%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN386+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 : n008.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 01:50:27 PM UTC 2026
% Result : Theorem 0.20s 1.15s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 107 ( 34 ~; 26 |; 29 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 138 ( 99 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0] :
? [X1] : big_f(X0,X1)
& ? [X0] :
! [X2] :
? [X3] :
! [X4] :
( big_s(X3,X4)
=> big_d(X4,X0,X2) )
& ! [X2] :
? [X5] :
! [X6,X7] :
( big_d(X6,X7,X5)
=> ! [X1,X8] :
( ( big_f(X6,X1)
& big_f(X7,X8) )
=> big_d(X1,X8,X2) ) ) )
=> ? [X1] :
! [X2] :
? [X9] :
! [X4] :
( big_s(X9,X4)
=> ! [X8] :
( big_f(X4,X8)
=> big_d(X8,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2138) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
? [X1] : big_f(X0,X1)
& ? [X0] :
! [X2] :
? [X3] :
! [X4] :
( big_s(X3,X4)
=> big_d(X4,X0,X2) )
& ! [X2] :
? [X5] :
! [X6,X7] :
( big_d(X6,X7,X5)
=> ! [X1,X8] :
( ( big_f(X6,X1)
& big_f(X7,X8) )
=> big_d(X1,X8,X2) ) ) )
=> ? [X1] :
! [X2] :
? [X9] :
! [X4] :
( big_s(X9,X4)
=> ! [X8] :
( big_f(X4,X8)
=> big_d(X8,X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X0] :
? [X1] : big_f(X0,X1)
& ? [X2] :
! [X3] :
? [X4] :
! [X5] :
( big_s(X4,X5)
=> big_d(X5,X2,X3) )
& ! [X6] :
? [X7] :
! [X8,X9] :
( big_d(X8,X9,X7)
=> ! [X10,X11] :
( ( big_f(X8,X10)
& big_f(X9,X11) )
=> big_d(X10,X11,X6) ) ) )
=> ? [X12] :
! [X13] :
? [X14] :
! [X15] :
( big_s(X14,X15)
=> ! [X16] :
( big_f(X15,X16)
=> big_d(X16,X12,X13) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X12] :
? [X13] :
! [X14] :
? [X15] :
( ? [X16] :
( ~ big_d(X16,X12,X13)
& big_f(X15,X16) )
& big_s(X14,X15) )
& ! [X0] :
? [X1] : big_f(X0,X1)
& ? [X2] :
! [X3] :
? [X4] :
! [X5] :
( big_d(X5,X2,X3)
| ~ big_s(X4,X5) )
& ! [X6] :
? [X7] :
! [X8,X9] :
( ! [X10,X11] :
( big_d(X10,X11,X6)
| ~ big_f(X8,X10)
| ~ big_f(X9,X11) )
| ~ big_d(X8,X9,X7) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X12] :
? [X13] :
! [X14] :
? [X15] :
( ? [X16] :
( ~ big_d(X16,X12,X13)
& big_f(X15,X16) )
& big_s(X14,X15) )
& ! [X0] :
? [X1] : big_f(X0,X1)
& ? [X2] :
! [X3] :
? [X4] :
! [X5] :
( big_d(X5,X2,X3)
| ~ big_s(X4,X5) )
& ! [X6] :
? [X7] :
! [X8,X9] :
( ! [X10,X11] :
( big_d(X10,X11,X6)
| ~ big_f(X8,X10)
| ~ big_f(X9,X11) )
| ~ big_d(X8,X9,X7) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ? [X4] :
( ~ big_d(X4,X0,X1)
& big_f(X3,X4) )
& big_s(X2,X3) )
& ! [X5] :
? [X6] : big_f(X5,X6)
& ? [X7] :
! [X8] :
? [X9] :
! [X10] :
( big_d(X10,X7,X8)
| ~ big_s(X9,X10) )
& ! [X11] :
? [X12] :
! [X13,X14] :
( ! [X15,X16] :
( big_d(X15,X16,X11)
| ~ big_f(X13,X15)
| ~ big_f(X14,X16) )
| ~ big_d(X13,X14,X12) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X0,X2] :
( ~ big_d(sK2(X0,X2),X0,sK0(X0))
& big_f(sK1(X0,X2),sK2(X0,X2))
& big_s(X2,sK1(X0,X2)) )
& ! [X5] : big_f(X5,sK3(X5))
& ! [X8,X10] :
( big_d(X10,sK4,X8)
| ~ big_s(sK5(X8),X10) )
& ! [X11,X13,X14] :
( ! [X15,X16] :
( big_d(X15,X16,X11)
| ~ big_f(X13,X15)
| ~ big_f(X14,X16) )
| ~ big_d(X13,X14,sK6(X11)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X0,X2)),skolemize(X4,sK2(X0,X2)),skolemize(X6,sK3(X5)),skolemize(X7,sK4),skolemize(X9,sK5(X8)),skolemize(X12,sK6(X11))],[f6]) ).
fof(f8,plain,
! [X11,X16,X14,X15,X13] :
( ~ big_d(X13,X14,sK6(X11))
| ~ big_f(X13,X15)
| ~ big_f(X14,X16)
| big_d(X15,X16,X11) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X10,X8] :
( big_d(X10,sK4,X8)
| ~ big_s(sK5(X8),X10) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X5] : big_f(X5,sK3(X5)),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X0] : big_s(X2,sK1(X0,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X0] : big_f(sK1(X0,X2),sK2(X0,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X0] : ~ big_d(sK2(X0,X2),X0,sK0(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ big_s(sK5(sK6(X3)),X0)
| ~ big_f(sK4,X2)
| big_d(X1,X2,X3)
| ~ big_f(X0,X1) ),
inference(resolution,[],[f8,f9]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( ~ big_f(sK1(X3,sK5(sK6(X2))),X1)
| big_d(X1,X0,X2)
| ~ big_f(sK4,X0) ),
inference(resolution,[],[f15,f11]) ).
fof(f17,plain,
! [X2,X0,X1] :
( big_d(sK2(X0,sK5(sK6(X1))),X2,X1)
| ~ big_f(sK4,X2) ),
inference(resolution,[],[f16,f12]) ).
fof(f19,plain,
! [X0] : ~ big_f(sK4,X0),
inference(resolution,[],[f17,f13]) ).
fof(f21,plain,
$false,
inference(resolution,[],[f19,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN386+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:53:38 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.20/1.15 % (2364416)Detected formulas, will run a generic FOF schedule.
% 0.20/1.15 % (2364425)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3291667770:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.15 % (2364425)First to succeed.
% 0.20/1.15 % (2364425)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2364416"
% 0.20/1.15 % (2364424)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3878097779:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.15 % (2364421)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=1243095492:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.15 % (2364422)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=1306985996:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.15 % (2364423)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=1726988010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.15 % (2364424)Also succeeded, but the first one will report.
% 0.20/1.15 % (2364426)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4138701603:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.15 % (2364427)dis-21_1_sil=8000:lcm=predicate:random_seed=3694671883: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)
% 0.20/1.15 % (2364427)Also succeeded, but the first one will report.
% 0.20/1.15 % (2364426)Also succeeded, but the first one will report.
% 0.20/1.15 % (2364425)Refutation found. Thanks to Tanya!
% 0.20/1.15 % SZS status Theorem for theBenchmark
% 0.20/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.15 % (2364425)------------------------------
% 0.20/1.15 % (2364425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.15 % (2364425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.15 % (2364425)CaDiCaL version: 2.1.3
% 0.20/1.15 % (2364425)Termination reason: Refutation
% 0.20/1.15 % (2364425)Time elapsed: 0.001 s
% 0.20/1.15 % (2364425)Peak memory usage: 88 MB
% 0.20/1.15 % (2364425)Instructions burned: 1 (million)
% 0.20/1.15 % (2364425)------------------------------
% 0.20/1.15 % (2364425)------------------------------
% 0.20/1.15 % (2364416)Success in time 0.29 s
% 0.20/1.15 % Vampire exiting
%------------------------------------------------------------------------------