%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:44:34 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 34 ~; 28 |; 17 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(image2(X0,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa12) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(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] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
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(f44,plain,
? [X0,X1,X2] :
( ~ equal_set(image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f45,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,[],[f34]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f46]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ( member(sK5(X0,X1,X2),X1)
& apply(X0,sK5(X0,X1,X2),X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f70]) ).
fof(f83,plain,
( ~ equal_set(image2(sK9,empty_set),empty_set)
& maps(sK9,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f44]) ).
fof(f85,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f87,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f96,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f121,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f135,plain,
~ equal_set(image2(sK9,empty_set),empty_set),
inference(cnf_transformation,[],[f83]) ).
fof(f141,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f85,f96]) ).
fof(f161,plain,
! [X0] :
( ~ subset(X0,empty_set)
| equal_set(X0,empty_set) ),
inference(resolution,[],[f87,f141]) ).
fof(f253,plain,
! [X0,X1] : ~ member(X0,image2(X1,empty_set)),
inference(resolution,[],[f121,f96]) ).
fof(f264,plain,
! [X0,X1] : subset(image2(X0,empty_set),X1),
inference(resolution,[],[f253,f85]) ).
fof(f292,plain,
! [X0] : equal_set(image2(X0,empty_set),empty_set),
inference(resolution,[],[f264,f161]) ).
fof(f301,plain,
$false,
inference(resolution,[],[f292,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:45:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % (2969606)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (2969613)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=525833716:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (2969611)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4121174908_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (2969614)dis+10_1_sil=32000:sp=arity:random_seed=1136718188:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (2969615)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3483981075:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (2969616)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=953665741:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (2969617)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=117083300:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % (2969614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2969606-2969614"...
% 0.10/0.46 % (2969612)% WARNING: option uhcvi not known.
% 0.10/0.46 % (2969614)...printing done.
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (2969614)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (2969614)------------------------------
% 0.10/0.46 % (2969614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (2969614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (2969614)CaDiCaL version: 2.1.3
% 0.10/0.46 % (2969614)Termination reason: Refutation
% 0.10/0.46 % (2969614)Time elapsed: 0.006 s
% 0.10/0.46 % (2969614)Peak memory usage: 11 MB
% 0.10/0.46 % (2969614)Instructions burned: 8 (million)
% 0.10/0.46 % (2969606)Success in time 0.042 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------