%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN321+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 : 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 0.06s 0.24s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 1 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 83 ( 26 ~; 24 |; 16 &)
% ( 3 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 67 ( 55 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X2] : big_g(X0,X2) )
=> ( ! [X2] :
( big_g(X2,X2)
=> big_f(X2,X1) )
=> ( big_f(X0,X1)
<=> ! [X2] : big_g(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_3_2) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X2] : big_g(X0,X2) )
=> ( ! [X2] :
( big_g(X2,X2)
=> big_f(X2,X1) )
=> ( big_f(X0,X1)
<=> ! [X2] : big_g(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X3] : big_g(X0,X3) )
=> ( ! [X4] :
( big_g(X4,X4)
=> big_f(X4,X1) )
=> ( big_f(X0,X1)
<=> ! [X5] : big_g(X0,X5) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
( ( big_f(X0,X1)
<~> ! [X5] : big_g(X0,X5) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( big_f(X0,X1)
<~> ! [X5] : big_g(X0,X5) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( ( ? [X5] : ~ big_g(X0,X5)
| ~ big_f(X0,X1) )
& ( ! [X5] : big_g(X0,X5)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ? [X5] : ~ big_g(X0,X5)
| ~ big_f(X0,X1) )
& ( ! [X5] : big_g(X0,X5)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ( ? [X2] : ~ big_g(X0,X2)
| ~ big_f(X0,X1) )
& ( ! [X3] : big_g(X0,X3)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X5] : big_g(X0,X5)
| ! [X6] : ~ big_f(X0,X6) ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ( ~ big_g(X0,sK0(X0))
| ~ big_f(X0,X1) )
& ( ! [X3] : big_g(X0,X3)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X5] : big_g(X0,X5)
| ! [X6] : ~ big_f(X0,X6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f8]) ).
fof(f10,plain,
! [X0,X6,X5] :
( big_g(X0,X5)
| ~ big_f(X0,X6) ),
inference(cnf_transformation,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( big_f(X0,X1)
| ~ big_g(X0,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X3,X0,X1] :
( big_g(X0,X3)
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_g(X0,sK0(X0))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f13,f12,f11,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN321+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n010.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 15:42:22 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
% 0.06/0.24 % (2026154)Will run a generic schedule for satisfiability detection.
% 0.06/0.24 % (2026160)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4254352355_3000 on theBenchmark for (3000ds/0Mi)
% 0.06/0.24 % TRYING [1]
% 0.06/0.24 % TRYING [2]
% 0.06/0.24 % (2026160) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2026154-2026160"...
% 0.06/0.24 % (2026160)...printing done.
% 0.06/0.24 % (2026160)Refutation found. Thanks to Tanya!
% 0.06/0.24 % SZS status Theorem for theBenchmark
% 0.06/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.24 % (2026160)------------------------------
% 0.06/0.24 % (2026160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.24 % (2026160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.24 % (2026160)CaDiCaL version: 2.1.3
% 0.06/0.24 % (2026160)Termination reason: Refutation
% 0.06/0.24 % (2026160)Time elapsed: 0.001 s
% 0.06/0.24 % (2026160)Peak memory usage: 11 MB
% 0.06/0.24 % (2026160)Instructions burned: 1 (million)
% 0.06/0.24 % (2026154)Success in time 0.019 s
% 0.06/0.24 % Vampire exiting
%------------------------------------------------------------------------------