%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET236-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:40:34 PM UTC 2026
% Result : Unsatisfiable 3.46s 1.26s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 10 unt; 2 def)
% Number of atoms : 55 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 29 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f122,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property11_1) ).
fof(f123,negated_conjecture,
member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property11_2) ).
fof(f124,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property11_3) ).
fof(f125,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| ~ subclass(X2,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f1,f3]) ).
fof(f148,plain,
! [X0,X1] :
( member(not_subclass_element(x,y),y)
| ~ member(not_subclass_element(x,y),cross_product(X0,X1)) ),
inference(superposition,[],[f123,f17]) ).
fof(f152,definition,
( spl0_3
<=> ! [X0,X1] : ~ member(not_subclass_element(x,y),cross_product(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f153,plain,
( ! [X0,X1] : ~ member(not_subclass_element(x,y),cross_product(X0,X1))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl0_4
<=> member(not_subclass_element(x,y),y) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f156,plain,
( member(not_subclass_element(x,y),y)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f148,f155,f152]) ).
fof(f158,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(x,y),X0)
| ~ subclass(X0,cross_product(X1,X2)) )
| ~ spl0_3 ),
inference(resolution,[],[f153,f1]) ).
fof(f162,plain,
( ! [X0,X1] :
( ~ subclass(x,cross_product(X0,X1))
| subclass(x,y) )
| ~ spl0_3 ),
inference(resolution,[],[f158,f2]) ).
fof(f164,plain,
( ! [X0,X1] : ~ subclass(x,cross_product(X0,X1))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f162,f124]) ).
fof(f169,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f164,f122]) ).
fof(f170,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f169]) ).
fof(f172,plain,
( ~ subclass(y,y)
| subclass(x,y)
| ~ spl0_4 ),
inference(resolution,[],[f156,f129]) ).
fof(f173,plain,
( subclass(x,y)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f172,f125]) ).
fof(f176,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f173,f124]) ).
fof(f177,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f176]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f157]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f170]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f177]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s5,s3]) ).
fof(f178,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET236-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.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 01:14:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.46/1.26 % (2176720)Input is clausal, will run a generic CNF schedule.
% 3.46/1.26 % (2176725)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=280250668:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.46/1.26 % (2176729)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=633439796:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.46/1.26 % (2176728)lrs+10_1_sil=8000:sp=occurrence:random_seed=4101934903:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.46/1.26 % (2176726)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2307760017:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.46/1.26 % (2176730)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4062413686:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.46/1.26 % (2176731)dis-21_1_sil=8000:lcm=predicate:random_seed=1355837222: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)
% 3.46/1.26 % (2176727)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1098874387:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.46/1.26 % (2176729)First to succeed.
% 3.46/1.26 % (2176729)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2176720"
% 3.46/1.26 % (2176731)Instruction limit reached!
% 3.46/1.26 % (2176731)------------------------------
% 3.46/1.26 % (2176731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.26 % (2176731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.26 % (2176731)CaDiCaL version: 2.1.3
% 3.46/1.26 % (2176731)Termination reason: Instruction limit
% 3.46/1.26 % (2176731)Termination phase: Saturation
% 3.46/1.26 % (2176731)Time elapsed: 0.070 s
% 3.46/1.26 % (2176731)Peak memory usage: 89 MB
% 3.46/1.26 % (2176731)Instructions burned: 117 (million)
% 3.46/1.26 % (2176730)Instruction limit reached!
% 3.46/1.26 % (2176730)------------------------------
% 3.46/1.26 % (2176730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.26 % (2176730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.26 % (2176730)CaDiCaL version: 2.1.3
% 3.46/1.26 % (2176730)Termination reason: Instruction limit
% 3.46/1.26 % (2176730)Termination phase: Saturation
% 3.46/1.26 % (2176730)Time elapsed: 0.073 s
% 3.46/1.26 % (2176730)Peak memory usage: 90 MB
% 3.46/1.26 % (2176730)Instructions burned: 180 (million)
% 3.46/1.26 % (2176728)Instruction limit reached!
% 3.46/1.26 % (2176728)------------------------------
% 3.46/1.26 % (2176728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.26 % (2176728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.26 % (2176728)CaDiCaL version: 2.1.3
% 3.46/1.26 % (2176728)Termination reason: Instruction limit
% 3.46/1.26 % (2176728)Termination phase: Saturation
% 3.46/1.26 % (2176728)Time elapsed: 0.075 s
% 3.46/1.26 % (2176728)Peak memory usage: 89 MB
% 3.46/1.26 % (2176728)Instructions burned: 108 (million)
% 3.46/1.26 % (2176740)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3983417733: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)
% 3.46/1.26 % (2176740)Also succeeded, but the first one will report.
% 3.46/1.26 % (2176739)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=1704157064:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.46/1.26 % (2176741)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=836752310:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.46/1.26 % (2176741)Also succeeded, but the first one will report.
% 3.46/1.26 % (2176729)Refutation found. Thanks to Tanya!
% 3.46/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.46/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.26 % (2176729)------------------------------
% 3.46/1.26 % (2176729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.26 % (2176729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.26 % (2176729)CaDiCaL version: 2.1.3
% 3.46/1.26 % (2176729)Termination reason: Refutation
% 3.46/1.26 % (2176729)Time elapsed: 0.004 s
% 3.46/1.26 % (2176729)Peak memory usage: 89 MB
% 3.46/1.26 % (2176729)Instructions burned: 3 (million)
% 3.46/1.26 % (2176729)------------------------------
% 3.46/1.26 % (2176729)------------------------------
% 3.46/1.26 % (2176720)Success in time 0.448 s
% 3.46/1.26 % Vampire exiting
%------------------------------------------------------------------------------