%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SYN332+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 09:27:26 PM UTC 2025
% Result : Theorem 77.51s 10.05s
% Output : CNFRefutation 77.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 38 ( 1 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 127 ( 49 ~; 54 |; 2 &)
% ( 10 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 53 ( 0 sgn 2 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_4,plain,
? [X,Y] :
! [Z] :
( ( ( big_f(X,Y)
& big_f(Y,X) )
<~> 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/sandbox/benchmark/theBenchmark.p',church_46_14_4) ).
fof(church_46_14_4_negated,plain,
~ ? [X,Y] :
! [Z] :
( ( ( big_f(X,Y)
& big_f(Y,X) )
<~> 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(negate_conjecture,[status(cth)],[church_46_14_4]) ).
cnf(0,plain,
( big_f(X0,X1)
| big_f(X0,sK1(X0,X1)) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l0,plain,
( big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(5,plain,
( ~ big_f(X0,sK1(X0,X1))
| big_f(X1,sK1(X0,X1)) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l3,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))
| big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(10,plain,
( ~ big_f(X0,X1)
| big_f(sK1(X0,X1),X1)
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l1,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| big_f(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| sP0(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(15,plain,
( big_f(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l45,plain,
( big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| ~ sP0(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(13,plain,
( ~ big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l2,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| ~ big_f(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(9,plain,
( ~ big_f(X0,X1)
| ~ big_f(sK1(X1,X0),sK1(X1,X0))
| big_f(X1,X0) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l4,plain,
( ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))
| ~ big_f(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))
| big_f(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(12,plain,
( ~ big_f(sK1(X0,X1),X1)
| big_f(X0,X1)
| big_f(X1,X0) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l48,plain,
( ~ big_f(sK1(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))
| big_f(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))
| big_f(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(3,plain,
( ~ big_f(X0,sK1(X0,X1))
| big_f(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l105,plain,
( ~ big_f(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))))
| big_f(sK1(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l5,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| sP0(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l108,plain,
( big_f(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))
| big_f(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(14,plain,
( big_f(X0,X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l197,plain,
( big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| ~ sP0(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(8,plain,
( ~ big_f(X0,X1)
| big_f(sK1(X0,X1),sK1(X0,X1)) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l194,plain,
( ~ big_f(X0_195,X0_195)
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(7,plain,
( big_f(X0,X1)
| big_f(sK1(X1,X0),sK1(X1,X0)) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l195,plain,
( big_f(X0_195,X0_195)
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l52,plain,
( ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(2,plain,
( ~ big_f(X0,X1)
| ~ big_f(X0,sK1(X0,X1))
| ~ big_f(X1,X0) ),
inference(cnf,[status(esa)],[church_46_14_4_negated]) ).
cnf(l58,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l214,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l88,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l50,plain,
( ~ big_f(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l54,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| ~ big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l79,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| ~ big_f(sK1(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195))) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l139,plain,
( ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l81,plain,
( ~ big_f(sK1(X0_195,X0_195),sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)))
| big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l57,plain,
( ~ big_f(sK1(sK1(X0_195,X0_195),sK1(X0_195,X0_195)),sK1(X0_195,X0_195))
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195))
| big_f(sK1(X0_195,X0_195),sK1(X0_195,X0_195)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l1,l45,l2,l4,l48,l105,l5,l108,l197,l194,l195,l52,l58,l214,l88,l50,l54,l79,l139,l81,l57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYN332+1 : TPTP v9.0.0. Released v2.0.0.
% 0.02/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jul 22 15:51:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 9
% 0.19/0.47 % launching worker at depth: 10
% 16.81/2.45 % launching worker at depth: 11
% 77.51/10.05 % SZS status Theorem for theBenchmark
% 77.51/10.05 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------