%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN986+1.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 02:23:01 PM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 37 ( 18 ~; 13 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 39 ( 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r(X0,zero,succ(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN002+0.ax',hyp1) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( r(X0,X1,X2)
=> ( r(X2,X1,X3)
=> r(X0,succ(X1),X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN002+0.ax',hyp2) ).
fof(f3,conjecture,
? [X0,X1,X2] :
( r(zero,zero,X0)
& r(zero,X0,X1)
& r(zero,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).
fof(f4,negated_conjecture,
~ ? [X0,X1,X2] :
( r(zero,zero,X0)
& r(zero,X0,X1)
& r(zero,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2,X3] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( ~ r(zero,zero,X0)
| ~ r(zero,X0,X1)
| ~ r(zero,X1,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f8,plain,
! [X0] : r(X0,zero,succ(X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( ~ r(X2,X1,X3)
| r(X0,succ(X1),X3)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X0,X1] :
( ~ r(zero,zero,X0)
| ~ r(zero,X0,X1)
| ~ r(zero,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( ~ r(zero,succ(zero),X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[],[f8,f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ r(X0,zero,X1)
| r(X0,succ(zero),succ(X1)) ),
inference(resolution,[],[f9,f8]) ).
fof(f13,plain,
! [X0] : r(X0,succ(zero),succ(succ(X0))),
inference(resolution,[],[f12,f8]) ).
fof(f14,plain,
! [X0] : ~ r(zero,succ(succ(zero)),X0),
inference(resolution,[],[f13,f11]) ).
fof(f15,plain,
! [X0,X1] :
( ~ r(X0,succ(zero),X1)
| r(X0,succ(succ(zero)),succ(succ(X1))) ),
inference(resolution,[],[f13,f9]) ).
fof(f16,plain,
! [X0] : r(X0,succ(succ(zero)),succ(succ(succ(succ(X0))))),
inference(resolution,[],[f15,f13]) ).
fof(f17,plain,
$false,
inference(resolution,[],[f16,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 17:19:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 % (4171707)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (4171717)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=941247774:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.09/0.25 % (4171717) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4171707-4171717"...
% 0.09/0.25 % (4171717)...printing done.
% 0.09/0.25 % (4171717)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (4171717)------------------------------
% 0.09/0.25 % (4171717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (4171717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (4171717)CaDiCaL version: 2.1.3
% 0.09/0.25 % (4171717)Termination reason: Refutation
% 0.09/0.25 % (4171717)Time elapsed: 0.001 s
% 0.09/0.25 % (4171717)Peak memory usage: 11 MB
% 0.09/0.25 % (4171717)Instructions burned: 1 (million)
% 0.09/0.25 % (4171707)Success in time 0.015 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------