%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN935+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:06:01 PM UTC 2026
% Result : Theorem 2.71s 1.15s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 80 ( 31 ~; 27 |; 12 &)
% ( 3 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 26 ( 15 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( p(X0)
=> c )
<=> ( ! [X0] : p(X0)
=> c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( p(X0)
=> c )
<=> ( ! [X0] : p(X0)
=> c ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
( p(X0)
=> c )
<=> ( ! [X1] : p(X1)
=> c ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
( c
| ~ p(X0) )
<~> ( c
| ? [X1] : ~ p(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ( ~ c
& ! [X1] : p(X1) )
| ! [X0] :
( ~ c
& p(X0) ) )
& ( c
| ? [X1] : ~ p(X1)
| ? [X0] :
( c
| ~ p(X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ( ~ c
& ! [X1] : p(X1) )
| ! [X0] :
( ~ c
& p(X0) ) )
& ( c
| ? [X1] : ~ p(X1)
| ? [X0] :
( c
| ~ p(X0) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ( ( ~ c
& ! [X0] : p(X0) )
| ! [X1] :
( ~ c
& p(X1) ) )
& ( c
| ? [X2] : ~ p(X2)
| ? [X3] :
( c
| ~ p(X3) ) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
( ( ( ~ c
& ! [X0] : p(X0) )
| ! [X1] :
( ~ c
& p(X1) ) )
& ( c
| ~ p(sK0)
| c
| ~ p(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f7]) ).
fof(f9,plain,
( c
| ~ p(sK0)
| c
| ~ p(sK1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( p(X1)
| p(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
( ~ c
| ~ c ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
( c
| ~ p(sK0)
| ~ p(sK1) ),
inference(duplicate_literal_removal,[],[f9]) ).
fof(f15,plain,
~ c,
inference(duplicate_literal_removal,[],[f13]) ).
fof(f16,plain,
( ~ p(sK1)
| ~ p(sK0) ),
inference(forward_subsumption_resolution,[],[f14,f15]) ).
fof(f17,plain,
! [X0] :
( ~ p(sK0)
| p(X0) ),
inference(resolution,[],[f16,f10]) ).
fof(f18,plain,
! [X0] : p(X0),
inference(forward_subsumption_resolution,[],[f17,f10]) ).
fof(f19,plain,
~ p(sK0),
inference(resolution,[],[f18,f16]) ).
fof(f20,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN935+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n007.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 17:11:40 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.71/1.15 % (2569356)Detected formulas, will run a generic FOF schedule.
% 2.71/1.15 % (2569365)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3569047645:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.15 % (2569365)First to succeed.
% 2.71/1.15 % (2569365)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2569356"
% 2.71/1.15 % (2569366)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=683353132:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.15 % (2569363)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=1708443297:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.15 % (2569362)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=359421095:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.15 % (2569361)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=2186182280:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.15 % (2569367)dis-21_1_sil=8000:lcm=predicate:random_seed=2675797409: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)
% 2.71/1.15 % (2569364)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2021903899:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.15 % (2569367)Also succeeded, but the first one will report.
% 2.71/1.15 % (2569366)Also succeeded, but the first one will report.
% 2.71/1.15 % (2569364)Also succeeded, but the first one will report.
% 2.71/1.15 % (2569365)Refutation found. Thanks to Tanya!
% 2.71/1.15 % SZS status Theorem for theBenchmark
% 2.71/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.15 % (2569365)------------------------------
% 2.71/1.15 % (2569365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.15 % (2569365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.15 % (2569365)CaDiCaL version: 2.1.3
% 2.71/1.15 % (2569365)Termination reason: Refutation
% 2.71/1.15 % (2569365)Time elapsed: 0.001 s
% 2.71/1.15 % (2569365)Peak memory usage: 88 MB
% 2.71/1.15 % (2569365)------------------------------
% 2.71/1.15 % (2569365)------------------------------
% 2.71/1.15 % (2569356)Success in time 0.29 s
% 2.71/1.15 % Vampire exiting
%------------------------------------------------------------------------------