%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN319+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 : n010.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 02:07:17 PM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 7 unt; 2 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 105 ( 36 ~; 28 |; 25 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% Number of variables : 32 ( 0 sgn 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2,X3] :
( ( ( big_f(X1)
=> big_g(X2) )
=> ( big_g(X0)
& ~ big_f(X2) ) )
=> ( ( ( big_f(X0)
| big_g(X0) )
=> big_h(X0) )
=> ( big_h(X3)
& ( big_h(X1)
=> ( ( big_f(X3)
| big_g(X3) )
=> big_h(X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_2_5) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2,X3] :
( ( ( big_f(X1)
=> big_g(X2) )
=> ( big_g(X0)
& ~ big_f(X2) ) )
=> ( ( ( big_f(X0)
| big_g(X0) )
=> big_h(X0) )
=> ( big_h(X3)
& ( big_h(X1)
=> ( ( big_f(X3)
| big_g(X3) )
=> big_h(X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2,X3] :
( ( ~ big_h(X3)
| ( ~ big_h(X3)
& ( big_f(X3)
| big_g(X3) )
& big_h(X1) ) )
& ( big_h(X0)
| ( ~ big_f(X0)
& ~ big_g(X0) ) )
& ( ( big_g(X0)
& ~ big_f(X2) )
| ( ~ big_g(X2)
& big_f(X1) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2,X3] :
( ( ~ big_h(X3)
| ( ~ big_h(X3)
& ( big_f(X3)
| big_g(X3) )
& big_h(X1) ) )
& ( big_h(X0)
| ( ~ big_f(X0)
& ~ big_g(X0) ) )
& ( ( big_g(X0)
& ~ big_f(X2) )
| ( ~ big_g(X2)
& big_f(X1) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( ~ big_h(sK1(X0,X1))
| ( ~ big_h(sK1(X0,X1))
& ( big_f(sK1(X0,X1))
| big_g(sK1(X0,X1)) )
& big_h(X1) ) )
& ( big_h(X0)
| ( ~ big_f(X0)
& ~ big_g(X0) ) )
& ( ( big_g(X0)
& ~ big_f(sK0(X0,X1)) )
| ( ~ big_g(sK0(X0,X1))
& big_f(X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f4]) ).
fof(f8,plain,
! [X0,X1] :
( big_g(X0)
| big_f(X1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X0] :
( ~ big_g(X0)
| big_h(X0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
! [X0] :
( big_h(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( ~ big_h(sK1(X0,X1))
| ~ big_h(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
! [X0,X1] : ~ big_h(sK1(X0,X1)),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f17,definition,
( spl2_1
<=> ! [X1] : big_f(X1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f18,plain,
( ! [X1] : big_f(X1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,definition,
( spl2_2
<=> ! [X0] : big_g(X0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f21,plain,
( ! [X0] : big_g(X0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f8,f20,f17]) ).
fof(f23,plain,
( ! [X0] : big_h(X0)
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f10,f21]) ).
fof(f24,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f15,f23]) ).
fof(f25,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f24]) ).
fof(f26,plain,
( ! [X0] : big_h(X0)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f11,f18]) ).
fof(f27,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f15,f26]) ).
fof(f28,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f27]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f29,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN319+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n010.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 15:42:21 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
% 0.09/0.24 % (2025867)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (2025875)dis+10_1_sil=32000:sp=arity:random_seed=134524204:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.24 % (2025875) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2025867-2025875"...
% 0.09/0.24 % (2025875)...printing done.
% 0.09/0.24 % (2025875)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (2025875)------------------------------
% 0.09/0.24 % (2025875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (2025875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (2025875)CaDiCaL version: 2.1.3
% 0.09/0.24 % (2025875)Termination reason: Refutation
% 0.09/0.24 % (2025875)Time elapsed: 0.001 s
% 0.09/0.24 % (2025875)Peak memory usage: 12 MB
% 0.09/0.24 % (2025875)Instructions burned: 1 (million)
% 0.09/0.24 % (2025867)Success in time 0.024 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------