%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET071-6 : 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 12:39:56 PM UTC 2026
% Result : Unsatisfiable 6.10s 1.84s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 16 unt; 3 def)
% Number of atoms : 64 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 27 ~; 25 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 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(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f101,negated_conjecture,
unordered_pair(x,y) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_unordered_pair_1) ).
fof(f102,plain,
null_class != unordered_pair(x,y),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_unordered_pair_2) ).
fof(f104,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_unordered_pair_3) ).
fof(f156,definition,
sF0 = unordered_pair(x,y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f157,plain,
unordered_pair(x,y) = sF0,
inference(reorient_equations,[],[f156]) ).
fof(f158,plain,
null_class != sF0,
inference(definition_folding,[],[f102,f157]) ).
fof(f162,plain,
! [X0] :
( ~ member(X0,sF0)
| x = X0
| y = X0 ),
inference(superposition,[],[f8,f157]) ).
fof(f163,plain,
( x = regular(sF0)
| y = regular(sF0)
| null_class = sF0 ),
inference(resolution,[],[f162,f68]) ).
fof(f164,plain,
( x = regular(sF0)
| y = regular(sF0) ),
inference(forward_subsumption_resolution,[],[f163,f158]) ).
fof(f166,definition,
( spl1_1
<=> y = regular(sF0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f168,plain,
( y = regular(sF0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f170,definition,
( spl1_2
<=> x = regular(sF0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f172,plain,
( x = regular(sF0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f164,f170,f166]) ).
fof(f175,plain,
( member(x,sF0)
| null_class = sF0
| ~ spl1_2 ),
inference(superposition,[],[f68,f172]) ).
fof(f176,plain,
( member(x,sF0)
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f175,f158]) ).
fof(f179,plain,
! [X0] :
( ~ member(x,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[],[f1,f103]) ).
fof(f180,plain,
! [X0] :
( ~ member(y,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[],[f1,f104]) ).
fof(f183,plain,
! [X0] : ~ member(y,X0),
inference(forward_subsumption_resolution,[],[f180,f4]) ).
fof(f184,plain,
! [X0] : ~ member(x,X0),
inference(forward_subsumption_resolution,[],[f179,f4]) ).
fof(f186,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f184,f176]) ).
fof(f188,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f186]) ).
fof(f191,plain,
( member(y,sF0)
| null_class = sF0
| ~ spl1_1 ),
inference(superposition,[],[f68,f168]) ).
fof(f192,plain,
( null_class = sF0
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f191,f183]) ).
fof(f194,plain,
( $false
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f192,f158]) ).
fof(f195,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f194]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f173]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f188]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f195]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f196,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n013.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 00:29:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 5.07/1.65 % (700299)Input is clausal, will run a generic CNF schedule.
% 5.07/1.65 % (700306)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1938799829:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.07/1.65 % (700307)lrs+10_1_sil=8000:sp=occurrence:random_seed=2851097813:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.07/1.65 % (700305)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3917537664:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.07/1.65 % (700304)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=515705363:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.07/1.65 % (700308)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1105647423:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.07/1.65 % (700310)dis-21_1_sil=8000:lcm=predicate:random_seed=3193518453: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)
% 5.07/1.65 % (700309)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3989799524:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.07/1.65 % (700307)Refutation not found, incomplete strategy
% 5.07/1.65 % (700307)------------------------------
% 5.07/1.65 % (700307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.65 % (700307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.65 % (700307)CaDiCaL version: 2.1.3
% 5.07/1.65 % (700307)Termination reason: Refutation not found, incomplete strategy
% 5.07/1.65 % (700307)Time elapsed: 0.001 s
% 5.07/1.65 % (700307)Peak memory usage: 88 MB
% 5.07/1.65 % (700307)Instructions burned: 1 (million)
% 5.07/1.65 % (700310)Instruction limit reached!
% 5.07/1.65 % (700310)------------------------------
% 5.07/1.65 % (700310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.65 % (700310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.65 % (700310)CaDiCaL version: 2.1.3
% 5.07/1.65 % (700310)Termination reason: Instruction limit
% 5.07/1.65 % (700310)Termination phase: Saturation
% 5.07/1.65 % (700310)Time elapsed: 0.064 s
% 5.07/1.65 % (700310)Peak memory usage: 89 MB
% 5.07/1.65 % (700310)Instructions burned: 118 (million)
% 5.07/1.65 % (700308)Instruction limit reached!
% 5.07/1.65 % (700308)------------------------------
% 5.07/1.65 % (700308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.65 % (700308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.65 % (700308)CaDiCaL version: 2.1.3
% 5.07/1.65 % (700308)Termination reason: Instruction limit
% 5.07/1.65 % (700308)Termination phase: Saturation
% 5.07/1.65 % (700308)Time elapsed: 0.067 s
% 5.07/1.65 % (700308)Peak memory usage: 89 MB
% 5.07/1.65 % (700308)Instructions burned: 115 (million)
% 5.07/1.65 % (700309)Instruction limit reached!
% 5.07/1.65 % (700309)------------------------------
% 5.07/1.65 % (700309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.65 % (700309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.65 % (700309)CaDiCaL version: 2.1.3
% 5.07/1.65 % (700309)Termination reason: Instruction limit
% 5.07/1.65 % (700309)Termination phase: Saturation
% 5.07/1.65 % (700309)Time elapsed: 0.136 s
% 5.07/1.65 % (700309)Peak memory usage: 91 MB
% 5.07/1.65 % (700309)Instructions burned: 180 (million)
% 5.07/1.65 % (700318)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=1574732645:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.07/1.65 % (700318)Refutation not found, incomplete strategy
% 5.07/1.65 % (700318)------------------------------
% 5.07/1.65 % (700318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.65 % (700318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.65 % (700318)CaDiCaL version: 2.1.3
% 5.07/1.65 % (700318)Termination reason: Refutation not found, incomplete strategy
% 5.07/1.65 % (700318)Time elapsed: 0.003 s
% 5.07/1.65 % (700318)Peak memory usage: 88 MB
% 5.07/1.65 % (700318)Instructions burned: 3 (million)
% 5.07/1.65 % (700319)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=69453258: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)
% 6.10/1.84 % (700307)------------------------------
% 6.10/1.84 % (700307)------------------------------
% 6.10/1.84 % (700320)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2455323413:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.10/1.84 % (700319)Instruction limit reached!
% 6.10/1.84 % (700319)------------------------------
% 6.10/1.84 % (700319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.84 % (700319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.84 % (700319)CaDiCaL version: 2.1.3
% 6.10/1.84 % (700319)Termination reason: Instruction limit
% 6.10/1.84 % (700319)Termination phase: Saturation
% 6.10/1.84 % (700319)Time elapsed: 0.110 s
% 6.10/1.84 % (700319)Peak memory usage: 91 MB
% 6.10/1.84 % (700319)Instructions burned: 189 (million)
% 6.10/1.84 % (700323)lrs+10_64_to=lpo:sil=8000:random_seed=3887712066:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 6.10/1.84 % (700306)First to succeed.
% 6.10/1.84 % (700306)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-700299"
% 6.10/1.84 % (700323)Instruction limit reached!
% 6.10/1.84 % (700323)------------------------------
% 6.10/1.84 % (700323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.84 % (700323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.84 % (700323)CaDiCaL version: 2.1.3
% 6.10/1.84 % (700323)Termination reason: Instruction limit
% 6.10/1.84 % (700323)Termination phase: Saturation
% 6.10/1.84 % (700323)Time elapsed: 0.044 s
% 6.10/1.84 % (700323)Peak memory usage: 89 MB
% 6.10/1.84 % (700323)Instructions burned: 127 (million)
% 6.10/1.84 % (700320)Instruction limit reached!
% 6.10/1.84 % (700320)------------------------------
% 6.10/1.84 % (700320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.84 % (700320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.84 % (700320)CaDiCaL version: 2.1.3
% 6.10/1.84 % (700320)Termination reason: Instruction limit
% 6.10/1.84 % (700320)Termination phase: Saturation
% 6.10/1.84 % (700320)Time elapsed: 0.132 s
% 6.10/1.84 % (700320)Peak memory usage: 89 MB
% 6.10/1.84 % (700320)Instructions burned: 221 (million)
% 6.10/1.84 % (700318)------------------------------
% 6.10/1.84 % (700318)------------------------------
% 6.10/1.84 % (700325)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3282649695:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.10/1.84 % (700327)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=688620522:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 6.10/1.84 % (700327)Also succeeded, but the first one will report.
% 6.10/1.84 % (700328)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=528755854:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 6.10/1.84 % (700325)Instruction limit reached!
% 6.10/1.84 % (700325)------------------------------
% 6.10/1.84 % (700325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.84 % (700325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.84 % (700325)CaDiCaL version: 2.1.3
% 6.10/1.84 % (700325)Termination reason: Instruction limit
% 6.10/1.84 % (700325)Termination phase: Saturation
% 6.10/1.84 % (700325)Time elapsed: 0.118 s
% 6.10/1.84 % (700325)Peak memory usage: 89 MB
% 6.10/1.84 % (700325)Instructions burned: 194 (million)
% 6.10/1.84 % (700330)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=301209593:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 6.10/1.84 % (700306)Refutation found. Thanks to Tanya!
% 6.10/1.84 % SZS status Unsatisfiable for theBenchmark
% 6.10/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 6.10/1.84 % (700306)------------------------------
% 6.10/1.84 % (700306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.84 % (700306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.84 % (700306)CaDiCaL version: 2.1.3
% 6.10/1.84 % (700306)Termination reason: Refutation
% 6.10/1.84 % (700306)Time elapsed: 0.408 s
% 6.10/1.84 % (700306)Peak memory usage: 130 MB
% 6.10/1.84 % (700306)Instructions burned: 966 (million)
% 6.10/1.84 % (700306)------------------------------
% 6.10/1.84 % (700306)------------------------------
% 6.10/1.84 % (700299)Success in time 0.779 s
% 6.10/1.84 % Vampire exiting
%------------------------------------------------------------------------------