%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET011-1 : 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 : n011.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 3.53s 1.45s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 8 unt; 4 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 51 ~; 55 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2)
| member(h(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2)
| member(h(X0,X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).
fof(f12,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).
fof(f13,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(f14,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(f15,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(f19,axiom,
difference(a,b,aDb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_minus_b) ).
fof(f20,axiom,
difference(a,aDb,aD_aDb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_minus_aDb) ).
fof(f21,negated_conjecture,
~ intersection(a,b,aD_aDb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
fof(f27,plain,
! [X0] :
( ~ member(X0,aD_aDb)
| member(X0,a) ),
inference(resolution,[],[f13,f20]) ).
fof(f28,plain,
! [X0] :
( ~ member(X0,aDb)
| ~ member(X0,b) ),
inference(resolution,[],[f14,f19]) ).
fof(f29,plain,
! [X0] :
( ~ member(X0,aD_aDb)
| ~ member(X0,aDb) ),
inference(resolution,[],[f14,f20]) ).
fof(f30,plain,
! [X0] :
( member(X0,aDb)
| ~ member(X0,a)
| member(X0,b) ),
inference(resolution,[],[f15,f19]) ).
fof(f31,plain,
! [X0] :
( member(X0,aD_aDb)
| ~ member(X0,a)
| member(X0,aDb) ),
inference(resolution,[],[f15,f20]) ).
fof(f32,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),a) ),
inference(resolution,[],[f10,f21]) ).
fof(f37,definition,
( spl0_1
<=> member(h(a,b,aD_aDb),a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f40,definition,
( spl0_2
<=> member(h(a,b,aD_aDb),aD_aDb) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f41,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f32,f40,f37]) ).
fof(f43,plain,
( ~ member(h(a,b,aD_aDb),aDb)
| ~ spl0_2 ),
inference(resolution,[],[f41,f29]) ).
fof(f44,plain,
( member(h(a,b,aD_aDb),a)
| ~ spl0_2 ),
inference(resolution,[],[f41,f27]) ).
fof(f45,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f44,f40,f37]) ).
fof(f48,plain,
( ~ member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),b)
| ~ spl0_2 ),
inference(resolution,[],[f30,f43]) ).
fof(f50,definition,
( spl0_3
<=> member(h(a,b,aD_aDb),b) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f53,plain,
( spl0_3
| ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f48,f40,f37,f50]) ).
fof(f54,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),b) ),
inference(resolution,[],[f11,f21]) ).
fof(f58,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f54,f40,f50]) ).
fof(f75,plain,
( ~ member(h(a,b,aD_aDb),b)
| ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolution,[],[f12,f21]) ).
fof(f79,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f81,plain,
( ~ spl0_2
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f75,f50,f37,f40]) ).
fof(f82,plain,
( ~ member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),aDb)
| spl0_2 ),
inference(resolution,[],[f79,f31]) ).
fof(f85,definition,
( spl0_4
<=> member(h(a,b,aD_aDb),aDb) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f86,plain,
( member(h(a,b,aD_aDb),aDb)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( spl0_4
| ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f82,f40,f37,f85]) ).
fof(f88,plain,
( ~ member(h(a,b,aD_aDb),b)
| ~ spl0_4 ),
inference(resolution,[],[f86,f28]) ).
fof(f90,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f88,f85,f50]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f58]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f81]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f87]) ).
cnf(s7,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f90]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s1,s2]) ).
cnf(s9,plain,
spl0_2,
inference(rat,[],[s7,s4,s6,s8]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s5,s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s8,s10,s9]) ).
fof(f91,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 00:03:16 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.53/1.45 % (2903199)Input is clausal, will run a generic CNF schedule.
% 3.53/1.45 % (2903206)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2050455914:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.53/1.45 % (2903205)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1477722053:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.53/1.45 % (2903204)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=236247535:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.53/1.45 % (2903209)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2250088683:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.53/1.45 % (2903207)lrs+10_1_sil=8000:sp=occurrence:random_seed=3644180123:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.53/1.45 % (2903210)dis-21_1_sil=8000:lcm=predicate:random_seed=1371518953: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)
% 3.53/1.45 % (2903208)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2437671839:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.53/1.45 % (2903208)Refutation not found, incomplete strategy
% 3.53/1.45 % (2903208)------------------------------
% 3.53/1.45 % (2903208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (2903208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (2903208)CaDiCaL version: 2.1.3
% 3.53/1.45 % (2903208)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.45 % (2903208)Time elapsed: 0.001 s
% 3.53/1.45 % (2903208)Peak memory usage: 87 MB
% 3.53/1.45 % (2903210)First to succeed.
% 3.53/1.45 % (2903210)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2903199"
% 3.53/1.45 % (2903209)Also succeeded, but the first one will report.
% 3.53/1.45 % (2903207)Instruction limit reached!
% 3.53/1.45 % (2903207)------------------------------
% 3.53/1.45 % (2903207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (2903207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (2903207)CaDiCaL version: 2.1.3
% 3.53/1.45 % (2903207)Termination reason: Instruction limit
% 3.53/1.45 % (2903207)Termination phase: Saturation
% 3.53/1.45 % (2903207)Time elapsed: 0.066 s
% 3.53/1.45 % (2903207)Peak memory usage: 88 MB
% 3.53/1.45 % (2903207)Instructions burned: 108 (million)
% 3.53/1.45 % (2903218)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=4164460042:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.53/1.45 % (2903218)Also succeeded, but the first one will report.
% 3.53/1.45 % (2903208)------------------------------
% 3.53/1.45 % (2903208)------------------------------
% 3.53/1.45 % (2903210)Refutation found. Thanks to Tanya!
% 3.53/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.53/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.45 % (2903210)------------------------------
% 3.53/1.45 % (2903210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (2903210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (2903210)CaDiCaL version: 2.1.3
% 3.53/1.45 % (2903210)Termination reason: Refutation
% 3.53/1.45 % (2903210)Time elapsed: 0.003 s
% 3.53/1.45 % (2903210)Peak memory usage: 89 MB
% 3.53/1.45 % (2903210)Instructions burned: 3 (million)
% 3.53/1.45 % (2903210)------------------------------
% 3.53/1.45 % (2903210)------------------------------
% 3.53/1.45 % (2903199)Success in time 0.417 s
% 3.53/1.45 % Vampire exiting
%------------------------------------------------------------------------------