%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 02:18:08 PM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 7 unt; 5 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 47 ~; 49 |; 4 &)
% ( 12 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( r(X0)
=> s(X0) )
<=> ! [X0] :
( ( r(X0)
& s(X0) )
<=> r(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm31) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( r(X0)
=> s(X0) )
<=> ! [X0] :
( ( r(X0)
& s(X0) )
<=> r(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( r(X0)
=> s(X0) )
<=> ! [X1] :
( ( r(X1)
& s(X1) )
<=> r(X1) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( s(X0)
| ~ r(X0) )
<~> ! [X1] :
( ( r(X1)
& s(X1) )
<=> r(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ~ s(sK1)
| ~ r(sK1)
| r(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
( r(sK1)
| r(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f8,plain,
( ~ s(sK1)
| ~ r(sK1)
| ~ s(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
( r(sK1)
| ~ s(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0,X1] :
( ~ r(X1)
| s(X1)
| ~ r(X0)
| s(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f13,definition,
( spl2_1
<=> r(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f15,plain,
( r(sK0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f17,definition,
( spl2_2
<=> r(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f18,plain,
( r(sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f21,definition,
( spl2_3
<=> s(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f23,plain,
( ~ s(sK1)
| spl2_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f5,f21,f17,f13]) ).
fof(f25,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f7,f17,f13]) ).
fof(f27,definition,
( spl2_4
<=> s(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f29,plain,
( ~ s(sK0)
| spl2_4 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f30,plain,
( ~ spl2_4
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f8,f21,f17,f27]) ).
fof(f31,plain,
( ~ spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f10,f17,f27]) ).
fof(f33,definition,
( spl2_5
<=> ! [X0] :
( ~ r(X0)
| s(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f34,plain,
( ! [X0] :
( s(X0)
| ~ r(X0) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f35,plain,
( spl2_5
| spl2_5 ),
inference(avatar_split_clause,[],[f11,f33,f33]) ).
fof(f36,plain,
( ~ r(sK1)
| spl2_3
| ~ spl2_5 ),
inference(resolution,[],[f34,f23]) ).
fof(f37,plain,
( $false
| ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f36,f18]) ).
fof(f38,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f37]) ).
fof(f39,plain,
( ~ r(sK0)
| spl2_4
| ~ spl2_5 ),
inference(resolution,[],[f29,f34]) ).
fof(f40,plain,
( $false
| ~ spl2_1
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f39,f15]) ).
fof(f41,plain,
( ~ spl2_1
| spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f40]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
( spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( spl2_5
| spl2_5 ),
inference(sat_conversion,[],[f35]) ).
cnf(s6,plain,
spl2_5,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f38]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f41]) ).
cnf(s9,plain,
spl2_1,
inference(rat,[],[s1,s7,s2,s6]) ).
cnf(s10,plain,
spl2_4,
inference(rat,[],[s8,s6,s9]) ).
cnf(s11,plain,
spl2_2,
inference(rat,[],[s4,s10]) ).
cnf(s12,plain,
~ spl2_3,
inference(rat,[],[s3,s11,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s7,s6,s12,s11]) ).
fof(f42,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.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 16:51:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.08/0.26 % (4013073)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (4013082)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=820549554:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (4013082) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4013073-4013082"...
% 0.08/0.26 % (4013082)...printing done.
% 0.08/0.26 % (4013082)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (4013082)------------------------------
% 0.08/0.26 % (4013082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (4013082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (4013082)CaDiCaL version: 2.1.3
% 0.08/0.26 % (4013082)Termination reason: Refutation
% 0.08/0.26 % (4013082)Time elapsed: 0.001 s
% 0.08/0.26 % (4013082)Peak memory usage: 12 MB
% 0.08/0.26 % (4013082)Instructions burned: 1 (million)
% 0.08/0.26 % (4013073)Success in time 0.029 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------