%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN354+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 02:07:26 PM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 2 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 116 ( 41 ~; 41 |; 12 &)
% ( 8 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 25 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X1)
=> ( big_g(X0,X1)
=> ( ( ( big_g(X1,X4)
<=> big_g(X3,X4) )
=> ( big_f(X2,X3)
=> big_f(X1,X3) ) )
=> ( ( big_g(X1,X4)
<=> big_g(X2,X4) )
=> ( big_f(X0,X2)
& big_f(X1,X2)
& big_f(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_20_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X1)
=> ( big_g(X0,X1)
=> ( ( ( big_g(X1,X4)
<=> big_g(X3,X4) )
=> ( big_f(X2,X3)
=> big_f(X1,X3) ) )
=> ( ( big_g(X1,X4)
<=> big_g(X2,X4) )
=> ( big_f(X0,X2)
& big_f(X1,X2)
& big_f(X2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X2)
| ~ big_f(X1,X2)
| ~ big_f(X2,X3) )
& ( big_g(X1,X4)
<=> big_g(X2,X4) )
& ( big_f(X1,X3)
| ~ big_f(X2,X3)
| ( big_g(X1,X4)
<~> big_g(X3,X4) ) )
& big_g(X0,X1)
& big_f(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X2)
| ~ big_f(X1,X2)
| ~ big_f(X2,X3) )
& ( big_g(X1,X4)
<=> big_g(X2,X4) )
& ( big_f(X1,X3)
| ~ big_f(X2,X3)
| ( big_g(X1,X4)
<~> big_g(X3,X4) ) )
& big_g(X0,X1)
& big_f(X0,X1) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X2,X3] :
( big_g(X3,sK2(X2,X3))
| big_g(sK1,sK2(X2,X3))
| ~ big_f(X2,X3)
| big_f(sK1,X3) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X2,X3] :
( ~ big_g(X3,sK2(X2,X3))
| ~ big_g(sK1,sK2(X2,X3))
| ~ big_f(X2,X3)
| big_f(sK1,X3) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X2,X3] :
( ~ big_f(X2,X3)
| ~ big_f(sK0,X2)
| ~ big_f(sK1,X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
big_f(sK0,sK1),
inference(cnf_transformation,[],[f4]) ).
fof(f12,plain,
! [X0] :
( ~ big_f(sK1,X0)
| ~ big_f(sK1,sK1) ),
inference(resolution,[],[f7,f10]) ).
fof(f14,definition,
( spl3_1
<=> big_f(sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f15,plain,
( big_f(sK1,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f16,plain,
( ~ big_f(sK1,sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f18,definition,
( spl3_2
<=> ! [X0] : ~ big_f(sK1,X0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f19,plain,
( ! [X0] : ~ big_f(sK1,X0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f20,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f12,f18,f14]) ).
fof(f25,plain,
! [X0] :
( big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1)
| big_f(sK1,sK1) ),
inference(factoring,[],[f5]) ).
fof(f27,plain,
( ! [X0] :
( big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1) )
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f25,f16]) ).
fof(f36,plain,
( ! [X0] :
( ~ big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1)
| big_f(sK1,sK1)
| ~ big_f(X0,sK1) )
| spl3_1 ),
inference(resolution,[],[f6,f27]) ).
fof(f37,plain,
( ! [X0] :
( ~ big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1)
| big_f(sK1,sK1) )
| spl3_1 ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f42,plain,
( ! [X0] :
( ~ big_f(X0,sK1)
| big_f(sK1,sK1) )
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f37,f27]) ).
fof(f46,plain,
( ! [X0] : ~ big_f(X0,sK1)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f42,f16]) ).
fof(f49,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f46,f10]) ).
fof(f50,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f51,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(resolution,[],[f19,f15]) ).
fof(f52,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f50]) ).
cnf(s3,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
~ spl3_2,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN354+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.18 % Computer : n019.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 15:48:19 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.21 Running first-order model finding
% 0.06/0.21 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
% 0.06/0.25 % (4113502)Will run a generic schedule for satisfiability detection.
% 0.06/0.25 % (4113511)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3472963123:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.25 % (4113511) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4113502-4113511"...
% 0.06/0.25 % (4113511)...printing done.
% 0.06/0.25 % (4113511)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (4113511)------------------------------
% 0.06/0.25 % (4113511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (4113511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (4113511)CaDiCaL version: 2.1.3
% 0.06/0.25 % (4113511)Termination reason: Refutation
% 0.06/0.25 % (4113511)Time elapsed: 0.001 s
% 0.06/0.25 % (4113511)Peak memory usage: 12 MB
% 0.06/0.25 % (4113511)Instructions burned: 2 (million)
% 0.06/0.25 % (4113502)Success in time 0.028 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------