%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN940+1 : TPTP v9.3.1. Released v3.1.0.
% 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 02:22:54 PM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 10 unt; 6 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 66 ~; 51 |; 15 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ! [X2] : q(f(X2))
=> ? [X3,X4] :
( ( p(f(X4))
=> ( p(X3)
& ( r(X4)
=> ( r(X0)
& r(X1) ) ) ) )
& q(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] : q(f(X2))
=> ? [X3,X4] :
( ( p(f(X4))
=> ( p(X3)
& ( r(X4)
=> ( r(X0)
& r(X1) ) ) ) )
& q(X3) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
( ! [X3,X4] :
( ( ( ~ p(X3)
| ( ( ~ r(X0)
| ~ r(X1) )
& r(X4) ) )
& p(f(X4)) )
| ~ q(X3) )
& ! [X2] : q(f(X2)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
( ! [X2,X3] :
( ( ( ~ p(X2)
| ( ( ~ r(X0)
| ~ r(X1) )
& r(X3) ) )
& p(f(X3)) )
| ~ q(X2) )
& ! [X4] : q(f(X4)) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
( ! [X2,X3] :
( ( ( ~ p(X2)
| ( ( ~ r(sK0)
| ~ r(sK1) )
& r(X3) ) )
& p(f(X3)) )
| ~ q(X2) )
& ! [X4] : q(f(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f4]) ).
fof(f6,plain,
! [X4] : q(f(X4)),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( p(f(X3))
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
! [X2,X3] :
( ~ p(X2)
| r(X3)
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X2] :
( ~ p(X2)
| ~ r(sK0)
| ~ r(sK1)
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X2] :
( ~ p(X2)
| r(sK0)
| r(sK1)
| ~ q(X2) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f11,plain,
! [X2,X3] :
( ~ p(X2)
| ~ r(X3)
| ~ q(X2) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f13,definition,
( spl2_1
<=> ! [X2] : ~ q(X2) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f14,plain,
( ! [X2] : ~ q(X2)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f16,definition,
( spl2_2
<=> ! [X3] : p(f(X3)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f17,plain,
( ! [X3] : p(f(X3))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f7,f16,f13]) ).
fof(f20,definition,
( spl2_3
<=> ! [X3] : ~ r(X3) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f21,plain,
( ! [X3] : ~ r(X3)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,definition,
( spl2_4
<=> ! [X2] :
( ~ p(X2)
| ~ q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f24,plain,
( ! [X2] :
( ~ p(X2)
| ~ q(X2) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f25,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f11,f23,f20]) ).
fof(f27,definition,
( spl2_5
<=> r(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f29,plain,
( r(sK1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f31,definition,
( spl2_6
<=> r(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f33,plain,
( r(sK0)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
( spl2_5
| spl2_6
| spl2_4 ),
inference(avatar_split_clause,[],[f10,f23,f31,f27]) ).
fof(f35,plain,
( ! [X0] : ~ q(f(X0))
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f24,f17]) ).
fof(f36,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f35,f6]) ).
fof(f37,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f36]) ).
fof(f38,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f14,f6]) ).
fof(f39,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f40,plain,
( $false
| ~ spl2_3
| ~ spl2_6 ),
inference(resolution,[],[f33,f21]) ).
fof(f41,plain,
( ~ spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f40]) ).
fof(f42,plain,
( $false
| ~ spl2_3
| ~ spl2_5 ),
inference(resolution,[],[f29,f21]) ).
fof(f43,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f42]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
( spl2_4
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f39]) ).
cnf(s6,plain,
( ~ spl2_3
| ~ spl2_6 ),
inference(sat_conversion,[],[f41]) ).
cnf(s7,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s8,plain,
spl2_2,
inference(rat,[],[s1,s5]) ).
cnf(s9,plain,
~ spl2_4,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
spl2_3,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
~ spl2_5,
inference(rat,[],[s7,s10]) ).
cnf(s12,plain,
~ spl2_6,
inference(rat,[],[s6,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s3,s9,s12,s11]) ).
fof(f44,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN940+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 17:14:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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 % (4164808)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (4164819)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4138679067:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (4164819) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4164808-4164819"...
% 0.09/0.25 % (4164819)...printing done.
% 0.09/0.25 % (4164819)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 % (4164819)------------------------------
% 0.09/0.25 % (4164819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (4164819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (4164819)CaDiCaL version: 2.1.3
% 0.09/0.25 % (4164819)Termination reason: Refutation
% 0.09/0.25 % (4164819)Time elapsed: 0.001 s
% 0.09/0.25 % (4164819)Peak memory usage: 12 MB
% 0.09/0.25 % (4164819)Instructions burned: 1 (million)
% 0.09/0.25 % (4164808)Success in time 0.028 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------