%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:39:29 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.72s
% Output : Refutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 95 ( 12 unt; 7 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 225 ( 108 ~; 110 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 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/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',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/theBenchmark.p',union_axiom3) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',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/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',member_of_difference) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
fof(f25,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f26,axiom,
difference(c,a,cDa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_a) ).
fof(f27,axiom,
difference(c,b,cDb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_b) ).
fof(f28,axiom,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_aIb) ).
fof(f29,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
fof(f34,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,a) ),
inference(resolution,[],[f13,f25]) ).
fof(f35,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,b) ),
inference(resolution,[],[f14,f25]) ).
fof(f36,plain,
! [X0] :
( ~ member(X0,cDa)
| member(X0,c) ),
inference(resolution,[],[f19,f26]) ).
fof(f37,plain,
! [X0] :
( ~ member(X0,cDb)
| member(X0,c) ),
inference(resolution,[],[f19,f27]) ).
fof(f38,plain,
! [X0] :
( ~ member(X0,cD_aIb)
| member(X0,c) ),
inference(resolution,[],[f19,f28]) ).
fof(f39,plain,
! [X0] :
( ~ member(X0,cDa)
| ~ member(X0,a) ),
inference(resolution,[],[f20,f26]) ).
fof(f40,plain,
! [X0] :
( ~ member(X0,cDb)
| ~ member(X0,b) ),
inference(resolution,[],[f20,f27]) ).
fof(f41,plain,
! [X0] :
( ~ member(X0,cD_aIb)
| ~ member(X0,aIb) ),
inference(resolution,[],[f20,f28]) ).
fof(f42,plain,
! [X0] :
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[],[f15,f25]) ).
fof(f43,plain,
! [X0] :
( member(X0,cDa)
| ~ member(X0,c)
| member(X0,a) ),
inference(resolution,[],[f21,f26]) ).
fof(f44,plain,
! [X0] :
( member(X0,cDb)
| ~ member(X0,c)
| member(X0,b) ),
inference(resolution,[],[f21,f27]) ).
fof(f45,plain,
! [X0] :
( member(X0,cD_aIb)
| ~ member(X0,c)
| member(X0,aIb) ),
inference(resolution,[],[f21,f28]) ).
fof(f46,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[],[f11,f29]) ).
fof(f51,definition,
( spl0_1
<=> member(g(cDa,cDb,cD_aIb),cDa) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_2
<=> member(g(cDa,cDb,cD_aIb),cD_aIb) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f55,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f46,f54,f51]) ).
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,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f57,f54,f62]) ).
fof(f74,definition,
( spl0_4
<=> member(g(cDa,cDb,cD_aIb),a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f77,definition,
( spl0_5
<=> member(g(cDa,cDb,cD_aIb),c) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f78,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| spl0_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f111,definition,
( spl0_6
<=> member(g(cDa,cDb,cD_aIb),b) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f157,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(f161,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f162,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f163,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f164,plain,
( spl0_2
| spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f157,f51,f62,f54]) ).
fof(f170,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| ~ spl0_1 ),
inference(resolution,[],[f163,f39]) ).
fof(f171,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_1 ),
inference(resolution,[],[f163,f36]) ).
fof(f172,plain,
( $false
| ~ spl0_1
| spl0_5 ),
inference(resolution,[],[f171,f78]) ).
fof(f178,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f180,definition,
( spl0_8
<=> member(g(cDa,cDb,cD_aIb),aIb) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f181,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f220,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),a)
| spl0_1 ),
inference(resolution,[],[f52,f43]) ).
fof(f222,plain,
( spl0_4
| ~ spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f220,f51,f77,f74]) ).
fof(f226,plain,
( ~ member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_3 ),
inference(resolution,[],[f162,f40]) ).
fof(f227,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_3 ),
inference(resolution,[],[f162,f37]) ).
fof(f228,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f226,f62,f111]) ).
fof(f243,plain,
( $false
| ~ spl0_3
| spl0_5 ),
inference(resolution,[],[f227,f78]) ).
fof(f247,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f249,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),b)
| spl0_3 ),
inference(resolution,[],[f63,f44]) ).
fof(f251,plain,
( spl0_6
| ~ spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f249,f62,f77,f111]) ).
fof(f261,plain,
( ~ member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_2 ),
inference(resolution,[],[f161,f41]) ).
fof(f262,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_2 ),
inference(resolution,[],[f161,f38]) ).
fof(f264,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| ~ member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_2 ),
inference(resolution,[],[f261,f42]) ).
fof(f266,plain,
( ~ spl0_6
| ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f264,f54,f74,f111]) ).
fof(f276,plain,
( $false
| ~ spl0_2
| spl0_5 ),
inference(resolution,[],[f262,f78]) ).
fof(f277,plain,
( ~ spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f280,plain,
( ~ spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f170,f51,f74]) ).
fof(f281,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),aIb)
| spl0_2 ),
inference(resolution,[],[f55,f45]) ).
fof(f283,plain,
( spl0_8
| ~ spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f281,f54,f77,f180]) ).
fof(f306,plain,
( member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_8 ),
inference(resolution,[],[f181,f35]) ).
fof(f307,plain,
( member(g(cDa,cDb,cD_aIb),a)
| ~ spl0_8 ),
inference(resolution,[],[f181,f34]) ).
fof(f308,plain,
( spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f307,f180,f74]) ).
fof(f309,plain,
( spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f306,f180,f111]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f164]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f178]) ).
cnf(s18,plain,
( spl0_1
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f222]) ).
cnf(s19,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f228]) ).
cnf(s24,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f247]) ).
cnf(s25,plain,
( spl0_3
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f251]) ).
cnf(s27,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f266]) ).
cnf(s28,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f277]) ).
cnf(s31,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f280]) ).
cnf(s32,plain,
( spl0_2
| ~ spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f283]) ).
cnf(s36,plain,
( spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f308]) ).
cnf(s37,plain,
( spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f309]) ).
cnf(s38,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s37,s32,s19,s24,s5]) ).
cnf(s39,plain,
spl0_1,
inference(rat,[],[s27,s25,s18,s2,s28,s38]) ).
cnf(s40,plain,
~ spl0_4,
inference(rat,[],[s31,s39]) ).
cnf(s41,plain,
spl0_5,
inference(rat,[],[s6,s39]) ).
cnf(s42,plain,
~ spl0_2,
inference(rat,[],[s1,s39]) ).
cnf(s43,plain,
~ spl0_8,
inference(rat,[],[s36,s40]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s32,s42,s43,s41]) ).
fof(f310,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 28 00:05:42 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.47 Running first-order theorem proving
% 0.17/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/1.72 % (3350809)Input is clausal, will run a generic CNF schedule.
% 1.23/1.72 % (3350824)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=444987557:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.23/1.72 % (3350830)dis-21_1_sil=8000:lcm=predicate:random_seed=903182236: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)
% 1.23/1.72 % (3350830)First to succeed.
% 1.23/1.72 % (3350830)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3350809"
% 1.23/1.72 % (3350826)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=293288944:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.23/1.72 % (3350827)lrs+10_1_sil=8000:sp=occurrence:random_seed=3607081802:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.23/1.72 % (3350828)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2973744790:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.23/1.72 % (3350829)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3539454564:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.23/1.72 % (3350825)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=507431464:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.23/1.72 % (3350828)Refutation not found, incomplete strategy
% 1.23/1.72 % (3350828)------------------------------
% 1.23/1.72 % (3350828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.23/1.72 % (3350828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/1.72 % (3350828)CaDiCaL version: 2.1.3
% 1.23/1.72 % (3350828)Termination reason: Refutation not found, incomplete strategy
% 1.23/1.72 % (3350828)Time elapsed: 0.002 s
% 1.23/1.72 % (3350828)Peak memory usage: 87 MB
% 1.23/1.72 % (3350828)Instructions burned: 1 (million)
% 1.23/1.72 % (3350829)Also succeeded, but the first one will report.
% 1.23/1.72 % (3350827)Instruction limit reached!
% 1.23/1.72 % (3350827)------------------------------
% 1.23/1.72 % (3350827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.23/1.72 % (3350827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/1.72 % (3350827)CaDiCaL version: 2.1.3
% 1.23/1.72 % (3350827)Termination reason: Instruction limit
% 1.23/1.72 % (3350827)Termination phase: Saturation
% 1.23/1.72 % (3350827)Time elapsed: 0.107 s
% 1.23/1.72 % (3350827)Peak memory usage: 89 MB
% 1.23/1.72 % (3350827)Instructions burned: 107 (million)
% 1.23/1.72 % (3350830)Refutation found. Thanks to Tanya!
% 1.23/1.72 % SZS status Unsatisfiable for theBenchmark
% 1.23/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 4.93/1.96 % (3350830)------------------------------
% 4.93/1.96 % (3350830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.96 % (3350830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.96 % (3350830)CaDiCaL version: 2.1.3
% 4.93/1.96 % (3350830)Termination reason: Refutation
% 4.93/1.96 % (3350830)Time elapsed: 0.007 s
% 4.93/1.96 % (3350830)Peak memory usage: 89 MB
% 4.93/1.96 % (3350830)Instructions burned: 8 (million)
% 4.93/1.96 % (3350830)------------------------------
% 4.93/1.96 % (3350830)------------------------------
% 4.93/1.96 % (3350809)Success in time 0.564 s
% 4.93/1.96 % Vampire exiting
%------------------------------------------------------------------------------