%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN361+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 01:50:22 PM UTC 2026
% Result : Theorem 2.23s 0.72s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 61 ( 24 ~; 10 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 54 ( 39 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ? [X0] :
! [X1] : big_p(X1,X0)
& ! [X1] :
( big_s(X1)
=> ? [X2] : big_q(X2,X1) )
& ! [X1,X2] :
( big_p(X1,X2)
=> ~ big_q(X1,X2) ) )
=> ? [X3] : ~ big_s(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2112) ).
fof(f2,negated_conjecture,
~ ( ( ? [X0] :
! [X1] : big_p(X1,X0)
& ! [X1] :
( big_s(X1)
=> ? [X2] : big_q(X2,X1) )
& ! [X1,X2] :
( big_p(X1,X2)
=> ~ big_q(X1,X2) ) )
=> ? [X3] : ~ big_s(X3) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ? [X0] :
! [X1] : big_p(X1,X0)
& ! [X2] :
( big_s(X2)
=> ? [X3] : big_q(X3,X2) )
& ! [X4,X5] :
( big_p(X4,X5)
=> ~ big_q(X4,X5) ) )
=> ? [X6] : ~ big_s(X6) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X6] : big_s(X6)
& ? [X0] :
! [X1] : big_p(X1,X0)
& ! [X2] :
( ? [X3] : big_q(X3,X2)
| ~ big_s(X2) )
& ! [X4,X5] :
( ~ big_q(X4,X5)
| ~ big_p(X4,X5) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X6] : big_s(X6)
& ? [X0] :
! [X1] : big_p(X1,X0)
& ! [X2] :
( ? [X3] : big_q(X3,X2)
| ~ big_s(X2) )
& ! [X4,X5] :
( ~ big_q(X4,X5)
| ~ big_p(X4,X5) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ! [X0] : big_s(X0)
& ? [X1] :
! [X2] : big_p(X2,X1)
& ! [X3] :
( ? [X4] : big_q(X4,X3)
| ~ big_s(X3) )
& ! [X5,X6] :
( ~ big_q(X5,X6)
| ~ big_p(X5,X6) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X0] : big_s(X0)
& ! [X2] : big_p(X2,sK0)
& ! [X3] :
( big_q(sK1(X3),X3)
| ~ big_s(X3) )
& ! [X5,X6] :
( ~ big_q(X5,X6)
| ~ big_p(X5,X6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X4,sK1(X3))],[f6]) ).
fof(f8,plain,
! [X6,X5] :
( ~ big_q(X5,X6)
| ~ big_p(X5,X6) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X3] :
( big_q(sK1(X3),X3)
| ~ big_s(X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2] : big_p(X2,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0] : big_s(X0),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X3] : big_q(sK1(X3),X3),
inference(forward_subsumption_resolution,[],[f9,f11]) ).
fof(f13,plain,
! [X0] : ~ big_p(sK1(X0),X0),
inference(resolution,[],[f12,f8]) ).
fof(f14,plain,
$false,
inference(resolution,[],[f13,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN361+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 15:48:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running first-order theorem proving
% 0.08/0.13 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
% 2.23/0.72 % (3473354)Detected formulas, will run a generic FOF schedule.
% 2.23/0.72 % (3473412)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=2501785221:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.23/0.72 % (3473410)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=2081923062:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.23/0.72 % (3473414)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=595800515:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.23/0.72 % (3473418)dis-21_1_sil=8000:lcm=predicate:random_seed=2043940520: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)
% 2.23/0.72 % (3473418)Also succeeded, but the first one will report.
% 2.23/0.72 % (3473414)First to succeed.
% 2.23/0.72 % (3473414)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3473354"
% 2.23/0.72 % (3473416)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=143923562:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.23/0.72 % (3473416)Also succeeded, but the first one will report.
% 2.23/0.72 % (3473409)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=4035056103:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.23/0.72 % (3473413)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=306541600:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.23/0.72 % (3473413)Also succeeded, but the first one will report.
% 2.23/0.72 % (3473414)Refutation found. Thanks to Tanya!
% 2.23/0.72 % SZS status Theorem for theBenchmark
% 2.23/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.23/0.72 % (3473414)------------------------------
% 2.23/0.72 % (3473414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/0.72 % (3473414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.72 % (3473414)CaDiCaL version: 2.1.3
% 2.23/0.72 % (3473414)Termination reason: Refutation
% 2.23/0.72 % (3473414)Time elapsed: 0.001 s
% 2.23/0.72 % (3473414)Peak memory usage: 87 MB
% 2.23/0.72 % (3473414)------------------------------
% 2.23/0.72 % (3473414)------------------------------
% 2.23/0.72 % (3473354)Success in time 0.278 s
% 2.23/0.72 % Vampire exiting
%------------------------------------------------------------------------------