%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:39:28 PM UTC 2026
% Result : Unsatisfiable 3.47s 1.44s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 9 unt; 3 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 22 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn 12 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p',intersection_axiom2) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_difference) ).
fof(f19,axiom,
difference(b,a,bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_minus_a) ).
fof(f20,negated_conjecture,
~ intersection(a,bDa,aI_bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bDa) ).
fof(f21,negated_conjecture,
! [X0] : ~ member(X0,aI_bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aI_bDa_is_empty) ).
fof(f27,plain,
! [X0] :
( ~ member(X0,bDa)
| ~ member(X0,a) ),
inference(resolution,[],[f14,f19]) ).
fof(f33,plain,
( member(h(a,bDa,aI_bDa),aI_bDa)
| member(h(a,bDa,aI_bDa),a) ),
inference(resolution,[],[f10,f20]) ).
fof(f38,definition,
( spl0_1
<=> member(h(a,bDa,aI_bDa),a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f39,plain,
( member(h(a,bDa,aI_bDa),a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl0_2
<=> member(h(a,bDa,aI_bDa),aI_bDa) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( member(h(a,bDa,aI_bDa),aI_bDa)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f33,f41,f38]) ).
fof(f44,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f42,f21]) ).
fof(f45,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f49,plain,
( member(h(a,bDa,aI_bDa),aI_bDa)
| member(h(a,bDa,aI_bDa),bDa) ),
inference(resolution,[],[f11,f20]) ).
fof(f54,definition,
( spl0_3
<=> member(h(a,bDa,aI_bDa),bDa) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f55,plain,
( member(h(a,bDa,aI_bDa),bDa)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f41,f54]) ).
fof(f57,plain,
( ~ member(h(a,bDa,aI_bDa),a)
| ~ spl0_3 ),
inference(resolution,[],[f55,f27]) ).
fof(f58,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f57,f39]) ).
fof(f60,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f58]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
spl0_3,
inference(rat,[],[s3,s2]) ).
cnf(s6,plain,
~ spl0_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
fof(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:00:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.47/1.44 % (1910020)Input is clausal, will run a generic CNF schedule.
% 3.47/1.44 % (1910029)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1807011998:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.47/1.44 % (1910029)Refutation not found, incomplete strategy
% 3.47/1.44 % (1910029)------------------------------
% 3.47/1.44 % (1910029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (1910029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (1910029)CaDiCaL version: 2.1.3
% 3.47/1.44 % (1910029)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.44 % (1910029)Time elapsed: 0.001 s
% 3.47/1.44 % (1910029)Peak memory usage: 87 MB
% 3.47/1.44 % (1910028)lrs+10_1_sil=8000:sp=occurrence:random_seed=1085438497:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.47/1.44 % (1910031)dis-21_1_sil=8000:lcm=predicate:random_seed=2418450629: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)
% 3.47/1.44 % (1910026)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=641405321:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.47/1.44 % (1910025)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=2653292751:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.47/1.44 % (1910027)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2161535883:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.47/1.44 % (1910031)First to succeed.
% 3.47/1.44 % (1910031)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1910020"
% 3.47/1.44 % (1910028)Also succeeded, but the first one will report.
% 3.47/1.44 % (1910030)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3384477921:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.47/1.44 % (1910030)Also succeeded, but the first one will report.
% 3.47/1.44 % (1910029)------------------------------
% 3.47/1.44 % (1910029)------------------------------
% 3.47/1.44 % (1910039)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=532184557:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.47/1.44 % (1910039)Also succeeded, but the first one will report.
% 3.47/1.44 % (1910031)Refutation found. Thanks to Tanya!
% 3.47/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.47/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.44 % (1910031)------------------------------
% 3.47/1.44 % (1910031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (1910031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (1910031)CaDiCaL version: 2.1.3
% 3.47/1.44 % (1910031)Termination reason: Refutation
% 3.47/1.44 % (1910031)Time elapsed: 0.003 s
% 3.47/1.44 % (1910031)Peak memory usage: 89 MB
% 3.47/1.44 % (1910031)Instructions burned: 2 (million)
% 3.47/1.44 % (1910031)------------------------------
% 3.47/1.44 % (1910031)------------------------------
% 3.47/1.44 % (1910020)Success in time 0.405 s
% 3.47/1.44 % Vampire exiting
%------------------------------------------------------------------------------