%------------------------------------------------------------------------------
% File : Vampire---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 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 12:41:51 PM UTC 2026
% Result : Theorem 3.43s 1.24s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 28 ~; 20 |; 13 &)
% ( 3 <=>; 6 =>; 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 : 60 ( 53 !; 7 ?)
% 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(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ~ equal_set(image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f41,plain,
( ~ equal_set(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)],[f35]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ( member(sK4(X0,X1,X2),X1)
& apply(X0,sK4(X0,X1,X2),X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f40]) ).
fof(f48,plain,
~ equal_set(image2(sK0,empty_set),empty_set),
inference(cnf_transformation,[],[f41]) ).
fof(f49,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f55,plain,
! [X2,X0,X1] :
( member(sK4(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f57,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f57,f50]) ).
fof(f62,plain,
( ~ subset(image2(sK0,empty_set),empty_set)
| ~ subset(empty_set,image2(sK0,empty_set)) ),
inference(resolution,[],[f49,f48]) ).
fof(f63,plain,
~ subset(image2(sK0,empty_set),empty_set),
inference(forward_subsumption_resolution,[],[f62,f59]) ).
fof(f64,plain,
! [X0,X1] : ~ member(X0,image2(X1,empty_set)),
inference(resolution,[],[f55,f50]) ).
fof(f65,plain,
! [X0,X1] : subset(image2(X0,empty_set),X1),
inference(resolution,[],[f64,f57]) ).
fof(f67,plain,
$false,
inference(resolution,[],[f65,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:43:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.43/1.24 % (1389369)Detected formulas, will run a generic FOF schedule.
% 3.43/1.24 % (1389375)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=546956047:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/1.24 % (1389380)dis-21_1_sil=8000:lcm=predicate:random_seed=2292900779: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)
% 3.43/1.24 % (1389378)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=567923315:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/1.24 % (1389374)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=2461668886:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/1.24 % (1389376)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=3869905623:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/1.24 % (1389379)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=821688274:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/1.24 % (1389377)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3646434548:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/1.24 % (1389378)First to succeed.
% 3.43/1.24 % (1389380)Also succeeded, but the first one will report.
% 3.43/1.24 % (1389378)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1389369"
% 3.43/1.24 % (1389377)Refutation not found, incomplete strategy
% 3.43/1.24 % (1389377)------------------------------
% 3.43/1.24 % (1389377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.24 % (1389377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.24 % (1389377)CaDiCaL version: 2.1.3
% 3.43/1.24 % (1389377)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.24 % (1389377)Time elapsed: 0.003 s
% 3.43/1.24 % (1389377)Peak memory usage: 88 MB
% 3.43/1.24 % (1389377)Instructions burned: 2 (million)
% 3.43/1.24 % (1389379)Also succeeded, but the first one will report.
% 3.43/1.24 % (1389377)------------------------------
% 3.43/1.24 % (1389377)------------------------------
% 3.43/1.24 % (1389378)Refutation found. Thanks to Tanya!
% 3.43/1.24 % SZS status Theorem for theBenchmark
% 3.43/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.24 % (1389378)------------------------------
% 3.43/1.24 % (1389378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.24 % (1389378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.24 % (1389378)CaDiCaL version: 2.1.3
% 3.43/1.24 % (1389378)Termination reason: Refutation
% 3.43/1.24 % (1389378)Time elapsed: 0.003 s
% 3.43/1.24 % (1389378)Peak memory usage: 88 MB
% 3.43/1.24 % (1389378)Instructions burned: 1 (million)
% 3.43/1.24 % (1389378)------------------------------
% 3.43/1.24 % (1389378)------------------------------
% 3.43/1.24 % (1389369)Success in time 0.43 s
% 3.43/1.24 % Vampire exiting
%------------------------------------------------------------------------------