%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:50:32 PM UTC 2026
% Result : Theorem 2.78s 1.18s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 61 ( 24 ~; 16 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 41 ( 29 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
? [X1] :
! [X2] :
( f(X2,X1)
<=> ( f(X2,X0)
& ~ f(X2,X2) ) )
=> ~ ? [X3] :
! [X4] : f(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish256) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
? [X1] :
! [X2] :
( f(X2,X1)
<=> ( f(X2,X0)
& ~ f(X2,X2) ) )
=> ~ ? [X3] :
! [X4] : f(X4,X3) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X3] :
! [X4] : f(X4,X3)
& ! [X0] :
? [X1] :
! [X2] :
( f(X2,X1)
<=> ( f(X2,X0)
& ~ f(X2,X2) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ? [X3] :
! [X4] : f(X4,X3)
& ! [X0] :
? [X1] :
! [X2] :
( ( f(X2,X1)
| ~ f(X2,X0)
| f(X2,X2) )
& ( ( f(X2,X0)
& ~ f(X2,X2) )
| ~ f(X2,X1) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X3] :
! [X4] : f(X4,X3)
& ! [X0] :
? [X1] :
! [X2] :
( ( f(X2,X1)
| ~ f(X2,X0)
| f(X2,X2) )
& ( ( f(X2,X0)
& ~ f(X2,X2) )
| ~ f(X2,X1) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ? [X0] :
! [X1] : f(X1,X0)
& ! [X2] :
? [X3] :
! [X4] :
( ( f(X4,X3)
| ~ f(X4,X2)
| f(X4,X4) )
& ( ( f(X4,X2)
& ~ f(X4,X4) )
| ~ f(X4,X3) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X1] : f(X1,sK0)
& ! [X2,X4] :
( ( f(X4,sK1(X2))
| ~ f(X4,X2)
| f(X4,X4) )
& ( ( f(X4,X2)
& ~ f(X4,X4) )
| ~ f(X4,sK1(X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X2))],[f6]) ).
fof(f8,plain,
! [X2,X4] :
( ~ f(X4,sK1(X2))
| ~ f(X4,X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2,X4] :
( f(X4,sK1(X2))
| ~ f(X4,X2)
| f(X4,X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X1] : f(X1,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0] : ~ f(sK1(X0),sK1(X0)),
inference(factoring,[],[f8]) ).
fof(f15,plain,
! [X0] :
( ~ f(sK1(X0),X0)
| f(sK1(X0),sK1(X0)) ),
inference(resolution,[],[f10,f12]) ).
fof(f16,plain,
! [X0] : ~ f(sK1(X0),X0),
inference(forward_subsumption_resolution,[],[f15,f12]) ).
fof(f17,plain,
$false,
inference(resolution,[],[f16,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:55:03 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.78/1.18 % (4117611)Detected formulas, will run a generic FOF schedule.
% 2.78/1.18 % (4117620)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3074271592:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.18 % (4117620)First to succeed.
% 2.78/1.18 % (4117620)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4117611"
% 2.78/1.18 % (4117619)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=148756787:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.18 % (4117618)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=2617284288:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.18 % (4117621)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2392956016:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.18 % (4117616)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=1111980430:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.18 % (4117622)dis-21_1_sil=8000:lcm=predicate:random_seed=3651607595: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)
% 2.78/1.18 % (4117617)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=2934085738:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.18 % (4117619)Also succeeded, but the first one will report.
% 2.78/1.18 % (4117621)Also succeeded, but the first one will report.
% 2.78/1.18 % (4117622)Also succeeded, but the first one will report.
% 2.78/1.18 % (4117620)Refutation found. Thanks to Tanya!
% 2.78/1.18 % SZS status Theorem for theBenchmark
% 2.78/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.18 % (4117620)------------------------------
% 2.78/1.18 % (4117620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.18 % (4117620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.18 % (4117620)CaDiCaL version: 2.1.3
% 2.78/1.18 % (4117620)Termination reason: Refutation
% 2.78/1.18 % (4117620)Time elapsed: 0.001 s
% 2.78/1.18 % (4117620)Peak memory usage: 88 MB
% 2.78/1.18 % (4117620)------------------------------
% 2.78/1.18 % (4117620)------------------------------
% 2.78/1.18 % (4117611)Success in time 0.299 s
% 2.78/1.18 % Vampire exiting
%------------------------------------------------------------------------------