%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN374+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 : n012.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 01:50:24 PM UTC 2026
% Result : Theorem 2.31s 0.73s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 3 unt; 0 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 189 ( 80 ~; 82 |; 15 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 99 ( 79 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2125) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<~> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ( ( ? [X3] : ~ big_p(X3)
| ! [X2] : ~ big_p(X2) )
& ( ! [X3] : big_p(X3)
| ? [X2] : big_p(X2) ) )
| ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) ) )
& ( ( ( ? [X2] : big_p(X2)
| ? [X3] : ~ big_p(X3) )
& ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_p(X2) ) )
| ? [X0] :
! [X1] :
( ( big_p(X0)
| ~ big_p(X1) )
& ( big_p(X1)
| ~ big_p(X0) ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ( ( ? [X0] : ~ big_p(X0)
| ! [X1] : ~ big_p(X1) )
& ( ! [X2] : big_p(X2)
| ? [X3] : big_p(X3) ) )
| ! [X4] :
? [X5] :
( ( ~ big_p(X5)
| ~ big_p(X4) )
& ( big_p(X5)
| big_p(X4) ) ) )
& ( ( ( ? [X6] : big_p(X6)
| ? [X7] : ~ big_p(X7) )
& ( ! [X8] : big_p(X8)
| ! [X9] : ~ big_p(X9) ) )
| ? [X10] :
! [X11] :
( ( big_p(X10)
| ~ big_p(X11) )
& ( big_p(X11)
| ~ big_p(X10) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ( ( ~ big_p(sK0)
| ! [X1] : ~ big_p(X1) )
& ( ! [X2] : big_p(X2)
| big_p(sK1) ) )
| ! [X4] :
( ( ~ big_p(sK2(X4))
| ~ big_p(X4) )
& ( big_p(sK2(X4))
| big_p(X4) ) ) )
& ( ( ( big_p(sK3)
| ~ big_p(sK4) )
& ( ! [X8] : big_p(X8)
| ! [X9] : ~ big_p(X9) ) )
| ! [X11] :
( ( big_p(sK5)
| ~ big_p(X11) )
& ( big_p(X11)
| ~ big_p(sK5) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X5,sK2(X4)),skolemize(X6,sK3),skolemize(X7,sK4),skolemize(X10,sK5)],[f6]) ).
fof(f8,plain,
! [X11,X8,X9] :
( big_p(X11)
| ~ big_p(X9)
| big_p(X8)
| ~ big_p(sK5) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X11,X8,X9] :
( big_p(sK5)
| ~ big_p(X9)
| big_p(X8)
| ~ big_p(X11) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X4] :
( big_p(sK2(X4))
| big_p(sK1)
| big_p(X2)
| big_p(X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X1,X4] :
( ~ big_p(sK2(X4))
| ~ big_p(X1)
| ~ big_p(sK0)
| ~ big_p(X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0] :
( ~ big_p(sK2(X0))
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(factoring,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ big_p(sK0)
| ~ big_p(X0)
| ~ big_p(X1)
| big_p(X2)
| ~ big_p(sK5) ),
inference(resolution,[],[f24,f8]) ).
fof(f31,plain,
! [X2,X0,X1] :
( big_p(X2)
| ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(sK0) ),
inference(forward_subsumption_resolution,[],[f29,f9]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(sK0)
| ~ big_p(sK0)
| ~ big_p(X2) ),
inference(resolution,[],[f31,f24]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(sK0)
| ~ big_p(X2) ),
inference(duplicate_literal_removal,[],[f32]) ).
fof(f39,plain,
! [X2,X1] :
( ~ big_p(sK0)
| ~ big_p(X1)
| ~ big_p(X2) ),
inference(forward_subsumption_resolution,[],[f36,f31]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(X2)
| big_p(X3)
| ~ big_p(sK5) ),
inference(resolution,[],[f39,f8]) ).
fof(f43,plain,
! [X0] :
( ~ big_p(sK0)
| ~ big_p(X0) ),
inference(factoring,[],[f39]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( big_p(X3)
| ~ big_p(X1)
| ~ big_p(X2)
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[],[f42,f9]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| big_p(X2)
| ~ big_p(sK5) ),
inference(resolution,[],[f43,f8]) ).
fof(f50,plain,
! [X2,X0,X1] :
( big_p(X2)
| ~ big_p(X1)
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[],[f48,f9]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(X2)
| ~ big_p(X3) ),
inference(resolution,[],[f45,f43]) ).
fof(f60,plain,
! [X2,X3,X1] :
( ~ big_p(X1)
| ~ big_p(X2)
| ~ big_p(X3) ),
inference(forward_subsumption_resolution,[],[f57,f45]) ).
fof(f73,plain,
! [X2,X3] :
( ~ big_p(X3)
| ~ big_p(X2) ),
inference(forward_subsumption_resolution,[],[f60,f50]) ).
fof(f81,plain,
! [X0] : ~ big_p(X0),
inference(factoring,[],[f73]) ).
fof(f94,plain,
! [X0,X1] :
( big_p(sK1)
| big_p(X0)
| big_p(X1) ),
inference(resolution,[],[f81,f12]) ).
fof(f95,plain,
! [X0] :
( big_p(sK1)
| big_p(X0) ),
inference(forward_subsumption_resolution,[],[f94,f81]) ).
fof(f99,plain,
big_p(sK1),
inference(forward_subsumption_resolution,[],[f95,f81]) ).
fof(f100,plain,
$false,
inference(forward_subsumption_resolution,[],[f99,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Mon Sep 28 15:50:06 UTC 2026
% 0.09/0.12 % CPUTime :
% 0.09/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 Running first-order theorem proving
% 0.09/0.14 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
% 2.31/0.73 % (3476760)Detected formulas, will run a generic FOF schedule.
% 2.31/0.73 % (3476813)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=283113211:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.31/0.73 % (3476811)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=1342465565:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.31/0.73 % (3476810)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=1153124301:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.31/0.73 % (3476818)dis-21_1_sil=8000:lcm=predicate:random_seed=2220038713:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.31/0.73 % (3476809)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=2285443113:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.31/0.73 % (3476815)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3200136065:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.31/0.73 % (3476817)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=103305854:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.31/0.73 % (3476815)First to succeed.
% 2.31/0.73 % (3476817)Also succeeded, but the first one will report.
% 2.31/0.73 % (3476813)Also succeeded, but the first one will report.
% 2.31/0.73 % (3476818)Also succeeded, but the first one will report.
% 2.31/0.73 % (3476815)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3476760"
% 2.31/0.73 % (3476815)Refutation found. Thanks to Tanya!
% 2.31/0.73 % SZS status Theorem for theBenchmark
% 2.31/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.73 % (3476815)------------------------------
% 2.31/0.73 % (3476815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.73 % (3476815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.73 % (3476815)CaDiCaL version: 2.1.3
% 2.31/0.73 % (3476815)Termination reason: Refutation
% 2.31/0.73 % (3476815)Time elapsed: 0.001 s
% 2.31/0.73 % (3476815)Peak memory usage: 88 MB
% 2.31/0.73 % (3476815)Instructions burned: 2 (million)
% 2.31/0.73 % (3476815)------------------------------
% 2.31/0.73 % (3476815)------------------------------
% 2.31/0.73 % (3476760)Success in time 0.287 s
% 2.31/0.73 % Vampire exiting
%------------------------------------------------------------------------------