%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET125-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:40:13 PM UTC 2026
% Result : Unsatisfiable 3.36s 1.35s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 31 ( 14 unt; 2 def)
% Number of atoms : 50 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn3_1) ).
fof(f103,negated_conjecture,
~ member(x,set_builder(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn3_2) ).
fof(f109,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f113,plain,
~ member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(definition_unfolding,[],[f103,f109]) ).
fof(f175,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f182,plain,
( ~ member(x,universal_class)
| member(x,intersection(complement(unordered_pair(y,y)),complement(z))) ),
inference(resolution,[],[f25,f113]) ).
fof(f185,definition,
( spl1_1
<=> member(x,intersection(complement(unordered_pair(y,y)),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f186,plain,
( member(x,intersection(complement(unordered_pair(y,y)),complement(z)))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,definition,
( spl1_2
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f189,plain,
( ~ member(x,universal_class)
| spl1_2 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f182,f188,f185]) ).
fof(f191,plain,
( ! [X0] : ~ member(x,X0)
| spl1_2 ),
inference(resolution,[],[f189,f175]) ).
fof(f192,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f191,f102]) ).
fof(f199,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f200,plain,
( member(x,complement(z))
| ~ spl1_1 ),
inference(resolution,[],[f186,f22]) ).
fof(f202,plain,
( ~ member(x,z)
| ~ spl1_1 ),
inference(resolution,[],[f200,f24]) ).
fof(f203,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f202,f102]) ).
fof(f204,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f203]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f190]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f199]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f204]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f205,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET125-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n018.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 00:52:54 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.36/1.35 % (2893617)Input is clausal, will run a generic CNF schedule.
% 3.36/1.35 % (2893624)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2540403434:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.36/1.35 % (2893627)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1765540126:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.36/1.35 % (2893625)lrs+10_1_sil=8000:sp=occurrence:random_seed=1211660549:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.36/1.35 % (2893623)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3308297116:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.36/1.35 % (2893628)dis-21_1_sil=8000:lcm=predicate:random_seed=464546738: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)
% 3.36/1.35 % (2893626)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2239703942:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.36/1.35 % (2893622)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=1531558372:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.36/1.35 % (2893625)Refutation not found, incomplete strategy
% 3.36/1.35 % (2893625)------------------------------
% 3.36/1.35 % (2893625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.35 % (2893625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.35 % (2893625)CaDiCaL version: 2.1.3
% 3.36/1.35 % (2893625)Termination reason: Refutation not found, incomplete strategy
% 3.36/1.35 % (2893625)Time elapsed: 0.002 s
% 3.36/1.35 % (2893625)Peak memory usage: 88 MB
% 3.36/1.35 % (2893625)Instructions burned: 2 (million)
% 3.36/1.35 % (2893628)First to succeed.
% 3.36/1.35 % (2893626)Also succeeded, but the first one will report.
% 3.36/1.35 % (2893628)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2893617"
% 3.36/1.35 % (2893627)Instruction limit reached!
% 3.36/1.35 % (2893627)------------------------------
% 3.36/1.35 % (2893627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.35 % (2893627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.35 % (2893627)CaDiCaL version: 2.1.3
% 3.36/1.35 % (2893627)Termination reason: Instruction limit
% 3.36/1.35 % (2893627)Termination phase: Saturation
% 3.36/1.35 % (2893627)Time elapsed: 0.140 s
% 3.36/1.35 % (2893627)Peak memory usage: 90 MB
% 3.36/1.35 % (2893627)Instructions burned: 182 (million)
% 3.36/1.35 % (2893625)------------------------------
% 3.36/1.35 % (2893625)------------------------------
% 3.36/1.35 % (2893628)Refutation found. Thanks to Tanya!
% 3.36/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.36/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.35 % (2893628)------------------------------
% 3.36/1.35 % (2893628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.35 % (2893628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.35 % (2893628)CaDiCaL version: 2.1.3
% 3.36/1.35 % (2893628)Termination reason: Refutation
% 3.36/1.35 % (2893628)Time elapsed: 0.005 s
% 3.36/1.35 % (2893628)Peak memory usage: 89 MB
% 3.36/1.35 % (2893628)Instructions burned: 6 (million)
% 3.36/1.35 % (2893628)------------------------------
% 3.36/1.35 % (2893628)------------------------------
% 3.36/1.35 % (2893617)Success in time 0.406 s
% 3.36/1.35 % Vampire exiting
%------------------------------------------------------------------------------