%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET084-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:40:01 PM UTC 2026
% Result : Unsatisfiable 3.98s 1.53s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 48 ( 18 unt; 4 def)
% Number of atoms : 86 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 39 ~; 34 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f101,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_1) ).
fof(f102,negated_conjecture,
member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_2) ).
fof(f103,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_3) ).
fof(f113,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f114,plain,
( member(x,singleton(y))
| ~ member(x,universal_class) ),
inference(superposition,[],[f113,f101]) ).
fof(f116,definition,
( spl0_1
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f118,plain,
( ~ member(x,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f120,definition,
( spl0_2
<=> member(x,singleton(y)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f122,plain,
( member(x,singleton(y))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f114,f120,f116]) ).
fof(f152,plain,
( ! [X0] :
( ~ member(x,X0)
| ~ subclass(X0,universal_class) )
| spl0_1 ),
inference(resolution,[],[f1,f118]) ).
fof(f153,plain,
( ! [X0] : ~ member(x,X0)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f152,f4]) ).
fof(f297,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f298,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f297]) ).
fof(f302,plain,
! [X0] : ordered_pair(X0,x) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(y))),
inference(superposition,[],[f13,f101]) ).
fof(f311,plain,
! [X0] : ordered_pair(X0,x) = ordered_pair(X0,y),
inference(forward_demodulation,[],[f302,f13]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,y),cross_product(X1,X2))
| member(x,X2) ),
inference(superposition,[],[f15,f311]) ).
fof(f420,plain,
( ! [X2,X0,X1] : ~ member(ordered_pair(X0,y),cross_product(X1,X2))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f312,f153]) ).
fof(f425,plain,
( ! [X2,X0,X1] :
( ~ member(y,X0)
| ~ member(X1,X2) )
| spl0_1 ),
inference(resolution,[],[f420,f16]) ).
fof(f428,definition,
( spl0_28
<=> ! [X2,X1] : ~ member(X1,X2) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f429,plain,
( ! [X2,X1] : ~ member(X1,X2)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f431,definition,
( spl0_29
<=> ! [X0] : ~ member(y,X0) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f432,plain,
( ! [X0] : ~ member(y,X0)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( spl0_28
| spl0_29
| spl0_1 ),
inference(avatar_split_clause,[],[f425,f116,f431,f428]) ).
fof(f471,plain,
( $false
| ~ spl0_28 ),
inference(resolution,[],[f429,f11]) ).
fof(f491,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f495,plain,
( $false
| ~ spl0_29 ),
inference(resolution,[],[f432,f102]) ).
fof(f503,plain,
~ spl0_29,
inference(avatar_contradiction_clause,[],[f495]) ).
fof(f631,plain,
( x = y
| ~ spl0_2 ),
inference(resolution,[],[f298,f122]) ).
fof(f640,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f631,f103]) ).
fof(f641,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f640]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s18,plain,
( spl0_1
| spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f433]) ).
cnf(s24,plain,
~ spl0_28,
inference(sat_conversion,[],[f491]) ).
cnf(s25,plain,
~ spl0_29,
inference(sat_conversion,[],[f503]) ).
cnf(s34,plain,
~ spl0_2,
inference(sat_conversion,[],[f641]) ).
cnf(s36,plain,
spl0_1,
inference(rat,[],[s18,s25,s24]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s1,s34,s36]) ).
fof(f642,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET084-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 00:34:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.98/1.53 % (701902)Input is clausal, will run a generic CNF schedule.
% 3.98/1.53 % (701908)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2131053944:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.98/1.53 % (701911)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2102364837:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.98/1.53 % (701913)dis-21_1_sil=8000:lcm=predicate:random_seed=2870868673: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)
% 3.98/1.53 % (701910)lrs+10_1_sil=8000:sp=occurrence:random_seed=3185913786:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.98/1.53 % (701909)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3404162326:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.98/1.53 % (701907)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=1843118220:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.98/1.53 % (701910)Refutation not found, incomplete strategy
% 3.98/1.53 % (701910)------------------------------
% 3.98/1.53 % (701910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.53 % (701910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.53 % (701910)CaDiCaL version: 2.1.3
% 3.98/1.53 % (701910)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.53 % (701910)Time elapsed: 0.001 s
% 3.98/1.53 % (701910)Peak memory usage: 88 MB
% 3.98/1.53 % (701912)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3147054604:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.98/1.53 % (701912)First to succeed.
% 3.98/1.53 % (701912)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-701902"
% 3.98/1.53 % (701913)Instruction limit reached!
% 3.98/1.53 % (701913)------------------------------
% 3.98/1.53 % (701913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.53 % (701913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.53 % (701913)CaDiCaL version: 2.1.3
% 3.98/1.53 % (701913)Termination reason: Instruction limit
% 3.98/1.53 % (701913)Termination phase: Saturation
% 3.98/1.53 % (701913)Time elapsed: 0.064 s
% 3.98/1.53 % (701913)Peak memory usage: 89 MB
% 3.98/1.53 % (701913)Instructions burned: 118 (million)
% 3.98/1.53 % (701911)Instruction limit reached!
% 3.98/1.53 % (701911)------------------------------
% 3.98/1.53 % (701911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.53 % (701911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.53 % (701911)CaDiCaL version: 2.1.3
% 3.98/1.53 % (701911)Termination reason: Instruction limit
% 3.98/1.53 % (701911)Termination phase: Saturation
% 3.98/1.53 % (701911)Time elapsed: 0.070 s
% 3.98/1.53 % (701911)Peak memory usage: 89 MB
% 3.98/1.53 % (701911)Instructions burned: 115 (million)
% 3.98/1.53 % (701921)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=1200697909:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.98/1.53 % (701922)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3727603149:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.98/1.53 % (701921)Also succeeded, but the first one will report.
% 3.98/1.53 % (701910)------------------------------
% 3.98/1.53 % (701910)------------------------------
% 3.98/1.53 % (701922)Also succeeded, but the first one will report.
% 3.98/1.53 % (701912)Refutation found. Thanks to Tanya!
% 3.98/1.53 % SZS status Unsatisfiable for theBenchmark
% 3.98/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.53 % (701912)------------------------------
% 3.98/1.53 % (701912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.53 % (701912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.53 % (701912)CaDiCaL version: 2.1.3
% 3.98/1.53 % (701912)Termination reason: Refutation
% 3.98/1.53 % (701912)Time elapsed: 0.020 s
% 3.98/1.53 % (701912)Peak memory usage: 90 MB
% 3.98/1.53 % (701912)Instructions burned: 23 (million)
% 3.98/1.53 % (701912)------------------------------
% 3.98/1.53 % (701912)------------------------------
% 3.98/1.53 % (701902)Success in time 0.48 s
% 3.98/1.53 % Vampire exiting
%------------------------------------------------------------------------------