%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:41:52 PM UTC 2026
% Result : Theorem 2.43s 1.19s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 10 unt; 2 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 41 ~; 36 |; 17 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(inverse_image2(X0,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa14) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(inverse_image2(X0,empty_set),empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f34,plain,
? [X0,X1,X2] :
( ~ equal_set(inverse_image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
( ~ equal_set(inverse_image2(sK0,empty_set),empty_set)
& maps(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f34]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X2,X4) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ( member(sK4(X0,X1,X2),X1)
& apply(X0,X2,sK4(X0,X1,X2)) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f47,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f47]) ).
fof(f53,plain,
~ equal_set(inverse_image2(sK0,empty_set),empty_set),
inference(cnf_transformation,[],[f40]) ).
fof(f54,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(sK4(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f65,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f84,plain,
( ~ subset(inverse_image2(sK0,empty_set),empty_set)
| ~ subset(empty_set,inverse_image2(sK0,empty_set)) ),
inference(resolution,[],[f54,f53]) ).
fof(f86,definition,
( spl7_1
<=> subset(empty_set,inverse_image2(sK0,empty_set)) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f87,plain,
( ~ subset(empty_set,inverse_image2(sK0,empty_set))
| spl7_1 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,definition,
( spl7_2
<=> subset(inverse_image2(sK0,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f90,plain,
( ~ subset(inverse_image2(sK0,empty_set),empty_set)
| spl7_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f84,f89,f86]) ).
fof(f93,plain,
( member(sK5(empty_set,inverse_image2(sK0,empty_set)),empty_set)
| spl7_1 ),
inference(resolution,[],[f87,f65]) ).
fof(f95,plain,
( $false
| spl7_1 ),
inference(resolution,[],[f93,f55]) ).
fof(f96,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f95]) ).
fof(f101,plain,
( member(sK5(inverse_image2(sK0,empty_set),empty_set),inverse_image2(sK0,empty_set))
| spl7_2 ),
inference(resolution,[],[f90,f65]) ).
fof(f103,plain,
! [X0,X1] : ~ member(X0,inverse_image2(X1,empty_set)),
inference(resolution,[],[f60,f55]) ).
fof(f104,plain,
( $false
| spl7_2 ),
inference(resolution,[],[f103,f101]) ).
fof(f106,plain,
spl7_2,
inference(avatar_contradiction_clause,[],[f104]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
spl7_1,
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
spl7_2,
inference(sat_conversion,[],[f106]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 28 02:45:16 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 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
% 2.43/1.19 % (2970167)Detected formulas, will run a generic FOF schedule.
% 2.43/1.19 % (2970178)dis-21_1_sil=8000:lcm=predicate:random_seed=2588047759:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.43/1.19 % (2970178)First to succeed.
% 2.43/1.19 % (2970178)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2970167"
% 2.43/1.19 % (2970174)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=628646796:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.43/1.19 % (2970175)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2715040492:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.43/1.19 % (2970173)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=22369669:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.43/1.19 % (2970176)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3672582406:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.43/1.19 % (2970172)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=313348179:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.43/1.19 % (2970176)Also succeeded, but the first one will report.
% 2.43/1.19 % (2970175)Refutation not found, incomplete strategy
% 2.43/1.19 % (2970175)------------------------------
% 2.43/1.19 % (2970175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.19 % (2970175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.19 % (2970175)CaDiCaL version: 2.1.3
% 2.43/1.19 % (2970175)Termination reason: Refutation not found, incomplete strategy
% 2.43/1.19 % (2970175)Time elapsed: 0.002 s
% 2.43/1.19 % (2970175)Peak memory usage: 88 MB
% 2.43/1.19 % (2970175)Instructions burned: 2 (million)
% 2.43/1.19 % (2970177)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=5410172:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.43/1.19 % (2970177)Also succeeded, but the first one will report.
% 2.43/1.19 % (2970178)Refutation found. Thanks to Tanya!
% 2.43/1.19 % SZS status Theorem for theBenchmark
% 2.43/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/1.19 % (2970178)------------------------------
% 2.43/1.19 % (2970178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.19 % (2970178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.19 % (2970178)CaDiCaL version: 2.1.3
% 2.43/1.19 % (2970178)Termination reason: Refutation
% 2.43/1.19 % (2970178)Time elapsed: 0.002 s
% 2.43/1.19 % (2970178)Peak memory usage: 89 MB
% 2.43/1.19 % (2970178)Instructions burned: 2 (million)
% 2.43/1.19 % (2970178)------------------------------
% 2.43/1.19 % (2970178)------------------------------
% 2.43/1.19 % (2970167)Success in time 0.278 s
% 2.43/1.19 % Vampire exiting
%------------------------------------------------------------------------------