%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN375+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 : n013.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 01:50:25 PM UTC 2026
% Result : Theorem 2.59s 1.16s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 164 ( 67 ~; 70 |; 15 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 89 ( 67 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<=> ( ! [X0] : big_p(X0)
<=> ? [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2126) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<=> ( ! [X0] : big_p(X0)
<=> ? [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<=> ( ! [X2] : big_p(X2)
<=> ? [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(X0)
<=> ? [X1] : 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) )
& ( ? [X1] : big_p(X1)
| big_p(X0) ) ) )
& ( ( ( ! [X2] : big_p(X2)
| ! [X3] : ~ big_p(X3) )
& ( ? [X3] : big_p(X3)
| ? [X2] : ~ big_p(X2) ) )
| ! [X0] :
( ( big_p(X0)
| ! [X1] : ~ big_p(X1) )
& ( ? [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) )
& ( ? [X6] : big_p(X6)
| big_p(X4) ) ) )
& ( ( ( ! [X7] : big_p(X7)
| ! [X8] : ~ big_p(X8) )
& ( ? [X9] : big_p(X9)
| ? [X10] : ~ big_p(X10) ) )
| ! [X11] :
( ( big_p(X11)
| ! [X12] : ~ big_p(X12) )
& ( ? [X13] : big_p(X13)
| ~ big_p(X11) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ( ( ! [X0] : ~ big_p(X0)
| ~ big_p(sK0) )
& ( big_p(sK1)
| ! [X3] : big_p(X3) ) )
| ( ( ! [X5] : ~ big_p(X5)
| ~ big_p(sK2) )
& ( big_p(sK3)
| big_p(sK2) ) ) )
& ( ( ( ! [X7] : big_p(X7)
| ! [X8] : ~ big_p(X8) )
& ( big_p(sK4)
| ~ big_p(sK5) ) )
| ! [X11] :
( ( big_p(X11)
| ! [X12] : ~ big_p(X12) )
& ( big_p(sK6)
| ~ big_p(X11) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(X4,sK2),skolemize(X6,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6)],[f6]) ).
fof(f11,plain,
! [X11,X8,X7,X12] :
( big_p(X11)
| ~ big_p(X8)
| big_p(X7)
| ~ big_p(X12) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X3] :
( big_p(sK3)
| big_p(X3)
| big_p(sK1)
| big_p(sK2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X5] :
( ~ big_p(sK2)
| ~ big_p(sK0)
| ~ big_p(X5)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X2,X3,X0,X1,X4] :
( ~ big_p(sK0)
| ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(X2)
| big_p(X3)
| ~ big_p(X4) ),
inference(resolution,[],[f15,f11]) ).
fof(f17,plain,
! [X0] :
( ~ big_p(sK2)
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(factoring,[],[f15]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( ~ big_p(sK0)
| ~ big_p(X0)
| ~ big_p(X1)
| ~ big_p(X2)
| big_p(X3) ),
inference(forward_subsumption_resolution,[],[f16,f11]) ).
fof(f20,plain,
! [X3,X0,X1] :
( ~ big_p(sK0)
| ~ big_p(X0)
| ~ big_p(X1)
| big_p(X3) ),
inference(forward_subsumption_resolution,[],[f19,f11]) ).
fof(f21,plain,
! [X3,X0] :
( big_p(X3)
| ~ big_p(X0)
| ~ big_p(sK0) ),
inference(forward_subsumption_resolution,[],[f20,f11]) ).
fof(f29,plain,
! [X0,X1] :
( ~ big_p(X0)
| ~ big_p(sK0)
| ~ big_p(sK0)
| ~ big_p(X1) ),
inference(resolution,[],[f21,f17]) ).
fof(f32,plain,
! [X0,X1] :
( ~ big_p(X0)
| ~ big_p(sK0)
| ~ big_p(X1) ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f35,plain,
! [X1] :
( ~ big_p(sK0)
| ~ big_p(X1) ),
inference(forward_subsumption_resolution,[],[f32,f21]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| big_p(X2)
| ~ big_p(X3) ),
inference(resolution,[],[f35,f11]) ).
fof(f39,plain,
~ big_p(sK0),
inference(factoring,[],[f35]) ).
fof(f40,plain,
! [X2,X0,X1] :
( big_p(X2)
| ~ big_p(X1)
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[],[f38,f11]) ).
fof(f46,plain,
! [X0,X1] :
( ~ big_p(X1)
| ~ big_p(X0) ),
inference(resolution,[],[f40,f39]) ).
fof(f56,plain,
! [X0] : ~ big_p(X0),
inference(factoring,[],[f46]) ).
fof(f67,plain,
! [X0] :
( big_p(X0)
| big_p(sK1)
| big_p(sK2) ),
inference(resolution,[],[f56,f12]) ).
fof(f74,plain,
( big_p(sK1)
| big_p(sK2) ),
inference(forward_subsumption_resolution,[],[f67,f56]) ).
fof(f76,plain,
big_p(sK1),
inference(forward_subsumption_resolution,[],[f74,f56]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f76,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:50:07 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
% 0.09/0.24 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
% 2.59/1.16 % (1294108)Detected formulas, will run a generic FOF schedule.
% 2.59/1.16 % (1294117)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3459634987:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.16 % (1294117)First to succeed.
% 2.59/1.16 % (1294117)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1294108"
% 2.59/1.16 % (1294118)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=381188298:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.16 % (1294116)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2924632:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.16 % (1294115)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=4124043945:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.16 % (1294114)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=233263011:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.16 % (1294113)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=103693716:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.16 % (1294119)dis-21_1_sil=8000:lcm=predicate:random_seed=18849520: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)
% 2.59/1.16 % (1294119)Also succeeded, but the first one will report.
% 2.59/1.16 % (1294118)Also succeeded, but the first one will report.
% 2.59/1.16 % (1294116)Also succeeded, but the first one will report.
% 2.59/1.16 % (1294117)Refutation found. Thanks to Tanya!
% 2.59/1.16 % SZS status Theorem for theBenchmark
% 2.59/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.16 % (1294117)------------------------------
% 2.59/1.16 % (1294117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.16 % (1294117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.16 % (1294117)CaDiCaL version: 2.1.3
% 2.59/1.16 % (1294117)Termination reason: Refutation
% 2.59/1.16 % (1294117)Time elapsed: 0.001 s
% 2.59/1.16 % (1294117)Peak memory usage: 88 MB
% 2.59/1.16 % (1294117)Instructions burned: 2 (million)
% 2.59/1.16 % (1294117)------------------------------
% 2.59/1.16 % (1294117)------------------------------
% 2.59/1.16 % (1294108)Success in time 0.279 s
% 2.59/1.16 % Vampire exiting
%------------------------------------------------------------------------------