%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN334+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 : n026.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 02:07:21 PM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 4 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 91 ( 35 ~; 32 |; 4 &)
% ( 10 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 54 ( 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2] :
( ( big_f(X0,X1)
=> ( big_f(X0,X2)
<=> big_g(X1,X2) ) )
=> ( ( big_f(X0,X1)
<=> ( big_f(X2,X2)
=> big_g(X2,X2) ) )
=> ( big_g(X0,X1)
<=> big_g(X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_6) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( ( big_f(X0,X1)
=> ( big_f(X0,X2)
<=> big_g(X1,X2) ) )
=> ( ( big_f(X0,X1)
<=> ( big_f(X2,X2)
=> big_g(X2,X2) ) )
=> ( big_g(X0,X1)
<=> big_g(X2,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2] :
( ( big_g(X0,X1)
<~> big_g(X2,X2) )
& ( big_f(X0,X1)
<=> ( big_g(X2,X2)
| ~ big_f(X2,X2) ) )
& ( ( big_f(X0,X2)
<=> big_g(X1,X2) )
| ~ big_f(X0,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2] :
( ( big_g(X0,X1)
<~> big_g(X2,X2) )
& ( big_f(X0,X1)
<=> ( big_g(X2,X2)
| ~ big_f(X2,X2) ) )
& ( ( big_f(X0,X2)
<=> big_g(X1,X2) )
| ~ big_f(X0,X1) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( big_g(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( big_f(sK0(X0,X1),sK0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X0,X1] :
( ~ big_g(sK0(X0,X1),sK0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f8,plain,
! [X0,X1] :
( ~ big_g(X1,sK0(X0,X1))
| ~ big_f(X0,X1)
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f4]) ).
fof(f9,plain,
! [X0,X1] :
( big_g(X1,sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
! [X0,X1] :
( big_g(sK0(X0,X1),sK0(X0,X1))
| big_g(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_g(sK0(X0,X1),sK0(X0,X1))
| ~ big_g(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f12,plain,
! [X0,X1] :
( big_g(X0,X1)
| big_f(X0,X1) ),
inference(resolution,[],[f10,f7]) ).
fof(f14,plain,
! [X0,X1] :
( ~ big_g(X0,X1)
| big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(resolution,[],[f12,f11]) ).
fof(f16,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| big_f(X1,sK0(X0,X1))
| ~ big_f(X0,X1) ),
inference(resolution,[],[f8,f12]) ).
fof(f17,plain,
! [X0,X1] :
( big_g(X0,X1)
| big_f(sK0(sK0(X0,X1),sK0(X0,X1)),sK0(sK0(X0,X1),sK0(X0,X1))) ),
inference(resolution,[],[f14,f10]) ).
fof(f22,plain,
! [X0] :
( big_f(X0,sK0(X0,X0))
| ~ big_f(X0,X0) ),
inference(factoring,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_g(X0,X1) ),
inference(resolution,[],[f5,f11]) ).
fof(f25,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X0,X1)
| big_f(sK0(sK0(X0,X1),sK0(X0,X1)),sK0(sK0(X0,X1),sK0(X0,X1))) ),
inference(resolution,[],[f5,f14]) ).
fof(f26,plain,
! [X0,X1] :
( big_f(sK0(sK0(X0,X1),sK0(X0,X1)),sK0(sK0(X0,X1),sK0(X0,X1)))
| ~ big_f(X0,X1) ),
inference(forward_subsumption_resolution,[],[f25,f6]) ).
fof(f27,plain,
! [X0,X1] :
( ~ big_g(X0,X1)
| ~ big_f(X0,X1) ),
inference(forward_subsumption_resolution,[],[f23,f14]) ).
fof(f31,plain,
! [X0,X1] :
( ~ big_f(X0,sK0(X1,X0))
| ~ big_f(X1,sK0(X1,X0))
| ~ big_f(X1,X0) ),
inference(resolution,[],[f27,f9]) ).
fof(f42,plain,
! [X0] :
( ~ big_f(X0,sK0(X0,X0))
| ~ big_f(X0,X0)
| ~ big_f(X0,X0) ),
inference(resolution,[],[f31,f22]) ).
fof(f43,plain,
! [X0] :
( ~ big_f(X0,sK0(X0,X0))
| ~ big_f(X0,X0) ),
inference(duplicate_literal_removal,[],[f42]) ).
fof(f47,plain,
! [X0] : ~ big_f(X0,X0),
inference(forward_subsumption_resolution,[],[f43,f22]) ).
fof(f50,plain,
! [X0,X1] :
( big_f(sK0(sK0(sK0(X0,X1),sK0(X0,X1)),sK0(sK0(X0,X1),sK0(X0,X1))),sK0(sK0(sK0(X0,X1),sK0(X0,X1)),sK0(sK0(X0,X1),sK0(X0,X1))))
| big_f(X0,X1) ),
inference(resolution,[],[f17,f7]) ).
fof(f55,plain,
! [X0,X1] : big_f(X0,X1),
inference(forward_subsumption_resolution,[],[f50,f47]) ).
fof(f59,plain,
! [X0,X1] : ~ big_f(X0,X1),
inference(resolution,[],[f26,f47]) ).
fof(f60,plain,
$false,
inference(forward_subsumption_resolution,[],[f59,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:48:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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 % (3968052)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3968061)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1266880476:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (3968061) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3968052-3968061"...
% 0.19/0.27 % (3968061)...printing done.
% 0.19/0.27 % (3968061)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 % (3968061)------------------------------
% 0.19/0.27 % (3968061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3968061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3968061)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3968061)Termination reason: Refutation
% 0.19/0.27 % (3968061)Time elapsed: 0.001 s
% 0.19/0.27 % (3968061)Peak memory usage: 11 MB
% 0.19/0.27 % (3968061)Instructions burned: 2 (million)
% 0.19/0.27 % (3968052)Success in time 0.037 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------