%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN730+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:01:22 PM UTC 2026
% Result : Theorem 2.72s 1.17s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 13 ( 4 ~; 5 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 14 ( 9 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
! [X1] :
? [X2] :
( ( p(a,X1,h(X1))
| p(X0,X1,k(X1)) )
=> p(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm75) ).
fof(f2,negated_conjecture,
~ ? [X0] :
! [X1] :
? [X2] :
( ( p(a,X1,h(X1))
| p(X0,X1,k(X1)) )
=> p(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0] :
? [X1] :
! [X2] :
( ~ p(X0,X1,X2)
& ( p(a,X1,h(X1))
| p(X0,X1,k(X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X2] :
( ~ p(X0,sK0(X0),X2)
& ( p(a,sK0(X0),h(sK0(X0)))
| p(X0,sK0(X0),k(sK0(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f3]) ).
fof(f5,plain,
! [X0] :
( p(a,sK0(X0),h(sK0(X0)))
| p(X0,sK0(X0),k(sK0(X0))) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X2,X0] : ~ p(X0,sK0(X0),X2),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
p(a,sK0(a),k(sK0(a))),
inference(resolution,[],[f5,f6]) ).
fof(f8,plain,
$false,
inference(forward_subsumption_resolution,[],[f7,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN730+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 16:45:36 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.72/1.17 % (3701875)Detected formulas, will run a generic FOF schedule.
% 2.72/1.17 % (3701932)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3699233342:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.17 % (3701932)First to succeed.
% 2.72/1.17 % (3701932)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3701875"
% 2.72/1.17 % (3701931)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=3213390291:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.17 % (3701929)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=2473443600:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.17 % (3701928)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=452299472:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.17 % (3701934)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2644920559:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.17 % (3701934)Also succeeded, but the first one will report.
% 2.72/1.17 % (3701938)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1013168454:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.17 % (3701938)Also succeeded, but the first one will report.
% 2.72/1.17 % (3701939)dis-21_1_sil=8000:lcm=predicate:random_seed=1452961302: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)
% 2.72/1.17 % (3701939)Also succeeded, but the first one will report.
% 2.72/1.17 % (3701932)Refutation found. Thanks to Tanya!
% 2.72/1.17 % SZS status Theorem for theBenchmark
% 2.72/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.17 % (3701932)------------------------------
% 2.72/1.17 % (3701932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.17 % (3701932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.17 % (3701932)CaDiCaL version: 2.1.3
% 2.72/1.17 % (3701932)Termination reason: Refutation
% 2.72/1.17 % (3701932)Time elapsed: 0.001 s
% 2.72/1.17 % (3701932)Peak memory usage: 88 MB
% 2.72/1.17 % (3701932)------------------------------
% 2.72/1.17 % (3701932)------------------------------
% 2.72/1.17 % (3701875)Success in time 0.294 s
% 2.72/1.17 % Vampire exiting
%------------------------------------------------------------------------------