%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN351+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 : 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 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 132 ( 40 ~; 41 |; 33 &)
% ( 6 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 56 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X3,X0,X4)
=> ( ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
=> ( big_f(X0,X2,X0,X3)
=> ( ( big_f(X0,X3,X2,X3)
=> big_f(X0,X4,X2,X4) )
& ( big_f(X0,X4,X2,X4)
=> ( big_f(X0,X2,X0,X3)
<=> big_f(X0,X3,X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_3) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X3,X0,X4)
=> ( ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
=> ( big_f(X0,X2,X0,X3)
=> ( ( big_f(X0,X3,X2,X3)
=> big_f(X0,X4,X2,X4) )
& ( big_f(X0,X4,X2,X4)
=> ( big_f(X0,X2,X0,X3)
<=> big_f(X0,X3,X2,X3) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( big_f(X0,X2,X0,X3)
<~> big_f(X0,X3,X2,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
& big_f(X0,X3,X0,X4) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( big_f(X0,X2,X0,X3)
<~> big_f(X0,X3,X2,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
& big_f(X0,X3,X0,X4) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( ~ big_f(X0,X3,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& ( big_f(X0,X3,X2,X3)
| big_f(X0,X2,X0,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
| ~ big_f(X2,X1,X2,X3) )
& ( big_f(X2,X1,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& big_f(X0,X3,X0,X4) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( ~ big_f(X0,X3,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& ( big_f(X0,X3,X2,X3)
| big_f(X0,X2,X0,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
| ~ big_f(X2,X1,X2,X3) )
& ( big_f(X2,X1,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& big_f(X0,X3,X0,X4) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( ( ( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
& big_f(sK0,X3,X2,X3) )
| ( ( ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) )
& ( big_f(sK0,X3,X2,X3)
| big_f(sK0,X2,sK0,X3) )
& big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ) )
& big_f(sK0,X2,sK0,X3)
& ( big_f(sK0,X2,sK0,X3)
| ~ big_f(X2,sK1,X2,X3) )
& ( big_f(X2,sK1,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) )
& big_f(sK0,X3,sK0,sK2(X2,X3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f6]) ).
fof(f8,plain,
! [X2,X3] : big_f(sK0,X3,sK0,sK2(X2,X3)),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3] :
( big_f(X2,sK1,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2,X3] :
( big_f(sK0,X2,sK0,X3)
| ~ big_f(X2,sK1,X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X3] : big_f(sK0,X2,sK0,X3),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X3] :
( big_f(sK0,X3,X2,X3)
| big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X3] :
( big_f(sK0,X3,X2,X3)
| big_f(sK0,X3,X2,X3)
| big_f(sK0,X2,sK0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X3] :
( big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3] :
( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X2,X3] :
( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| big_f(sK0,X3,X2,X3)
| big_f(sK0,X2,sK0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X2,X3] :
( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X2,X3] :
( big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| big_f(sK0,X3,X2,X3)
| big_f(sK0,X2,sK0,X3) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f19,plain,
! [X2,X3] :
( big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f20,plain,
! [X2,X3] :
( big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f21,plain,
! [X2,X3] :
( ~ big_f(sK0,X3,X2,X3)
| big_f(sK0,X3,X2,X3)
| big_f(sK0,X2,sK0,X3) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f22,plain,
! [X2,X3] :
( ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f23,plain,
! [X2,X3] :
( ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f24,plain,
! [X2,X3] : ~ big_f(sK0,X2,sK0,X3),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f25,plain,
! [X2,X3] :
( ~ big_f(sK0,X2,sK0,X3)
| big_f(X2,sK1,X2,X3) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f26,plain,
! [X2,X3] :
( ~ big_f(X2,sK1,X2,X3)
| big_f(sK0,X2,sK0,X3) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f27,plain,
! [X2,X3] : ~ big_f(sK0,X3,sK0,sK2(X2,X3)),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f80,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f18,f19,f20,f21,f22,f23,f24,f25,f26,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n019.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 15:47:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 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
% 0.08/0.25 % (4111511)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (4111516)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3298490913_3000 on theBenchmark for (3000ds/0Mi)
% 0.08/0.25 % TRYING [1]
% 0.08/0.25 % TRYING [2]
% 0.08/0.25 % TRYING [3]
% 0.08/0.25 % (4111516) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4111511-4111516"...
% 0.08/0.25 % (4111516)...printing done.
% 0.08/0.25 % (4111517)% WARNING: option uhcvi not known.
% 0.08/0.25 % (4111516)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (4111516)------------------------------
% 0.08/0.25 % (4111516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (4111516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (4111516)CaDiCaL version: 2.1.3
% 0.08/0.25 % (4111516)Termination reason: Refutation
% 0.08/0.25 % (4111516)Time elapsed: 0.002 s
% 0.08/0.25 % (4111516)Peak memory usage: 11 MB
% 0.08/0.25 % (4111516)Instructions burned: 9 (million)
% 0.08/0.25 % (4111511)Success in time 0.017 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------