) ).
fof(f414,plain,
( ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),bs)
| spl0_2 ),
inference(resolution,[],[f394,f34]) ).
fof(f415,plain,
( ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),as)
| spl0_2 ),
inference(resolution,[],[f394,f33]) ).
fof(f417,plain,
( ~ spl0_15
| spl0_2 ),
inference(avatar_split_clause,[],[f414,f60,f364]) ).
fof(f418,plain,
( ~ spl0_14
| spl0_2 ),
inference(avatar_split_clause,[],[f415,f60,f360]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s19,plain,
( spl0_2
| spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f367]) ).
cnf(s20,plain,
( spl0_1
| spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f376]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_16 ),
inference(sat_conversion,[],[f383]) ).
cnf(s22,plain,
( spl0_1
| ~ spl0_17 ),
inference(sat_conversion,[],[f387]) ).
cnf(s23,plain,
( spl0_2
| ~ spl0_15 ),
inference(sat_conversion,[],[f417]) ).
cnf(s24,plain,
( spl0_2
| ~ spl0_14 ),
inference(sat_conversion,[],[f418]) ).
cnf(s27,plain,
spl0_1,
inference(rat,[],[s20,s21,s22]) ).
cnf(s28,plain,
~ spl0_2,
inference(rat,[],[s1,s27]) ).
cnf(s29,plain,
~ spl0_14,
inference(rat,[],[s24,s28]) ).
cnf(s30,plain,
~ spl0_15,
inference(rat,[],[s23,s28]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s19,s29,s30,s28]) ).
fof(f419,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 % Computer : n016.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.08/15.64 % CPULimit : 300
% 0.08/15.64 % WCLimit : 300
% 0.08/15.64 % DateTime : Mon Sep 28 00:03:08 UTC 2026
% 0.08/15.64 % CPUTime :
% 0.08/15.64 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/15.67 Running first-order model finding
% 0.08/15.67 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/15.74 % (681373)Will run a generic schedule for satisfiability detection.
% 0.33/15.74 % (681383)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2825501610:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/15.74 % (681379)% WARNING: option uhcvi not known.
% 0.33/15.74 % (681378)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2635544290_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/15.74 % (681379)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4068726696:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/15.74 % (681380)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3708640756:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/15.74 % (681384)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3563886779:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/15.74 % (681381)dis+10_1_sil=32000:sp=arity:random_seed=2801076770:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/15.74 % (681382)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2624029232:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/15.74 % TRYING [1]
% 0.33/15.74 % TRYING [2]
% 0.33/15.74 % TRYING [3]
% 0.33/15.74 % TRYING [4]
% 0.33/15.74 % (681384) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-681373-681384"...
% 0.33/15.74 % (681384)...printing done.
% 0.33/15.74 % (681384)Refutation found. Thanks to Tanya!
% 0.33/15.74 % SZS status Unsatisfiable for theBenchmark
% 0.33/15.74 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/15.74 % (681384)------------------------------
% 0.33/15.74 % (681384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/15.74 % (681384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/15.74 % (681384)CaDiCaL version: 2.1.3
% 0.33/15.74 % (681384)Termination reason: Refutation
% 0.33/15.74 % (681384)Time elapsed: 0.010 s
% 0.33/15.74 % (681384)Peak memory usage: 12 MB
% 0.33/15.74 % (681384)Instructions burned: 14 (million)
% 0.33/15.74 % (681373)Success in time 0.053 s
% 0.33/15.74 % Vampire exiting
%------------------------------------------------------------------------------