%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET016-6 : 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 : n008.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 12:39:34 PM UTC 2026
% Result : Unsatisfiable 3.47s 1.15s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 15 unt; 2 def)
% Number of atoms : 65 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 26 ~; 26 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f101,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
fof(f102,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
fof(f103,negated_conjecture,
w != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
fof(f107,plain,
! [X0] : member(singleton(X0),universal_class),
inference(superposition,[],[f11,f12]) ).
fof(f111,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f335,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f336,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f335]) ).
fof(f338,plain,
! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| singleton(X0) = X2
| unordered_pair(X0,singleton(X1)) = X2 ),
inference(superposition,[],[f8,f13]) ).
fof(f340,plain,
! [X0,X1] :
( member(singleton(X0),ordered_pair(X0,X1))
| ~ member(singleton(X0),universal_class) ),
inference(superposition,[],[f9,f13]) ).
fof(f342,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[],[f340,f107]) ).
fof(f643,plain,
member(singleton(y),ordered_pair(w,x)),
inference(superposition,[],[f342,f101]) ).
fof(f1513,plain,
( singleton(y) = singleton(w)
| singleton(y) = unordered_pair(w,singleton(x)) ),
inference(resolution,[],[f338,f643]) ).
fof(f1548,definition,
( spl0_109
<=> singleton(y) = unordered_pair(w,singleton(x)) ),
introduced(definition,[new_symbols(definition,[spl0_109])],[avatar_definition]) ).
fof(f1550,plain,
( singleton(y) = unordered_pair(w,singleton(x))
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f1552,definition,
( spl0_110
<=> singleton(y) = singleton(w) ),
introduced(definition,[new_symbols(definition,[spl0_110])],[avatar_definition]) ).
fof(f1554,plain,
( singleton(y) = singleton(w)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f1555,plain,
( spl0_109
| spl0_110 ),
inference(avatar_split_clause,[],[f1513,f1552,f1548]) ).
fof(f1562,plain,
( member(w,singleton(y))
| ~ member(w,universal_class)
| ~ spl0_109 ),
inference(superposition,[],[f9,f1550]) ).
fof(f1564,plain,
( member(w,singleton(y))
| ~ spl0_109 ),
inference(forward_subsumption_resolution,[],[f1562,f102]) ).
fof(f1581,plain,
( w = y
| ~ spl0_109 ),
inference(resolution,[],[f1564,f336]) ).
fof(f1582,plain,
( $false
| ~ spl0_109 ),
inference(forward_subsumption_resolution,[],[f1581,f103]) ).
fof(f1583,plain,
~ spl0_109,
inference(avatar_contradiction_clause,[],[f1582]) ).
fof(f1602,plain,
( ! [X0] :
( ~ member(X0,singleton(w))
| y = X0 )
| ~ spl0_110 ),
inference(superposition,[],[f336,f1554]) ).
fof(f1700,plain,
( w = y
| ~ member(w,universal_class)
| ~ spl0_110 ),
inference(resolution,[],[f1602,f111]) ).
fof(f1778,plain,
( ~ member(w,universal_class)
| ~ spl0_110 ),
inference(forward_subsumption_resolution,[],[f1700,f103]) ).
fof(f1784,plain,
( $false
| ~ spl0_110 ),
inference(forward_subsumption_resolution,[],[f1778,f102]) ).
fof(f1785,plain,
~ spl0_110,
inference(avatar_contradiction_clause,[],[f1784]) ).
cnf(s77,plain,
( spl0_109
| spl0_110 ),
inference(sat_conversion,[],[f1555]) ).
cnf(s79,plain,
~ spl0_109,
inference(sat_conversion,[],[f1583]) ).
cnf(s96,plain,
~ spl0_110,
inference(sat_conversion,[],[f1785]) ).
cnf(s97,plain,
$false,
inference(rat,[],[s77,s96,s79]) ).
fof(f1786,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:08:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.41 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
% 3.47/1.15 % (1746818)Input is clausal, will run a generic CNF schedule.
% 3.47/1.15 % (1746827)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=470844534:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.47/1.15 % (1746824)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=651818351:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.47/1.15 % (1746823)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=2473439440:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.47/1.15 % (1746825)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3509906197:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.47/1.15 % (1746829)dis-21_1_sil=8000:lcm=predicate:random_seed=417585470: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)
% 3.47/1.15 % (1746828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2594124373:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.47/1.15 % (1746826)lrs+10_1_sil=8000:sp=occurrence:random_seed=3562014990:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.47/1.15 % (1746826)Refutation not found, incomplete strategy
% 3.47/1.15 % (1746826)------------------------------
% 3.47/1.15 % (1746826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.15 % (1746826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.15 % (1746826)CaDiCaL version: 2.1.3
% 3.47/1.15 % (1746826)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.15 % (1746826)Time elapsed: 0.002 s
% 3.47/1.15 % (1746826)Peak memory usage: 88 MB
% 3.47/1.15 % (1746826)Instructions burned: 1 (million)
% 3.47/1.15 % (1746827)Instruction limit reached!
% 3.47/1.15 % (1746827)------------------------------
% 3.47/1.15 % (1746827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.15 % (1746827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.15 % (1746827)CaDiCaL version: 2.1.3
% 3.47/1.15 % (1746827)Termination reason: Instruction limit
% 3.47/1.15 % (1746827)Termination phase: Saturation
% 3.47/1.15 % (1746827)Time elapsed: 0.048 s
% 3.47/1.15 % (1746827)Peak memory usage: 88 MB
% 3.47/1.15 % (1746827)Instructions burned: 115 (million)
% 3.47/1.15 % (1746828)First to succeed.
% 3.47/1.15 % (1746828)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1746818"
% 3.47/1.15 % (1746829)Instruction limit reached!
% 3.47/1.15 % (1746829)------------------------------
% 3.47/1.15 % (1746829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.15 % (1746829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.15 % (1746829)CaDiCaL version: 2.1.3
% 3.47/1.15 % (1746829)Termination reason: Instruction limit
% 3.47/1.15 % (1746829)Termination phase: Saturation
% 3.47/1.15 % (1746829)Time elapsed: 0.063 s
% 3.47/1.15 % (1746829)Peak memory usage: 88 MB
% 3.47/1.15 % (1746829)Instructions burned: 117 (million)
% 3.47/1.15 % (1746837)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=2100309538:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.47/1.15 % (1746837)Refutation not found, incomplete strategy
% 3.47/1.15 % (1746837)------------------------------
% 3.47/1.15 % (1746837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.15 % (1746837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.15 % (1746837)CaDiCaL version: 2.1.3
% 3.47/1.15 % (1746837)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.15 % (1746837)Time elapsed: 0.002 s
% 3.47/1.15 % (1746837)Peak memory usage: 88 MB
% 3.47/1.15 % (1746837)Instructions burned: 1 (million)
% 3.47/1.15 % (1746838)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1886605303: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)
% 3.47/1.15 % (1746826)------------------------------
% 3.47/1.15 % (1746826)------------------------------
% 3.47/1.15 % (1746828)Refutation found. Thanks to Tanya!
% 3.47/1.15 % SZS status Unsatisfiable for theBenchmark
% 3.47/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.15 % (1746828)------------------------------
% 3.47/1.15 % (1746828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.15 % (1746828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.15 % (1746828)CaDiCaL version: 2.1.3
% 3.47/1.15 % (1746828)Termination reason: Refutation
% 3.47/1.15 % (1746828)Time elapsed: 0.052 s
% 3.47/1.15 % (1746828)Peak memory usage: 90 MB
% 3.47/1.15 % (1746828)Instructions burned: 67 (million)
% 3.47/1.15 % (1746828)------------------------------
% 3.47/1.15 % (1746828)------------------------------
% 3.47/1.15 % (1746818)Success in time 0.448 s
% 3.47/1.15 % Vampire exiting
%------------------------------------------------------------------------------