%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 02:01:21 PM UTC 2026
% Result : Theorem 3.66s 1.28s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 143 ( 43 ~; 53 |; 35 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 133 ( 121 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( ! [X0,X1,X2] :
( ( p(X0,X1)
& p(X1,X2) )
=> p(X0,X2) )
& ! [X0,X1,X2] :
( ( q(X0,X1)
& q(X1,X2) )
=> q(X0,X2) )
& ! [X0,X1] :
( q(X0,X1)
=> q(X1,X0) )
& ! [X0,X1] :
( p(X0,X1)
| q(X0,X1) ) )
=> ! [X0,X1] : p(X0,X1) )
| ! [X0,X1] : q(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm400) ).
fof(f2,negated_conjecture,
~ ( ( ( ! [X0,X1,X2] :
( ( p(X0,X1)
& p(X1,X2) )
=> p(X0,X2) )
& ! [X0,X1,X2] :
( ( q(X0,X1)
& q(X1,X2) )
=> q(X0,X2) )
& ! [X0,X1] :
( q(X0,X1)
=> q(X1,X0) )
& ! [X0,X1] :
( p(X0,X1)
| q(X0,X1) ) )
=> ! [X0,X1] : p(X0,X1) )
| ! [X0,X1] : q(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ( ! [X0,X1,X2] :
( ( p(X0,X1)
& p(X1,X2) )
=> p(X0,X2) )
& ! [X3,X4,X5] :
( ( q(X3,X4)
& q(X4,X5) )
=> q(X3,X5) )
& ! [X6,X7] :
( q(X6,X7)
=> q(X7,X6) )
& ! [X8,X9] :
( p(X8,X9)
| q(X8,X9) ) )
=> ! [X10,X11] : p(X10,X11) )
| ! [X12,X13] : q(X12,X13) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X10,X11] : ~ p(X10,X11)
& ! [X0,X1,X2] :
( p(X0,X2)
| ~ p(X0,X1)
| ~ p(X1,X2) )
& ! [X3,X4,X5] :
( q(X3,X5)
| ~ q(X3,X4)
| ~ q(X4,X5) )
& ! [X6,X7] :
( q(X7,X6)
| ~ q(X6,X7) )
& ! [X8,X9] :
( p(X8,X9)
| q(X8,X9) )
& ? [X12,X13] : ~ q(X12,X13) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X10,X11] : ~ p(X10,X11)
& ! [X0,X1,X2] :
( p(X0,X2)
| ~ p(X0,X1)
| ~ p(X1,X2) )
& ! [X3,X4,X5] :
( q(X3,X5)
| ~ q(X3,X4)
| ~ q(X4,X5) )
& ! [X6,X7] :
( q(X7,X6)
| ~ q(X6,X7) )
& ! [X8,X9] :
( p(X8,X9)
| q(X8,X9) )
& ? [X12,X13] : ~ q(X12,X13) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ? [X0,X1] : ~ p(X0,X1)
& ! [X2,X3,X4] :
( p(X2,X4)
| ~ p(X2,X3)
| ~ p(X3,X4) )
& ! [X5,X6,X7] :
( q(X5,X7)
| ~ q(X5,X6)
| ~ q(X6,X7) )
& ! [X8,X9] :
( q(X9,X8)
| ~ q(X8,X9) )
& ! [X10,X11] :
( p(X10,X11)
| q(X10,X11) )
& ? [X12,X13] : ~ q(X12,X13) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ~ p(sK0,sK1)
& ! [X2,X3,X4] :
( p(X2,X4)
| ~ p(X2,X3)
| ~ p(X3,X4) )
& ! [X5,X6,X7] :
( q(X5,X7)
| ~ q(X5,X6)
| ~ q(X6,X7) )
& ! [X8,X9] :
( q(X9,X8)
| ~ q(X8,X9) )
& ! [X10,X11] :
( p(X10,X11)
| q(X10,X11) )
& ~ q(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X12,sK2),skolemize(X13,sK3)],[f6]) ).
fof(f8,plain,
~ q(sK2,sK3),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X10,X11] :
( q(X10,X11)
| p(X10,X11) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X8,X9] :
( ~ q(X8,X9)
| q(X9,X8) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X6,X7,X5] :
( ~ q(X6,X7)
| ~ q(X5,X6)
| q(X5,X7) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X3,X4] :
( ~ p(X3,X4)
| ~ p(X2,X3)
| p(X2,X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
~ p(sK0,sK1),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
p(sK2,sK3),
inference(resolution,[],[f9,f8]) ).
fof(f15,plain,
! [X0,X1] :
( q(X0,X1)
| p(X1,X0) ),
inference(resolution,[],[f10,f9]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ q(X0,X1)
| q(X0,X2)
| p(X1,X2) ),
inference(resolution,[],[f11,f9]) ).
fof(f17,plain,
p(sK3,sK2),
inference(resolution,[],[f15,f8]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ q(X2,X1)
| p(X0,X1)
| q(X2,X0) ),
inference(resolution,[],[f15,f11]) ).
fof(f20,plain,
! [X0] :
( ~ p(X0,sK2)
| p(X0,sK3) ),
inference(resolution,[],[f12,f14]) ).
fof(f21,plain,
! [X0] :
( ~ p(X0,sK3)
| p(X0,sK2) ),
inference(resolution,[],[f17,f12]) ).
fof(f22,plain,
! [X2,X0,X1] :
( q(X0,X1)
| p(X2,X1)
| p(X2,X0) ),
inference(resolution,[],[f16,f15]) ).
fof(f26,plain,
! [X2,X0,X1] :
( q(X2,X0)
| p(X0,X1)
| p(X2,X1) ),
inference(resolution,[],[f18,f9]) ).
fof(f28,plain,
! [X0] :
( p(X0,sK3)
| p(X0,sK2) ),
inference(resolution,[],[f22,f8]) ).
fof(f33,plain,
! [X0] : p(X0,sK3),
inference(forward_subsumption_resolution,[],[f28,f20]) ).
fof(f42,plain,
! [X0] : p(X0,sK2),
inference(resolution,[],[f21,f33]) ).
fof(f50,plain,
! [X0] :
( p(sK3,X0)
| p(sK2,X0) ),
inference(resolution,[],[f26,f8]) ).
fof(f55,plain,
! [X0,X1] :
( p(sK2,X0)
| ~ p(X1,sK3)
| p(X1,X0) ),
inference(resolution,[],[f50,f12]) ).
fof(f58,plain,
! [X0,X1] :
( p(sK2,X0)
| p(X1,X0) ),
inference(forward_subsumption_resolution,[],[f55,f33]) ).
fof(f67,plain,
! [X0] : p(sK2,X0),
inference(factoring,[],[f58]) ).
fof(f74,plain,
! [X0,X1] :
( ~ p(X0,sK2)
| p(X0,X1) ),
inference(resolution,[],[f67,f12]) ).
fof(f77,plain,
! [X0,X1] : p(X0,X1),
inference(forward_subsumption_resolution,[],[f74,f42]) ).
fof(f86,plain,
$false,
inference(resolution,[],[f77,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 16:52:07 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.66/1.28 % (509970)Detected formulas, will run a generic FOF schedule.
% 3.66/1.28 % (509977)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=1194721144:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.28 % (509975)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=2194340812:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.28 % (509981)dis-21_1_sil=8000:lcm=predicate:random_seed=739891459: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)
% 3.66/1.28 % (509979)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2945094383:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.28 % (509980)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2845420804:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.28 % (509976)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=90768229:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.28 % (509978)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3974510474:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.28 % (509978)First to succeed.
% 3.66/1.28 % (509978)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-509970"
% 3.66/1.28 % (509981)Also succeeded, but the first one will report.
% 3.66/1.28 % (509980)Also succeeded, but the first one will report.
% 3.66/1.28 % (509979)Also succeeded, but the first one will report.
% 3.66/1.28 % (509978)Refutation found. Thanks to Tanya!
% 3.66/1.28 % SZS status Theorem for theBenchmark
% 3.66/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.28 % (509978)------------------------------
% 3.66/1.28 % (509978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.28 % (509978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.28 % (509978)CaDiCaL version: 2.1.3
% 3.66/1.28 % (509978)Termination reason: Refutation
% 3.66/1.28 % (509978)Time elapsed: 0.003 s
% 3.66/1.28 % (509978)Peak memory usage: 88 MB
% 3.66/1.28 % (509978)Instructions burned: 3 (million)
% 3.66/1.28 % (509978)------------------------------
% 3.66/1.28 % (509978)------------------------------
% 3.66/1.28 % (509970)Success in time 0.435 s
% 3.66/1.28 % Vampire exiting
%------------------------------------------------------------------------------