%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET257-6 : 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 : n014.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 12:40:37 PM UTC 2026
% Result : Unsatisfiable 3.65s 1.42s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 11 unt; 3 def)
% Number of atoms : 61 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 24 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f122,negated_conjecture,
restrict(cross_product(x,y),x,y) != cross_product(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_property5_1) ).
fof(f123,plain,
cross_product(x,y) != restrict(cross_product(x,y),x,y),
inference(reorient_equations,[],[f122]) ).
fof(f136,plain,
cross_product(x,y) != intersection(cross_product(x,y),cross_product(x,y)),
inference(definition_unfolding,[],[f123,f29]) ).
fof(f180,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f181,plain,
~ sQ0_eqProxy(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))),
inference(equality_proxy_replacement,[],[f136,f180]) ).
fof(f182,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f180]) ).
fof(f218,plain,
( ~ subclass(intersection(cross_product(x,y),cross_product(x,y)),cross_product(x,y))
| ~ subclass(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))) ),
inference(resolution,[],[f182,f181]) ).
fof(f221,definition,
( spl1_1
<=> subclass(intersection(cross_product(x,y),cross_product(x,y)),cross_product(x,y)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f222,plain,
( ~ subclass(intersection(cross_product(x,y),cross_product(x,y)),cross_product(x,y))
| spl1_1 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,definition,
( spl1_2
<=> subclass(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f225,plain,
( ~ subclass(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y)))
| spl1_2 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f218,f221,f224]) ).
fof(f228,plain,
( ~ member(not_subclass_element(intersection(cross_product(x,y),cross_product(x,y)),cross_product(x,y)),cross_product(x,y))
| spl1_1 ),
inference(resolution,[],[f222,f3]) ).
fof(f229,plain,
( member(not_subclass_element(intersection(cross_product(x,y),cross_product(x,y)),cross_product(x,y)),intersection(cross_product(x,y),cross_product(x,y)))
| spl1_1 ),
inference(resolution,[],[f222,f2]) ).
fof(f230,plain,
( member(not_subclass_element(intersection(cross_product(x,y),cross_product(x,y)),cross_product(x,y)),cross_product(x,y))
| spl1_1 ),
inference(resolution,[],[f229,f22]) ).
fof(f232,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f230,f228]) ).
fof(f233,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f234,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))),intersection(cross_product(x,y),cross_product(x,y)))
| spl1_2 ),
inference(resolution,[],[f225,f3]) ).
fof(f235,plain,
( member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))),cross_product(x,y))
| spl1_2 ),
inference(resolution,[],[f225,f2]) ).
fof(f241,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))),cross_product(x,y))
| ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))),cross_product(x,y))
| spl1_2 ),
inference(resolution,[],[f23,f234]) ).
fof(f242,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),cross_product(x,y))),cross_product(x,y))
| spl1_2 ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f243,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f242,f235]) ).
fof(f244,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f243]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f227]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f233]) ).
cnf(s4,plain,
spl1_2,
inference(sat_conversion,[],[f244]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f245,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET257-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n014.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 01:13:46 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 3.65/1.42 % (1339742)Input is clausal, will run a generic CNF schedule.
% 3.65/1.42 % (1339750)lrs+10_1_sil=8000:sp=occurrence:random_seed=1622188781:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.42 % (1339750)Refutation not found, incomplete strategy
% 3.65/1.42 % (1339750)------------------------------
% 3.65/1.42 % (1339750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.42 % (1339750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.42 % (1339750)CaDiCaL version: 2.1.3
% 3.65/1.42 % (1339750)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.42 % (1339750)Time elapsed: 0.001 s
% 3.65/1.42 % (1339750)Peak memory usage: 88 MB
% 3.65/1.42 % (1339750)Instructions burned: 1 (million)
% 3.65/1.42 % (1339747)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=2618068802:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.42 % (1339749)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1383800288:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.42 % (1339753)dis-21_1_sil=8000:lcm=predicate:random_seed=848694519: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)
% 3.65/1.42 % (1339751)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2514461595:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.42 % (1339752)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1207477125:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.42 % (1339748)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3441630535:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.42 % (1339753)First to succeed.
% 3.65/1.42 % (1339753)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1339742"
% 3.65/1.42 % (1339751)Instruction limit reached!
% 3.65/1.42 % (1339751)------------------------------
% 3.65/1.42 % (1339751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.42 % (1339751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.42 % (1339751)CaDiCaL version: 2.1.3
% 3.65/1.42 % (1339751)Termination reason: Instruction limit
% 3.65/1.42 % (1339751)Termination phase: Saturation
% 3.65/1.42 % (1339751)Time elapsed: 0.066 s
% 3.65/1.42 % (1339751)Peak memory usage: 88 MB
% 3.65/1.42 % (1339751)Instructions burned: 114 (million)
% 3.65/1.42 % (1339750)------------------------------
% 3.65/1.42 % (1339750)------------------------------
% 3.65/1.42 % (1339752)Instruction limit reached!
% 3.65/1.42 % (1339752)------------------------------
% 3.65/1.42 % (1339752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.42 % (1339752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.42 % (1339752)CaDiCaL version: 2.1.3
% 3.65/1.42 % (1339752)Termination reason: Instruction limit
% 3.65/1.42 % (1339752)Termination phase: Saturation
% 3.65/1.42 % (1339752)Time elapsed: 0.131 s
% 3.65/1.42 % (1339752)Peak memory usage: 90 MB
% 3.65/1.42 % (1339752)Instructions burned: 181 (million)
% 3.65/1.42 % (1339761)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=3188064328:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.65/1.42 % (1339761)Refutation not found, incomplete strategy
% 3.65/1.42 % (1339761)------------------------------
% 3.65/1.42 % (1339761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.42 % (1339761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.42 % (1339761)CaDiCaL version: 2.1.3
% 3.65/1.42 % (1339761)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.42 % (1339761)Time elapsed: 0.002 s
% 3.65/1.42 % (1339761)Peak memory usage: 88 MB
% 3.65/1.42 % (1339761)Instructions burned: 2 (million)
% 3.65/1.42 % (1339762)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1680290074: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)
% 3.65/1.42 % (1339762)Refutation not found, incomplete strategy
% 3.65/1.42 % (1339762)------------------------------
% 3.65/1.42 % (1339762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.42 % (1339762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.42 % (1339762)CaDiCaL version: 2.1.3
% 3.65/1.42 % (1339762)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.42 % (1339762)Time elapsed: 0.006 s
% 3.65/1.42 % (1339762)Peak memory usage: 88 MB
% 3.65/1.42 % (1339762)Instructions burned: 21 (million)
% 3.65/1.42 % (1339753)Refutation found. Thanks to Tanya!
% 3.65/1.42 % SZS status Unsatisfiable for theBenchmark
% 3.65/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.42 % (1339753)------------------------------
% 3.65/1.42 % (1339753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.42 % (1339753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.42 % (1339753)CaDiCaL version: 2.1.3
% 3.65/1.42 % (1339753)Termination reason: Refutation
% 3.65/1.42 % (1339753)Time elapsed: 0.006 s
% 3.65/1.42 % (1339753)Peak memory usage: 89 MB
% 3.65/1.42 % (1339753)Instructions burned: 8 (million)
% 3.65/1.42 % (1339753)------------------------------
% 3.65/1.42 % (1339753)------------------------------
% 3.65/1.42 % (1339742)Success in time 0.442 s
% 3.65/1.42 % Vampire exiting
%------------------------------------------------------------------------------