%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET020-7 : 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 : n017.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 12:39:37 PM UTC 2026
% Result : Unsatisfiable 3.68s 1.41s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 12 unt; 2 def)
% Number of atoms : 56 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 30 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
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(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f134,axiom,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_in_its_singleton) ).
fof(f137,axiom,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f179,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
fof(f180,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
fof(f181,plain,
u != first(ordered_pair(u,v)),
inference(reorient_equations,[],[f180]) ).
fof(f246,plain,
member(u,universal_class),
inference(resolution,[],[f14,f179]) ).
fof(f248,plain,
member(v,universal_class),
inference(resolution,[],[f15,f179]) ).
fof(f333,plain,
ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),
inference(resolution,[],[f17,f179]) ).
fof(f341,plain,
! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X0,X1))
| member(first(ordered_pair(u,v)),X0) ),
inference(superposition,[],[f14,f333]) ).
fof(f669,plain,
! [X0,X1] :
( member(first(ordered_pair(u,v)),X0)
| ~ member(v,X1)
| ~ member(u,X0) ),
inference(resolution,[],[f341,f16]) ).
fof(f672,definition,
( spl0_26
<=> ! [X1] : ~ member(v,X1) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f673,plain,
( ! [X1] : ~ member(v,X1)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f675,definition,
( spl0_27
<=> ! [X0] :
( member(first(ordered_pair(u,v)),X0)
| ~ member(u,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f676,plain,
( ! [X0] :
( member(first(ordered_pair(u,v)),X0)
| ~ member(u,X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f677,plain,
( spl0_26
| spl0_27 ),
inference(avatar_split_clause,[],[f669,f675,f672]) ).
fof(f680,plain,
( $false
| ~ spl0_26 ),
inference(resolution,[],[f673,f248]) ).
fof(f688,plain,
~ spl0_26,
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f694,plain,
( ! [X0] :
( ~ member(u,singleton(X0))
| first(ordered_pair(u,v)) = X0 )
| ~ spl0_27 ),
inference(resolution,[],[f676,f137]) ).
fof(f722,plain,
( u = first(ordered_pair(u,v))
| ~ member(u,universal_class)
| ~ spl0_27 ),
inference(resolution,[],[f694,f134]) ).
fof(f723,plain,
( ~ member(u,universal_class)
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f722,f181]) ).
fof(f724,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f723,f246]) ).
fof(f725,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f724]) ).
cnf(s17,plain,
( spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f677]) ).
cnf(s18,plain,
~ spl0_26,
inference(sat_conversion,[],[f688]) ).
cnf(s20,plain,
~ spl0_27,
inference(sat_conversion,[],[f725]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s17,s20,s18]) ).
fof(f726,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET020-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.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
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 00:04:51 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 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
% 3.68/1.41 % (3097522)Input is clausal, will run a generic CNF schedule.
% 3.68/1.41 % (3097532)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=960489988:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.68/1.41 % (3097532)Instruction limit reached!
% 3.68/1.41 % (3097532)------------------------------
% 3.68/1.41 % (3097532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.41 % (3097532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.41 % (3097532)CaDiCaL version: 2.1.3
% 3.68/1.41 % (3097532)Termination reason: Instruction limit
% 3.68/1.41 % (3097532)Termination phase: Saturation
% 3.68/1.41 % (3097532)Time elapsed: 0.036 s
% 3.68/1.41 % (3097532)Peak memory usage: 88 MB
% 3.68/1.41 % (3097532)Instructions burned: 116 (million)
% 3.68/1.41 % (3097528)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=1778340280:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.68/1.41 % (3097530)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=343670682:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.68/1.41 % (3097531)lrs+10_1_sil=8000:sp=occurrence:random_seed=2074436129:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.68/1.41 % (3097529)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1630515950:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.68/1.41 % (3097533)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1171077939:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.68/1.41 % (3097534)dis-21_1_sil=8000:lcm=predicate:random_seed=308756830: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)
% 3.68/1.41 % (3097531)First to succeed.
% 3.68/1.41 % (3097531)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3097522"
% 3.68/1.41 % (3097533)Also succeeded, but the first one will report.
% 3.68/1.41 % (3097534)Instruction limit reached!
% 3.68/1.41 % (3097534)------------------------------
% 3.68/1.41 % (3097534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.41 % (3097534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.41 % (3097534)CaDiCaL version: 2.1.3
% 3.68/1.41 % (3097534)Termination reason: Instruction limit
% 3.68/1.41 % (3097534)Termination phase: Saturation
% 3.68/1.41 % (3097534)Time elapsed: 0.076 s
% 3.68/1.41 % (3097534)Peak memory usage: 88 MB
% 3.68/1.41 % (3097534)Instructions burned: 118 (million)
% 3.68/1.41 % (3097536)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=3123045122:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.68/1.41 % (3097536)Refutation not found, incomplete strategy
% 3.68/1.41 % (3097536)------------------------------
% 3.68/1.41 % (3097536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.41 % (3097536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.41 % (3097536)CaDiCaL version: 2.1.3
% 3.68/1.41 % (3097536)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.41 % (3097536)Time elapsed: 0.001 s
% 3.68/1.41 % (3097536)Peak memory usage: 88 MB
% 3.68/1.41 % (3097536)Instructions burned: 2 (million)
% 3.68/1.41 % (3097543)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2111175631: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)
% 3.68/1.41 % (3097536)------------------------------
% 3.68/1.41 % (3097536)------------------------------
% 3.68/1.41 % (3097531)Refutation found. Thanks to Tanya!
% 3.68/1.41 % SZS status Unsatisfiable for theBenchmark
% 3.68/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.41 % (3097531)------------------------------
% 3.68/1.41 % (3097531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.41 % (3097531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.41 % (3097531)CaDiCaL version: 2.1.3
% 3.68/1.41 % (3097531)Termination reason: Refutation
% 3.68/1.41 % (3097531)Time elapsed: 0.019 s
% 3.68/1.41 % (3097531)Peak memory usage: 90 MB
% 3.68/1.41 % (3097531)Instructions burned: 23 (million)
% 3.68/1.41 % (3097531)------------------------------
% 3.68/1.41 % (3097531)------------------------------
% 3.68/1.41 % (3097522)Success in time 0.453 s
% 3.68/1.41 % Vampire exiting
%------------------------------------------------------------------------------