%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:42:32 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 93 ( 11 unt; 5 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 228 ( 103 ~; 120 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 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(f7,axiom,
! [X2,X3,X0,X1] :
( ~ union(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0)
| member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_union_is_member_of_one_set) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ union(X0,X1,X2)
| ~ member(X3,X0)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set1_is_member_of_union) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ union(X0,X1,X2)
| ~ member(X3,X1)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set2_is_member_of_union) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
fof(f19,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_union_c) ).
fof(f20,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f21,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_c) ).
fof(f22,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bUc) ).
fof(f23,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).
fof(f26,plain,
! [X0] :
( member(X0,bUc)
| ~ member(X0,b) ),
inference(resolution,[],[f8,f19]) ).
fof(f27,plain,
! [X0] :
( member(X0,bUc)
| ~ member(X0,c) ),
inference(resolution,[],[f9,f19]) ).
fof(f28,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,a) ),
inference(resolution,[],[f13,f20]) ).
fof(f29,plain,
! [X0] :
( ~ member(X0,aIc)
| member(X0,a) ),
inference(resolution,[],[f13,f21]) ).
fof(f30,plain,
! [X0] :
( ~ member(X0,aI_bUc)
| member(X0,a) ),
inference(resolution,[],[f13,f22]) ).
fof(f31,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,b) ),
inference(resolution,[],[f14,f20]) ).
fof(f32,plain,
! [X0] :
( ~ member(X0,aIc)
| member(X0,c) ),
inference(resolution,[],[f14,f21]) ).
fof(f33,plain,
! [X0] :
( ~ member(X0,aI_bUc)
| member(X0,bUc) ),
inference(resolution,[],[f14,f22]) ).
fof(f34,plain,
! [X0] :
( ~ member(X0,bUc)
| member(X0,b)
| member(X0,c) ),
inference(resolution,[],[f7,f19]) ).
fof(f35,plain,
! [X0] :
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[],[f15,f20]) ).
fof(f36,plain,
! [X0] :
( member(X0,aIc)
| ~ member(X0,a)
| ~ member(X0,c) ),
inference(resolution,[],[f15,f21]) ).
fof(f37,plain,
! [X0] :
( member(X0,aI_bUc)
| ~ member(X0,a)
| ~ member(X0,bUc) ),
inference(resolution,[],[f15,f22]) ).
fof(f38,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolution,[],[f11,f23]) ).
fof(f43,definition,
( spl0_1
<=> member(g(aIb,aIc,aI_bUc),aIb) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f44,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIb)
| spl0_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl0_2
<=> member(g(aIb,aIc,aI_bUc),aI_bUc) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f48,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| spl0_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f38,f47,f43]) ).
fof(f51,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolution,[],[f12,f23]) ).
fof(f56,definition,
( spl0_3
<=> member(g(aIb,aIc,aI_bUc),aIc) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f57,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIc)
| spl0_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f51,f47,f56]) ).
fof(f66,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolution,[],[f10,f23]) ).
fof(f70,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aI_bUc)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f66,f45]) ).
fof(f71,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f70,f49]) ).
fof(f72,plain,
( spl0_3
| spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f71,f47,f43,f56]) ).
fof(f73,plain,
( member(g(aIb,aIc,aI_bUc),c)
| ~ spl0_3 ),
inference(resolution,[],[f57,f32]) ).
fof(f74,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ spl0_3 ),
inference(resolution,[],[f57,f29]) ).
fof(f88,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),bUc)
| spl0_2 ),
inference(resolution,[],[f37,f49]) ).
fof(f89,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f88,f74]) ).
fof(f90,plain,
( ~ member(g(aIb,aIc,aI_bUc),c)
| spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f89,f27]) ).
fof(f92,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f90,f73]) ).
fof(f93,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f92]) ).
fof(f95,definition,
( spl0_4
<=> member(g(aIb,aIc,aI_bUc),bUc) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f96,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| spl0_4 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f99,definition,
( spl0_5
<=> member(g(aIb,aIc,aI_bUc),a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f100,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| spl0_5 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f88,f47,f99,f95]) ).
fof(f103,plain,
( member(g(aIb,aIc,aI_bUc),b)
| ~ spl0_1 ),
inference(resolution,[],[f44,f31]) ).
fof(f104,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ spl0_1 ),
inference(resolution,[],[f44,f28]) ).
fof(f105,plain,
( spl0_5
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f104,f43,f99]) ).
fof(f106,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),c)
| spl0_3 ),
inference(resolution,[],[f58,f36]) ).
fof(f107,plain,
( ~ member(g(aIb,aIc,aI_bUc),c)
| spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f106,f100]) ).
fof(f133,plain,
( ~ member(g(aIb,aIc,aI_bUc),b)
| spl0_4 ),
inference(resolution,[],[f97,f26]) ).
fof(f135,plain,
( $false
| ~ spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f133,f103]) ).
fof(f136,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f135]) ).
fof(f137,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),b)
| spl0_1 ),
inference(resolution,[],[f45,f35]) ).
fof(f139,plain,
( ~ member(g(aIb,aIc,aI_bUc),b)
| spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f137,f100]) ).
fof(f140,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ spl0_2 ),
inference(resolution,[],[f48,f33]) ).
fof(f141,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ spl0_2 ),
inference(resolution,[],[f48,f30]) ).
fof(f143,plain,
( spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f140,f47,f95]) ).
fof(f176,plain,
( member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),c)
| ~ spl0_4 ),
inference(resolution,[],[f96,f34]) ).
fof(f179,plain,
( member(g(aIb,aIc,aI_bUc),c)
| spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f176,f139]) ).
fof(f180,plain,
( $false
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f179,f107]) ).
fof(f181,plain,
( spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f182,plain,
( $false
| ~ spl0_2
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f141,f101]) ).
fof(f183,plain,
( ~ spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f182]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f59]) ).
cnf(s3,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f72]) ).
cnf(s4,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f105]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f136]) ).
cnf(s8,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f143]) ).
cnf(s9,plain,
( spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f181]) ).
cnf(s10,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f183]) ).
cnf(s12,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s3,s4]) ).
cnf(s13,plain,
spl0_1,
inference(rat,[],[s9,s2,s8,s10,s12]) ).
cnf(s14,plain,
spl0_4,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
spl0_5,
inference(rat,[],[s6,s13]) ).
cnf(s16,plain,
~ spl0_2,
inference(rat,[],[s1,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s5,s15,s16,s14]) ).
fof(f193,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 28 00:07:49 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.45 Running first-order model finding
% 0.15/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 % (3134621)Will run a generic schedule for satisfiability detection.
% 0.21/0.49 % (3134630)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=968998158:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.49 % (3134630) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3134621-3134630"...
% 0.21/0.49 % (3134627)% WARNING: option uhcvi not known.
% 0.21/0.49 % (3134630)...printing done.
% 0.21/0.49 % (3134630)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (3134630)------------------------------
% 0.21/0.49 % (3134630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.49 % (3134630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.49 % (3134630)CaDiCaL version: 2.1.3
% 0.21/0.49 % (3134630)Termination reason: Refutation
% 0.21/0.49 % (3134630)Time elapsed: 0.003 s
% 0.21/0.49 % (3134630)Peak memory usage: 12 MB
% 0.21/0.49 % (3134630)Instructions burned: 8 (million)
% 0.21/0.49 % (3134621)Success in time 0.02 s
% 0.21/0.49 % Vampire exiting
%------------------------------------------------------------------------------