%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:41:55 PM UTC 2026
% Result : Unsatisfiable 3.73s 1.52s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 11 unt; 2 def)
% Number of atoms : 58 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( member(X0,unionE_sk1(X0,X1))
| ~ member(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
fof(f2,axiom,
! [X0,X1] :
( member(unionE_sk1(X0,X1),X1)
| ~ member(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,cons(X1,X2))
| X0 = X1
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
fof(f6,axiom,
! [X2,X0,X1] :
( member(X0,un(X1,X2))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI1) ).
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,un(X2,X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI2) ).
fof(f8,axiom,
! [X0] : ~ member(X0,eptset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
fof(f14,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
fof(f15,negated_conjecture,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
fof(f16,plain,
~ member(sk2,a),
inference(resolution,[],[f6,f15]) ).
fof(f17,plain,
~ member(sk2,b),
inference(resolution,[],[f7,f15]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,X2)))
| member(unionE_sk1(X0,cons(X1,X2)),X2)
| unionE_sk1(X0,cons(X1,X2)) = X1 ),
inference(resolution,[],[f5,f2]) ).
fof(f43,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| a = unionE_sk1(sk2,cons(a,cons(b,eptset))) ),
inference(resolution,[],[f19,f14]) ).
fof(f45,definition,
( spl0_1
<=> a = unionE_sk1(sk2,cons(a,cons(b,eptset))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f47,plain,
( a = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f49,definition,
( spl0_2
<=> member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f51,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f43,f49,f45]) ).
fof(f53,plain,
( b = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ spl0_2 ),
inference(resolution,[],[f51,f5]) ).
fof(f54,plain,
( b = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f53,f8]) ).
fof(f58,plain,
( member(sk2,b)
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_2 ),
inference(superposition,[],[f1,f54]) ).
fof(f59,plain,
( ~ member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f58,f17]) ).
fof(f61,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f59,f14]) ).
fof(f62,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f61]) ).
fof(f64,plain,
( member(sk2,a)
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_1 ),
inference(superposition,[],[f1,f47]) ).
fof(f65,plain,
( ~ member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f64,f16]) ).
fof(f67,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f65,f14]) ).
fof(f68,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f62]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f69,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n004.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 02:49:22 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.73/1.52 % (4101191)Input is clausal, will run a generic CNF schedule.
% 3.73/1.52 % (4101198)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3192621765:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.73/1.52 % (4101196)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=2222428801:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.73/1.52 % (4101202)dis-21_1_sil=8000:lcm=predicate:random_seed=1782442153: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)
% 3.73/1.52 % (4101199)lrs+10_1_sil=8000:sp=occurrence:random_seed=2037052527:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.73/1.52 % (4101197)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4210662557:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.73/1.52 % (4101200)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4155176603:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.73/1.52 % (4101201)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3283698700:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.73/1.52 % (4101201)First to succeed.
% 3.73/1.52 % (4101201)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4101191"
% 3.73/1.52 % (4101200)Also succeeded, but the first one will report.
% 3.73/1.52 % (4101199)Also succeeded, but the first one will report.
% 3.73/1.52 % (4101202)Instruction limit reached!
% 3.73/1.52 % (4101202)------------------------------
% 3.73/1.52 % (4101202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.52 % (4101202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.52 % (4101202)CaDiCaL version: 2.1.3
% 3.73/1.52 % (4101202)Termination reason: Instruction limit
% 3.73/1.52 % (4101202)Termination phase: Saturation
% 3.73/1.52 % (4101202)Time elapsed: 0.061 s
% 3.73/1.52 % (4101202)Peak memory usage: 89 MB
% 3.73/1.52 % (4101202)Instructions burned: 117 (million)
% 3.73/1.52 % (4101210)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=2024294965:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.73/1.52 % (4101210)Refutation not found, incomplete strategy
% 3.73/1.52 % (4101210)------------------------------
% 3.73/1.52 % (4101210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.52 % (4101210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.52 % (4101210)CaDiCaL version: 2.1.3
% 3.73/1.52 % (4101210)Termination reason: Refutation not found, incomplete strategy
% 3.73/1.52 % (4101210)Time elapsed: 0.001 s
% 3.73/1.52 % (4101210)Peak memory usage: 88 MB
% 3.73/1.52 % (4101201)Refutation found. Thanks to Tanya!
% 3.73/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.73/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.73/1.52 % (4101201)------------------------------
% 3.73/1.52 % (4101201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.52 % (4101201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.52 % (4101201)CaDiCaL version: 2.1.3
% 3.73/1.52 % (4101201)Termination reason: Refutation
% 3.73/1.52 % (4101201)Time elapsed: 0.004 s
% 3.73/1.52 % (4101201)Peak memory usage: 89 MB
% 3.73/1.52 % (4101201)Instructions burned: 4 (million)
% 3.73/1.52 % (4101201)------------------------------
% 3.73/1.52 % (4101201)------------------------------
% 3.73/1.52 % (4101191)Success in time 0.437 s
% 3.73/1.52 % Vampire exiting
%------------------------------------------------------------------------------