%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 02:06:43 PM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 5 unt; 5 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 62 ~; 61 |; 12 &)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 20 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( big_f(X0,f(X0))
<=> ? [X1] :
( ! [X2] :
( big_f(X2,X1)
=> big_f(X2,f(X0)) )
& big_f(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel60) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( big_f(X0,f(X0))
<=> ? [X1] :
( ! [X2] :
( big_f(X2,X1)
=> big_f(X2,f(X0)) )
& big_f(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
( big_f(X0,f(X0))
<~> ? [X1] :
( ! [X2] :
( big_f(X2,f(X0))
| ~ big_f(X2,X1) )
& big_f(X0,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ( ! [X1] :
( ? [X2] :
( ~ big_f(X2,f(X0))
& big_f(X2,X1) )
| ~ big_f(X0,X1) )
| ~ big_f(X0,f(X0)) )
& ( ? [X1] :
( ! [X2] :
( big_f(X2,f(X0))
| ~ big_f(X2,X1) )
& big_f(X0,X1) )
| big_f(X0,f(X0)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ( ! [X1] :
( ? [X2] :
( ~ big_f(X2,f(X0))
& big_f(X2,X1) )
| ~ big_f(X0,X1) )
| ~ big_f(X0,f(X0)) )
& ( ? [X3] :
( ! [X4] :
( big_f(X4,f(X0))
| ~ big_f(X4,X3) )
& big_f(X0,X3) )
| big_f(X0,f(X0)) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ( ! [X1] :
( ( ~ big_f(sK1(X1),f(sK0))
& big_f(sK1(X1),X1) )
| ~ big_f(sK0,X1) )
| ~ big_f(sK0,f(sK0)) )
& ( ( ! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2) )
& big_f(sK0,sK2) )
| big_f(sK0,f(sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1(X1)),skolemize(X3,sK2)],[f5]) ).
fof(f7,plain,
( big_f(sK0,sK2)
| big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2)
| big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X1] :
( big_f(sK1(X1),X1)
| ~ big_f(sK0,X1)
| ~ big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X1] :
( ~ big_f(sK1(X1),f(sK0))
| ~ big_f(sK0,X1)
| ~ big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,definition,
( spl3_1
<=> big_f(sK0,f(sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f13,plain,
( ~ big_f(sK0,f(sK0))
| spl3_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f14,plain,
( big_f(sK0,f(sK0))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f16,definition,
( spl3_2
<=> big_f(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f18,plain,
( big_f(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f19,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f7,f16,f12]) ).
fof(f21,definition,
( spl3_3
<=> ! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f8,f21,f12]) ).
fof(f25,definition,
( spl3_4
<=> ! [X1] :
( big_f(sK1(X1),X1)
| ~ big_f(sK0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f26,plain,
( ! [X1] :
( big_f(sK1(X1),X1)
| ~ big_f(sK0,X1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( ~ spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f9,f25,f12]) ).
fof(f29,definition,
( spl3_5
<=> ! [X1] :
( ~ big_f(sK1(X1),f(sK0))
| ~ big_f(sK0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f30,plain,
( ! [X1] :
( ~ big_f(sK1(X1),f(sK0))
| ~ big_f(sK0,X1) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_split_clause,[],[f10,f29,f12]) ).
fof(f32,plain,
( ~ big_f(sK0,sK2)
| spl3_1
| ~ spl3_3 ),
inference(resolution,[],[f22,f13]) ).
fof(f33,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f32,f18]) ).
fof(f34,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f33]) ).
fof(f35,plain,
( ~ big_f(sK0,f(sK0))
| ~ big_f(sK0,f(sK0))
| ~ spl3_4
| ~ spl3_5 ),
inference(resolution,[],[f30,f26]) ).
fof(f37,plain,
( ~ big_f(sK0,f(sK0))
| ~ spl3_4
| ~ spl3_5 ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f38,plain,
( $false
| ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f37,f14]) ).
fof(f39,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f38]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
( ~ spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f34]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f39]) ).
cnf(s7,plain,
spl3_1,
inference(rat,[],[s5,s1,s2]) ).
cnf(s8,plain,
spl3_5,
inference(rat,[],[s4,s7]) ).
cnf(s9,plain,
spl3_4,
inference(rat,[],[s3,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s7,s9]) ).
fof(f40,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 15:38:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.19/0.27 % (436597)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (436605)dis+10_1_sil=32000:sp=arity:random_seed=549096596:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (436605) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-436597-436605"...
% 0.19/0.27 % (436605)...printing done.
% 0.19/0.27 % (436605)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (436605)------------------------------
% 0.19/0.27 % (436605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (436605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (436605)CaDiCaL version: 2.1.3
% 0.19/0.27 % (436605)Termination reason: Refutation
% 0.19/0.27 % (436605)Time elapsed: 0.001 s
% 0.19/0.27 % (436605)Peak memory usage: 12 MB
% 0.19/0.27 % (436605)Instructions burned: 1 (million)
% 0.19/0.27 % (436597)Success in time 0.029 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------