%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN722+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 02:17:58 PM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 10 unt; 5 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 131 ( 59 ~; 56 |; 11 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ( ! [X0] :
( ( p(X0)
| r(X0) )
& q(X0) )
& ! [X1] :
? [X2] :
( p(X1)
| ~ q(X1)
| ~ q(X2)
| ~ q(c)
| ~ q(d) )
& ( ~ p(a)
| ~ p(b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm119) ).
fof(f2,negated_conjecture,
~ ~ ( ! [X0] :
( ( p(X0)
| r(X0) )
& q(X0) )
& ! [X1] :
? [X2] :
( p(X1)
| ~ q(X1)
| ~ q(X2)
| ~ q(c)
| ~ q(d) )
& ( ~ p(a)
| ~ p(b) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( ( p(X0)
| r(X0) )
& q(X0) )
& ! [X1] :
? [X2] :
( p(X1)
| ~ q(X1)
| ~ q(X2)
| ~ q(c)
| ~ q(d) )
& ( ~ p(a)
| ~ p(b) ) ),
inference(flattening,[],[f2]) ).
fof(f4,plain,
( ! [X0] : q(X0)
& ! [X1] :
? [X2] :
( p(X1)
| ~ q(X1)
| ~ q(X2)
| ~ q(c)
| ~ q(d) )
& ( ~ p(a)
| ~ p(b) ) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f5,plain,
! [X1] :
( ~ q(d)
| ~ q(c)
| ~ q(sK0(X1))
| ~ q(X1)
| p(X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
( ~ p(b)
| ~ p(a) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X0] : q(X0),
inference(cnf_transformation,[],[f4]) ).
fof(f9,definition,
( spl1_1
<=> ! [X1] :
( ~ q(sK0(X1))
| p(X1)
| ~ q(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f10,plain,
( ! [X1] :
( ~ q(sK0(X1))
| p(X1)
| ~ q(X1) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,definition,
( spl1_2
<=> q(c) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f14,plain,
( ~ q(c)
| spl1_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f16,definition,
( spl1_3
<=> q(d) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f18,plain,
( ~ q(d)
| spl1_3 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f19,plain,
( spl1_1
| ~ spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f5,f16,f12,f9]) ).
fof(f21,definition,
( spl1_4
<=> p(a) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f23,plain,
( ~ p(a)
| spl1_4 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl1_5
<=> p(b) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f27,plain,
( ~ p(b)
| spl1_5 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
( ~ spl1_4
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f6,f25,f21]) ).
fof(f29,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f14,f7]) ).
fof(f30,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f31,plain,
( $false
| spl1_3 ),
inference(forward_subsumption_resolution,[],[f18,f7]) ).
fof(f32,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f31]) ).
fof(f33,plain,
( ! [X1] :
( p(X1)
| ~ q(X1) )
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f10,f7]) ).
fof(f34,plain,
( ! [X1] : p(X1)
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f33,f7]) ).
fof(f35,plain,
( $false
| ~ spl1_1
| spl1_5 ),
inference(resolution,[],[f34,f27]) ).
fof(f36,plain,
( ~ spl1_1
| spl1_5 ),
inference(avatar_contradiction_clause,[],[f35]) ).
fof(f37,plain,
( $false
| ~ spl1_1
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f23,f34]) ).
fof(f38,plain,
( ~ spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( ~ spl1_4
| ~ spl1_5 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
spl1_2,
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
spl1_3,
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( ~ spl1_1
| spl1_5 ),
inference(sat_conversion,[],[f36]) ).
cnf(s6,plain,
( ~ spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s7,plain,
spl1_1,
inference(rat,[],[s1,s4,s3]) ).
cnf(s8,plain,
spl1_4,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl1_5,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
fof(f39,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN722+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n016.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 16:54:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (3756256)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (3756265)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1764323499:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.26 % (3756265) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3756256-3756265"...
% 0.09/0.26 % (3756265)...printing done.
% 0.09/0.26 % (3756265)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.26 % (3756265)------------------------------
% 0.28/0.26 % (3756265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.26 % (3756265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.26 % (3756265)CaDiCaL version: 2.1.3
% 0.28/0.26 % (3756265)Termination reason: Refutation
% 0.28/0.26 % (3756265)Time elapsed: 0.001 s
% 0.28/0.26 % (3756265)Peak memory usage: 12 MB
% 0.28/0.26 % (3756265)Instructions burned: 1 (million)
% 0.28/0.26 % (3756256)Success in time 0.028 s
% 0.28/0.26 % Vampire exiting
%------------------------------------------------------------------------------