%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 03:34:23 PM UTC 2026
% Result : Theorem 4.31s 1.29s
% Output : Proof 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 4 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 156 ( 50 ~; 50 |; 34 &)
% ( 10 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 45 ( 0 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X,Y] :
! [Z] :
( ( ( big_f(Y,X)
& big_f(X,Y) )
<~> big_f(X,Z) )
=> ( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( ( big_f(X,Z)
<=> big_f(Y,Z) )
=> ( ( ( big_f(Y,X)
=> big_f(X,Y) )
<=> big_f(Z,Z) )
=> ( ( big_f(X,Y)
<=> big_f(Y,X) )
<=> big_f(Z,Y) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_4) ).
fof(f0_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( ( ( big_f(Y,X)
& big_f(X,Y) )
<~> big_f(X,Z) )
=> ( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( ( big_f(X,Z)
<=> big_f(Y,Z) )
=> ( ( ( big_f(Y,X)
=> big_f(X,Y) )
<=> big_f(Z,Z) )
=> ( ( big_f(X,Y)
<=> big_f(Y,X) )
<=> big_f(Z,Y) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X,Y] :
? [Z] :
( ( ( big_f(Z,Y)
& ( ( big_f(Y,X)
& ~ big_f(X,Y) )
| ( ~ big_f(Y,X)
& big_f(X,Y) ) ) )
| ( ~ big_f(Z,Y)
& ( ~ big_f(Y,X)
| big_f(X,Y) )
& ( big_f(Y,X)
| ~ big_f(X,Y) ) ) )
& ( ~ big_f(Z,Z)
| big_f(X,Y)
| ~ big_f(Y,X) )
& ( big_f(Z,Z)
| ( ~ big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(Y,Z)
| big_f(X,Z) )
& ( big_f(Y,Z)
| ~ big_f(X,Z) )
& ( ~ big_f(Z,X)
| big_f(X,Z) )
& ( big_f(Z,X)
| ~ big_f(X,Z) )
& ( ( big_f(X,Z)
& ( ~ big_f(Y,X)
| ~ big_f(X,Y) ) )
| ( ~ big_f(X,Z)
& big_f(Y,X)
& big_f(X,Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( big_f(sk0(X,Y),Y)
& ( ( big_f(Y,X)
& ~ big_f(X,Y) )
| ( ~ big_f(Y,X)
& big_f(X,Y) ) ) )
| ( ~ big_f(sk0(X,Y),Y)
& ( ~ big_f(Y,X)
| big_f(X,Y) )
& ( big_f(Y,X)
| ~ big_f(X,Y) ) ) )
& ( ~ big_f(sk0(X,Y),sk0(X,Y))
| big_f(X,Y)
| ~ big_f(Y,X) )
& ( big_f(sk0(X,Y),sk0(X,Y))
| ( ~ big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(Y,sk0(X,Y))
| big_f(X,sk0(X,Y)) )
& ( big_f(Y,sk0(X,Y))
| ~ big_f(X,sk0(X,Y)) )
& ( ~ big_f(sk0(X,Y),X)
| big_f(X,sk0(X,Y)) )
& ( big_f(sk0(X,Y),X)
| ~ big_f(X,sk0(X,Y)) )
& ( ( big_f(X,sk0(X,Y))
& ( ~ big_f(Y,X)
| ~ big_f(X,Y) ) )
| ( ~ big_f(X,sk0(X,Y))
& big_f(Y,X)
& big_f(X,Y) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c12,plain,
( ~ big_f(sk0(X0,X1),sk0(X0,X1))
| big_f(X0,X1)
| ~ big_f(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c8,plain,
( big_f(X1,sk0(X0,X1))
| ~ big_f(X0,sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c1,plain,
( big_f(X0,sk0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( big_f(X1,X0)
| big_f(X0,sk0(X1,X0)) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(p49,plain,
( big_f(X0,X1)
| ~ big_f(sk0(sk0(X0,X1),X1),sk0(sk0(X0,X1),X1))
| big_f(sk0(X0,X1),X1) ),
inference(resolution,[status(thm)],[c12,p30]) ).
cnf(c24,plain,
( big_f(X1,X0)
| big_f(X0,X1)
| ~ big_f(sk0(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p44,plain,
( big_f(X0,X0)
| ~ big_f(sk0(X0,X0),X0) ),
inference(factoring,[status(thm)],[c24]) ).
cnf(c6,plain,
( big_f(sk0(X0,X1),X0)
| ~ big_f(X0,sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p28,plain,
( big_f(X0,X1)
| big_f(sk0(X0,X1),X0) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(p46,plain,
( big_f(X0,X0)
| big_f(X0,X0) ),
inference(resolution,[status(thm)],[p44,p28]) ).
cnf(p47,plain,
big_f(X0,X0),
inference(factoring,[status(thm)],[p46]) ).
cnf(p51,plain,
( big_f(X0,X1)
| big_f(sk0(X0,X1),X1) ),
inference(resolution,[status(thm)],[p49,p47]) ).
cnf(p52,plain,
( big_f(X1,X0)
| big_f(X0,X1)
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p51,c24]) ).
cnf(p53,plain,
( big_f(X1,X0)
| big_f(X0,X1) ),
inference(factoring,[status(thm)],[p52]) ).
cnf(c4,plain,
( ~ big_f(X1,X0)
| ~ big_f(X0,X1)
| ~ big_f(X0,sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p39,plain,
( ~ big_f(X0,X0)
| ~ big_f(X0,sk0(X0,X0)) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(p59,plain,
( ~ big_f(X0,X0)
| big_f(sk0(X0,X0),X0) ),
inference(resolution,[status(thm)],[p53,p39]) ).
cnf(p64,plain,
big_f(sk0(X0,X0),X0),
inference(resolution,[status(thm)],[p59,p47]) ).
cnf(c25,plain,
( ~ big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sk0(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( ~ big_f(X0,X0)
| ~ big_f(sk0(X0,X0),X0) ),
inference(factoring,[status(thm)],[c25]) ).
cnf(p67,plain,
~ big_f(X0,X0),
inference(resolution,[status(thm)],[p64,p48]) ).
cnf(p68,plain,
$false,
inference(resolution,[status(thm)],[p67,p47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.58 % Computer : n008.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Fri Sep 25 00:52:57 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.31/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.31/1.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------