%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN360+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 2.68s 1.17s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 13 ~; 5 |; 11 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 51 ( 36 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0] :
( ? [X1] : big_p(X0,X1)
=> ! [X1] : big_q(X0,X1) )
& ! [X2] :
? [X1] : big_p(X2,X1) )
=> ! [X1,X0] : big_q(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2111) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
( ? [X1] : big_p(X0,X1)
=> ! [X1] : big_q(X0,X1) )
& ! [X2] :
? [X1] : big_p(X2,X1) )
=> ! [X1,X0] : big_q(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X0] :
( ? [X1] : big_p(X0,X1)
=> ! [X2] : big_q(X0,X2) )
& ! [X3] :
? [X4] : big_p(X3,X4) )
=> ! [X5,X6] : big_q(X6,X5) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X5,X6] : ~ big_q(X6,X5)
& ! [X0] :
( ! [X2] : big_q(X0,X2)
| ! [X1] : ~ big_p(X0,X1) )
& ! [X3] :
? [X4] : big_p(X3,X4) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X5,X6] : ~ big_q(X6,X5)
& ! [X0] :
( ! [X2] : big_q(X0,X2)
| ! [X1] : ~ big_p(X0,X1) )
& ! [X3] :
? [X4] : big_p(X3,X4) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ? [X0,X1] : ~ big_q(X1,X0)
& ! [X2] :
( ! [X3] : big_q(X2,X3)
| ! [X4] : ~ big_p(X2,X4) )
& ! [X5] :
? [X6] : big_p(X5,X6) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ~ big_q(sK1,sK0)
& ! [X2] :
( ! [X3] : big_q(X2,X3)
| ! [X4] : ~ big_p(X2,X4) )
& ! [X5] : big_p(X5,sK2(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X6,sK2(X5))],[f6]) ).
fof(f8,plain,
! [X5] : big_p(X5,sK2(X5)),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3,X4] :
( big_q(X2,X3)
| ~ big_p(X2,X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
~ big_q(sK1,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0] : ~ big_p(sK1,X0),
inference(resolution,[],[f9,f10]) ).
fof(f12,plain,
$false,
inference(resolution,[],[f11,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN360+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 15:49:02 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/1.17 % (2031837)Detected formulas, will run a generic FOF schedule.
% 2.68/1.17 % (2031917)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=671513406:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.17 % (2031917)First to succeed.
% 2.68/1.17 % (2031917)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2031837"
% 2.68/1.17 % (2031919)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1925946683:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.17 % (2031921)dis-21_1_sil=8000:lcm=predicate:random_seed=2297611908: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)
% 2.68/1.17 % (2031916)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2983476681:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.17 % (2031913)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=2574800842:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.17 % (2031914)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=1183246292:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.17 % (2031915)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=1001640574:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.17 % (2031921)Also succeeded, but the first one will report.
% 2.68/1.17 % (2031916)Also succeeded, but the first one will report.
% 2.68/1.17 % (2031919)Also succeeded, but the first one will report.
% 2.68/1.17 % (2031917)Refutation found. Thanks to Tanya!
% 2.68/1.17 % SZS status Theorem for theBenchmark
% 2.68/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.17 % (2031917)------------------------------
% 2.68/1.17 % (2031917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.17 % (2031917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.17 % (2031917)CaDiCaL version: 2.1.3
% 2.68/1.17 % (2031917)Termination reason: Refutation
% 2.68/1.17 % (2031917)Time elapsed: 0.001 s
% 2.68/1.17 % (2031917)Peak memory usage: 88 MB
% 2.68/1.17 % (2031917)------------------------------
% 2.68/1.17 % (2031917)------------------------------
% 2.68/1.17 % (2031837)Success in time 0.294 s
% 2.68/1.17 % Vampire exiting
%------------------------------------------------------------------------------