%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN944+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:06:02 PM UTC 2026
% Result : Theorem 2.61s 1.05s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 88 ( 27 ~; 17 |; 35 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 62 ( 47 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( s(X0)
& s(X1)
& r(X1,X2)
& ! [X3] :
( s(X3)
=> p(X3) )
& ! [X3,X4] :
( r(X3,X4)
=> q(X3,X4) ) )
=> ? [X3,X4] :
( p(X3)
& q(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( s(X0)
& s(X1)
& r(X1,X2)
& ! [X3] :
( s(X3)
=> p(X3) )
& ! [X3,X4] :
( r(X3,X4)
=> q(X3,X4) ) )
=> ? [X3,X4] :
( p(X3)
& q(X3,X4) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ! [X0,X1,X2] :
( ( s(X0)
& s(X1)
& r(X1,X2)
& ! [X3] :
( s(X3)
=> p(X3) )
& ! [X4,X5] :
( r(X4,X5)
=> q(X4,X5) ) )
=> ? [X6,X7] :
( p(X6)
& q(X6,X7) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0,X1,X2] :
( ! [X6,X7] :
( ~ p(X6)
| ~ q(X6,X7) )
& s(X0)
& s(X1)
& r(X1,X2)
& ! [X3] :
( p(X3)
| ~ s(X3) )
& ! [X4,X5] :
( q(X4,X5)
| ~ r(X4,X5) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0,X1,X2] :
( ! [X6,X7] :
( ~ p(X6)
| ~ q(X6,X7) )
& s(X0)
& s(X1)
& r(X1,X2)
& ! [X3] :
( p(X3)
| ~ s(X3) )
& ! [X4,X5] :
( q(X4,X5)
| ~ r(X4,X5) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ p(X3)
| ~ q(X3,X4) )
& s(X0)
& s(X1)
& r(X1,X2)
& ! [X5] :
( p(X5)
| ~ s(X5) )
& ! [X6,X7] :
( q(X6,X7)
| ~ r(X6,X7) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X3,X4] :
( ~ p(X3)
| ~ q(X3,X4) )
& s(sK0)
& s(sK1)
& r(sK1,sK2)
& ! [X5] :
( p(X5)
| ~ s(X5) )
& ! [X6,X7] :
( q(X6,X7)
| ~ r(X6,X7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
fof(f8,plain,
! [X6,X7] :
( q(X6,X7)
| ~ r(X6,X7) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X5] :
( p(X5)
| ~ s(X5) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
r(sK1,sK2),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
s(sK1),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X3,X4] :
( ~ q(X3,X4)
| ~ p(X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1] :
( ~ p(X0)
| ~ r(X0,X1) ),
inference(resolution,[],[f8,f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ r(X0,X1)
| ~ s(X0) ),
inference(resolution,[],[f14,f9]) ).
fof(f16,plain,
~ s(sK1),
inference(resolution,[],[f15,f10]) ).
fof(f17,plain,
$false,
inference(resolution,[],[f16,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN944+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 17:18:18 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.61/1.05 % (4027907)Detected formulas, will run a generic FOF schedule.
% 2.61/1.05 % (4027918)dis-21_1_sil=8000:lcm=predicate:random_seed=889352519: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)
% 2.61/1.05 % (4027918)First to succeed.
% 2.61/1.05 % (4027918)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4027907"
% 2.61/1.05 % (4027914)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=396850822:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.61/1.05 % (4027912)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=2214154862:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.61/1.05 % (4027913)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=3605076439:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.61/1.05 % (4027915)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3024720798:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.61/1.05 % (4027915)Also succeeded, but the first one will report.
% 2.61/1.05 % (4027916)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1123728451:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.61/1.05 % (4027917)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3254179976:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.61/1.05 % (4027916)Also succeeded, but the first one will report.
% 2.61/1.05 % (4027917)Also succeeded, but the first one will report.
% 2.61/1.05 % (4027918)Refutation found. Thanks to Tanya!
% 2.61/1.05 % SZS status Theorem for theBenchmark
% 2.61/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.05 % (4027918)------------------------------
% 2.61/1.05 % (4027918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.05 % (4027918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.05 % (4027918)CaDiCaL version: 2.1.3
% 2.61/1.05 % (4027918)Termination reason: Refutation
% 2.61/1.05 % (4027918)Time elapsed: 0.001 s
% 2.61/1.05 % (4027918)Peak memory usage: 88 MB
% 2.61/1.05 % (4027918)------------------------------
% 2.61/1.05 % (4027918)------------------------------
% 2.61/1.05 % (4027907)Success in time 0.293 s
% 2.61/1.05 % Vampire exiting
%------------------------------------------------------------------------------