%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET067-7 : 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 : n009.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 12:39:55 PM UTC 2026
% Result : Unsatisfiable 6.41s 1.87s
% Output : Refutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 17 unt; 4 def)
% Number of atoms : 74 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 26 ~; 31 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f121,negated_conjecture,
~ subclass(singleton(x),unordered_pair(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair1_1) ).
fof(f174,plain,
~ subclass(unordered_pair(x,x),unordered_pair(x,y)),
inference(definition_unfolding,[],[f121,f12]) ).
fof(f178,definition,
sF0 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f179,plain,
unordered_pair(x,x) = sF0,
inference(reorient_equations,[],[f178]) ).
fof(f180,definition,
sF1 = unordered_pair(x,y),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f181,plain,
unordered_pair(x,y) = sF1,
inference(reorient_equations,[],[f180]) ).
fof(f182,plain,
~ subclass(sF0,sF1),
inference(definition_folding,[],[f174,f181,f179]) ).
fof(f185,plain,
( member(x,sF1)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f181]) ).
fof(f188,definition,
( spl2_1
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f190,plain,
( ~ member(x,universal_class)
| spl2_1 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f197,definition,
( spl2_3
<=> member(x,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f200,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f185,f197,f188]) ).
fof(f216,plain,
! [X0] :
( ~ member(X0,sF0)
| x = X0
| x = X0 ),
inference(superposition,[],[f8,f179]) ).
fof(f217,plain,
! [X0] :
( ~ member(X0,sF0)
| x = X0 ),
inference(duplicate_literal_removal,[],[f216]) ).
fof(f218,plain,
! [X0] :
( subclass(sF0,X0)
| x = not_subclass_element(sF0,X0) ),
inference(resolution,[],[f217,f2]) ).
fof(f219,plain,
x = not_subclass_element(sF0,sF1),
inference(resolution,[],[f218,f182]) ).
fof(f220,plain,
( ~ member(x,sF1)
| subclass(sF0,sF1) ),
inference(superposition,[],[f3,f219]) ).
fof(f223,plain,
~ member(x,sF1),
inference(forward_subsumption_resolution,[],[f220,f182]) ).
fof(f225,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f223,f197]) ).
fof(f422,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) ),
inference(resolution,[],[f23,f1]) ).
fof(f426,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f422,f4]) ).
fof(f433,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[],[f426,f2]) ).
fof(f445,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f433,f2]) ).
fof(f454,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f445]) ).
fof(f462,plain,
( member(x,universal_class)
| subclass(sF0,sF1) ),
inference(superposition,[],[f454,f219]) ).
fof(f466,plain,
( subclass(sF0,sF1)
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f462,f190]) ).
fof(f467,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f466,f182]) ).
fof(f468,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f467]) ).
cnf(s2,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
~ spl2_3,
inference(sat_conversion,[],[f225]) ).
cnf(s13,plain,
spl2_1,
inference(sat_conversion,[],[f468]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s5,s13]) ).
fof(f469,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET067-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:28:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 5.32/1.68 % (2563713)Input is clausal, will run a generic CNF schedule.
% 5.32/1.68 % (2563718)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=3578116268:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.32/1.68 % (2563722)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=966474093:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.32/1.68 % (2563723)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=689797330:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.32/1.68 % (2563719)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=334548192:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.32/1.68 % (2563721)lrs+10_1_sil=8000:sp=occurrence:random_seed=3820504582:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.32/1.68 % (2563720)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1073290730:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.32/1.68 % (2563721)Refutation not found, incomplete strategy
% 5.32/1.68 % (2563721)------------------------------
% 5.32/1.68 % (2563721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.32/1.68 % (2563721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.68 % (2563721)CaDiCaL version: 2.1.3
% 5.32/1.68 % (2563721)Termination reason: Refutation not found, incomplete strategy
% 5.32/1.68 % (2563721)Time elapsed: 0.009 s
% 5.32/1.68 % (2563721)Peak memory usage: 88 MB
% 5.32/1.68 % (2563721)Instructions burned: 11 (million)
% 5.32/1.68 % (2563724)dis-21_1_sil=8000:lcm=predicate:random_seed=1787992908: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)
% 5.32/1.68 % (2563722)Instruction limit reached!
% 5.32/1.68 % (2563722)------------------------------
% 5.32/1.68 % (2563722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.32/1.68 % (2563722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.68 % (2563722)CaDiCaL version: 2.1.3
% 5.32/1.68 % (2563722)Termination reason: Instruction limit
% 5.32/1.68 % (2563722)Termination phase: Saturation
% 5.32/1.68 % (2563722)Time elapsed: 0.068 s
% 5.32/1.68 % (2563722)Peak memory usage: 88 MB
% 5.32/1.68 % (2563722)Instructions burned: 115 (million)
% 5.32/1.68 % (2563723)Instruction limit reached!
% 5.32/1.68 % (2563723)------------------------------
% 5.32/1.68 % (2563723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.32/1.68 % (2563723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.68 % (2563723)CaDiCaL version: 2.1.3
% 5.32/1.68 % (2563723)Termination reason: Instruction limit
% 5.32/1.68 % (2563723)Termination phase: Saturation
% 5.32/1.68 % (2563723)Time elapsed: 0.086 s
% 5.32/1.68 % (2563723)Peak memory usage: 88 MB
% 5.32/1.68 % (2563723)Instructions burned: 180 (million)
% 5.32/1.68 % (2563724)Instruction limit reached!
% 5.32/1.68 % (2563724)------------------------------
% 5.32/1.68 % (2563724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.32/1.68 % (2563724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.68 % (2563724)CaDiCaL version: 2.1.3
% 5.32/1.68 % (2563724)Termination reason: Instruction limit
% 5.32/1.68 % (2563724)Termination phase: Saturation
% 5.32/1.68 % (2563724)Time elapsed: 0.074 s
% 5.32/1.68 % (2563724)Peak memory usage: 89 MB
% 5.32/1.68 % (2563724)Instructions burned: 117 (million)
% 5.32/1.68 % (2563732)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=2369568093:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.32/1.68 % (2563732)Refutation not found, incomplete strategy
% 5.32/1.68 % (2563732)------------------------------
% 5.32/1.68 % (2563732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.32/1.68 % (2563732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.68 % (2563732)CaDiCaL version: 2.1.3
% 5.32/1.68 % (2563732)Termination reason: Refutation not found, incomplete strategy
% 5.32/1.68 % (2563732)Time elapsed: 0.004 s
% 5.32/1.68 % (2563732)Peak memory usage: 88 MB
% 5.32/1.68 % (2563732)Instructions burned: 4 (million)
% 5.32/1.68 % (2563721)------------------------------
% 6.41/1.87 % (2563721)------------------------------
% 6.41/1.87 % (2563734)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2208293583:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.41/1.87 % (2563733)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2599462241: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)
% 6.41/1.87 % (2563734)Instruction limit reached!
% 6.41/1.87 % (2563734)------------------------------
% 6.41/1.87 % (2563734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.87 % (2563734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.87 % (2563734)CaDiCaL version: 2.1.3
% 6.41/1.87 % (2563734)Termination reason: Instruction limit
% 6.41/1.87 % (2563734)Termination phase: Saturation
% 6.41/1.87 % (2563734)Time elapsed: 0.086 s
% 6.41/1.87 % (2563734)Peak memory usage: 88 MB
% 6.41/1.87 % (2563734)Instructions burned: 221 (million)
% 6.41/1.87 % (2563733)Instruction limit reached!
% 6.41/1.87 % (2563733)------------------------------
% 6.41/1.87 % (2563733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.87 % (2563733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.87 % (2563733)CaDiCaL version: 2.1.3
% 6.41/1.87 % (2563733)Termination reason: Instruction limit
% 6.41/1.87 % (2563733)Termination phase: Saturation
% 6.41/1.87 % (2563733)Time elapsed: 0.096 s
% 6.41/1.87 % (2563733)Peak memory usage: 90 MB
% 6.41/1.87 % (2563733)Instructions burned: 189 (million)
% 6.41/1.87 % (2563718)First to succeed.
% 6.41/1.87 % (2563718)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2563713"
% 6.41/1.87 % (2563738)lrs+10_64_to=lpo:sil=8000:random_seed=1988925510:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.41/1.87 % (2563732)------------------------------
% 6.41/1.87 % (2563732)------------------------------
% 6.41/1.87 % (2563739)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1183078751:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 6.41/1.87 % (2563740)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2126459627:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 6.41/1.87 % (2563738)Instruction limit reached!
% 6.41/1.87 % (2563738)------------------------------
% 6.41/1.87 % (2563738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.87 % (2563738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.87 % (2563738)CaDiCaL version: 2.1.3
% 6.41/1.87 % (2563738)Termination reason: Instruction limit
% 6.41/1.87 % (2563738)Termination phase: Saturation
% 6.41/1.87 % (2563738)Time elapsed: 0.083 s
% 6.41/1.87 % (2563738)Peak memory usage: 89 MB
% 6.41/1.87 % (2563738)Instructions burned: 126 (million)
% 6.41/1.87 % (2563739)Instruction limit reached!
% 6.41/1.87 % (2563739)------------------------------
% 6.41/1.87 % (2563739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.87 % (2563739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.87 % (2563739)CaDiCaL version: 2.1.3
% 6.41/1.87 % (2563739)Termination reason: Instruction limit
% 6.41/1.87 % (2563739)Termination phase: Saturation
% 6.41/1.87 % (2563739)Time elapsed: 0.082 s
% 6.41/1.87 % (2563739)Peak memory usage: 88 MB
% 6.41/1.87 % (2563739)Instructions burned: 194 (million)
% 6.41/1.87 % (2563742)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=372008314:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.41/1.87 % (2563740)Also succeeded, but the first one will report.
% 6.41/1.87 % (2563718)Refutation found. Thanks to Tanya!
% 6.41/1.87 % SZS status Unsatisfiable for theBenchmark
% 6.41/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 6.41/1.87 % (2563718)------------------------------
% 6.41/1.87 % (2563718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.87 % (2563718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.87 % (2563718)CaDiCaL version: 2.1.3
% 6.41/1.87 % (2563718)Termination reason: Refutation
% 6.41/1.87 % (2563718)Time elapsed: 0.439 s
% 6.41/1.87 % (2563718)Peak memory usage: 130 MB
% 6.41/1.87 % (2563718)Instructions burned: 1006 (million)
% 6.41/1.87 % (2563718)------------------------------
% 6.41/1.87 % (2563718)------------------------------
% 6.41/1.87 % (2563713)Success in time 0.83 s
% 6.41/1.87 % Vampire exiting
%------------------------------------------------------------------------------