%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:42:32 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 96 ( 11 unt; 5 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 249 ( 114 ~; 130 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| member(g(X0,X1,X2),X0)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom2) ).
fof(f12,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom3) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X1,X2,X3)
| ~ member(X0,X1)
| member(X0,X3)
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).
fof(f25,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f26,axiom,
difference(c,a,cDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_a) ).
fof(f27,axiom,
difference(c,b,cDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_b) ).
fof(f28,axiom,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_aIb) ).
fof(f29,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
fof(f32,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,a) ),
inference(resolution,[],[f13,f25]) ).
fof(f33,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,b) ),
inference(resolution,[],[f14,f25]) ).
fof(f34,plain,
! [X0] :
( ~ member(X0,cDa)
| member(X0,c) ),
inference(resolution,[],[f19,f26]) ).
fof(f35,plain,
! [X0] :
( ~ member(X0,cDb)
| member(X0,c) ),
inference(resolution,[],[f19,f27]) ).
fof(f36,plain,
! [X0] :
( ~ member(X0,cD_aIb)
| member(X0,c) ),
inference(resolution,[],[f19,f28]) ).
fof(f37,plain,
! [X0] :
( ~ member(X0,cDa)
| ~ member(X0,a) ),
inference(resolution,[],[f20,f26]) ).
fof(f38,plain,
! [X0] :
( ~ member(X0,cDb)
| ~ member(X0,b) ),
inference(resolution,[],[f20,f27]) ).
fof(f39,plain,
! [X0] :
( ~ member(X0,cD_aIb)
| ~ member(X0,aIb) ),
inference(resolution,[],[f20,f28]) ).
fof(f40,plain,
! [X0] :
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[],[f15,f25]) ).
fof(f41,plain,
! [X0] :
( member(X0,cDa)
| ~ member(X0,c)
| member(X0,a) ),
inference(resolution,[],[f21,f26]) ).
fof(f42,plain,
! [X0] :
( member(X0,cDb)
| ~ member(X0,c)
| member(X0,b) ),
inference(resolution,[],[f21,f27]) ).
fof(f43,plain,
! [X0] :
( member(X0,cD_aIb)
| ~ member(X0,c)
| member(X0,aIb) ),
inference(resolution,[],[f21,f28]) ).
fof(f44,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[],[f11,f29]) ).
fof(f49,definition,
( spl0_1
<=> member(g(cDa,cDb,cD_aIb),cDa) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl0_2
<=> member(g(cDa,cDb,cD_aIb),cD_aIb) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f54,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f44,f53,f49]) ).
fof(f57,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolution,[],[f12,f29]) ).
fof(f62,definition,
( spl0_3
<=> member(g(cDa,cDb,cD_aIb),cDb) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f63,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDb)
| spl0_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f57,f53,f62]) ).
fof(f82,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),a)
| spl0_1 ),
inference(resolution,[],[f41,f51]) ).
fof(f84,definition,
( spl0_4
<=> member(g(cDa,cDb,cD_aIb),a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f85,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| spl0_4 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( member(g(cDa,cDb,cD_aIb),a)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_5
<=> member(g(cDa,cDb,cD_aIb),c) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f89,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| spl0_5 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_4
| ~ spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f82,f49,f88,f84]) ).
fof(f92,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolution,[],[f10,f29]) ).
fof(f96,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f92,f51]) ).
fof(f97,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f96,f55]) ).
fof(f98,plain,
( spl0_3
| spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f97,f53,f49,f62]) ).
fof(f99,plain,
( ~ member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_2 ),
inference(resolution,[],[f54,f39]) ).
fof(f100,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_2 ),
inference(resolution,[],[f54,f36]) ).
fof(f101,plain,
( $false
| ~ spl0_2
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f100,f90]) ).
fof(f102,plain,
( ~ spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f106,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| ~ spl0_1 ),
inference(resolution,[],[f50,f37]) ).
fof(f107,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_1 ),
inference(resolution,[],[f50,f34]) ).
fof(f108,plain,
( $false
| ~ spl0_1
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f107,f90]) ).
fof(f109,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f110,plain,
( ~ spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f106,f49,f84]) ).
fof(f115,plain,
( ~ member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_3 ),
inference(resolution,[],[f63,f38]) ).
fof(f116,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_3 ),
inference(resolution,[],[f63,f35]) ).
fof(f117,plain,
( $false
| ~ spl0_3
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f116,f90]) ).
fof(f118,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f117]) ).
fof(f123,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),aIb)
| spl0_2 ),
inference(resolution,[],[f43,f55]) ).
fof(f124,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f123,f89]) ).
fof(f187,plain,
( member(g(cDa,cDb,cD_aIb),b)
| spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f124,f33]) ).
fof(f188,plain,
( member(g(cDa,cDb,cD_aIb),a)
| spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f124,f32]) ).
fof(f191,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f187,f115]) ).
fof(f192,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f193,plain,
( $false
| spl0_2
| spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f188,f85]) ).
fof(f194,plain,
( spl0_2
| spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f202,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),b)
| spl0_3 ),
inference(resolution,[],[f64,f42]) ).
fof(f205,plain,
( member(g(cDa,cDb,cD_aIb),b)
| spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f202,f89]) ).
fof(f250,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| ~ member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_2 ),
inference(resolution,[],[f99,f40]) ).
fof(f254,plain,
( ~ member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f250,f86]) ).
fof(f255,plain,
( $false
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f254,f205]) ).
fof(f256,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f255]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( spl0_1
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f98]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f109]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s9,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f118]) ).
cnf(s10,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f192]) ).
cnf(s12,plain,
( spl0_2
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f194]) ).
cnf(s13,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f256]) ).
cnf(s14,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s10,s9,s4]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s13,s3,s2,s5,s14]) ).
cnf(s16,plain,
~ spl0_4,
inference(rat,[],[s7,s15]) ).
cnf(s17,plain,
spl0_5,
inference(rat,[],[s6,s15]) ).
cnf(s18,plain,
~ spl0_2,
inference(rat,[],[s1,s15]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s12,s18,s17,s16]) ).
fof(f257,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n004.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 00:02:52 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.18/0.48 % (4019784)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (4019800)dis+10_1_sil=32000:sp=arity:random_seed=2419360304:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (4019798)% WARNING: option uhcvi not known.
% 0.18/0.48 % (4019796)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3927423775_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (4019798)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=945381631:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (4019801)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=622069035:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (4019799)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1200695130:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % (4019803)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2732254663:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (4019802)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3803445819:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (4019801) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4019784-4019801"...
% 0.18/0.48 % (4019801)...printing done.
% 0.18/0.48 % (4019801)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (4019801)------------------------------
% 0.18/0.48 % (4019801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (4019801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (4019801)CaDiCaL version: 2.1.3
% 0.18/0.48 % (4019801)Termination reason: Refutation
% 0.18/0.48 % (4019801)Time elapsed: 0.009 s
% 0.18/0.48 % (4019801)Peak memory usage: 12 MB
% 0.18/0.48 % (4019801)Instructions burned: 14 (million)
% 0.18/0.48 % (4019784)Success in time 0.052 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------