%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 09:37:36 AM UTC 2026
% Result : Theorem 0.14s 5.80s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 133 ( 44 ~; 57 |; 18 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 78 ( 5 sgn 20 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_6,conjecture,
? [X,Y] :
! [Z] :
( ( big_f(X,Y)
=> ( big_f(X,Z)
<=> big_g(Y,Z) ) )
=> ( ( big_f(X,Y)
<=> ( big_f(Z,Z)
=> big_g(Z,Z) ) )
=> ( big_g(X,Y)
<=> big_g(Z,Z) ) ) ),
file('theBenchmark.p',church_46_14_6) ).
fof(church_46_14_6_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( ( big_f(X,Y)
=> ( big_f(X,Z)
<=> big_g(Y,Z) ) )
=> ( ( big_f(X,Y)
<=> ( big_f(Z,Z)
=> big_g(Z,Z) ) )
=> ( big_g(X,Y)
<=> big_g(Z,Z) ) ) ),
inference(assume_negation,[status(cth)],[church_46_14_6]) ).
fof(nnf_1,plain,
! [X,Y] :
? [Z] :
( ( ~ big_g(Z,Z)
| ~ big_g(X,Y) )
& ( big_g(Z,Z)
| big_g(X,Y) )
& ( ( ~ big_g(Z,Z)
& big_f(Z,Z) )
| big_f(X,Y) )
& ( big_g(Z,Z)
| ~ big_f(Z,Z)
| ~ big_f(X,Y) )
& ( ( ( ~ big_g(Y,Z)
| big_f(X,Z) )
& ( big_g(Y,Z)
| ~ big_f(X,Z) ) )
| ~ big_f(X,Y) ) ),
inference(fof_nnf,[status(thm)],[church_46_14_6_neg]) ).
fof(sk_church_46_14_6_neg_sk,plain,
! [X,Y] :
( ( ~ big_g(sK0(X,Y),sK0(X,Y))
| ~ big_g(X,Y) )
& ( big_g(sK0(X,Y),sK0(X,Y))
| big_g(X,Y) )
& ( ( ~ big_g(sK0(X,Y),sK0(X,Y))
& big_f(sK0(X,Y),sK0(X,Y)) )
| big_f(X,Y) )
& ( big_g(sK0(X,Y),sK0(X,Y))
| ~ big_f(sK0(X,Y),sK0(X,Y))
| ~ big_f(X,Y) )
& ( ( ( ~ big_g(Y,sK0(X,Y))
| big_f(X,sK0(X,Y)) )
& ( big_g(Y,sK0(X,Y))
| ~ big_f(X,sK0(X,Y)) ) )
| ~ big_f(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_church_46_14_6_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_g(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| ~ big_g(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_g(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| big_g(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ big_g(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_g(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| ~ big_f(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ big_g(VAR_1,sK0(VAR_0,VAR_1))
| big_f(VAR_0,sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_1,sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_14_6_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_g(B,sK0(A,B))
| ~ big_f(A,sK0(A,B))
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_3,negated_conjecture,
( ~ big_g(B,sK0(A,B))
| big_f(A,sK0(A,B))
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_4,negated_conjecture,
( big_g(sK0(A,B),sK0(A,B))
| ~ big_f(sK0(A,B),sK0(A,B))
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_5,negated_conjecture,
( big_f(sK0(A,B),sK0(A,B))
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_g(sK0(A,B),sK0(A,B))
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_7,negated_conjecture,
( big_g(sK0(A,B),sK0(A,B))
| big_g(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_8,negated_conjecture,
( ~ big_g(sK0(A,B),sK0(A,B))
| ~ big_g(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_6_neg]) ).
cnf(c_9,plain,
( big_f(A,B)
| big_g(A,B) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_10,plain,
( ~ big_g(A,B)
| big_f(sK0(A,B),sK0(A,B)) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_11,plain,
( big_f(B,sK0(B,A))
| ~ big_f(B,A)
| big_f(A,sK0(B,A)) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_12,plain,
( ~ big_f(A,A)
| big_f(A,sK0(A,A)) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_13,plain,
( big_f(A,B)
| big_f(sK0(A,B),sK0(sK0(A,B),sK0(A,B))) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_16,plain,
( big_g(sK0(A,B),sK0(sK0(A,B),sK0(A,B)))
| ~ big_f(sK0(A,B),sK0(A,B))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_13,c_2]) ).
cnf(c_39,negated_conjecture,
( big_f(A,B)
| big_g(sK0(A,B),sK0(sK0(A,B),sK0(A,B)))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_16,c_5]) ).
cnf(c_20,negated_conjecture,
( big_g(sK0(A,B),sK0(sK0(A,B),sK0(A,B)))
| big_f(A,B) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_21,plain,
( big_f(sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))),sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_23,plain,
( big_g(sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))),sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))))
| ~ big_f(sK0(A,B),sK0(sK0(A,B),sK0(A,B)))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_21,c_4]) ).
cnf(c_40,plain,
( big_f(A,B)
| big_g(sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))),sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_23,c_13]) ).
cnf(c_30,plain,
( big_g(sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))),sK0(sK0(A,B),sK0(sK0(A,B),sK0(A,B))))
| big_f(A,B) ),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_32,plain,
( ~ big_g(sK0(A,B),sK0(sK0(A,B),sK0(A,B)))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_30,c_8]) ).
cnf(c_41,plain,
( big_f(A,B)
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_32,c_20]) ).
cnf(c_34,plain,
big_f(A,B),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_42,negated_conjecture,
( big_g(sK0(A,B),sK0(A,B))
| ~ big_f(sK0(A,B),sK0(A,B)) ),
inference(resolve,[status(thm)],[c_34,c_4]) ).
cnf(c_35,negated_conjecture,
big_g(sK0(A,B),sK0(A,B)),
inference(resolve,[status(thm)],[c_34,c_42]) ).
cnf(c_43,negated_conjecture,
( big_g(B,sK0(A,B))
| ~ big_f(A,sK0(A,B)) ),
inference(resolve,[status(thm)],[c_34,c_2]) ).
cnf(c_36,negated_conjecture,
big_g(A,sK0(B,A)),
inference(resolve,[status(thm)],[c_34,c_43]) ).
cnf(c_37,negated_conjecture,
~ big_g(A,B),
inference(resolve,[status(thm)],[c_35,c_8]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.78 % Computer : n019.cluster.edu
% 0.10/5.78 % Model : x86_64 x86_64
% 0.10/5.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.78 % Memory : 8046.5625MB
% 0.10/5.78 % OS : Linux 6.8.0-71-generic
% 0.10/5.78 % CPULimit : 300
% 0.10/5.78 % WCLimit : 300
% 0.10/5.78 % DateTime : Sat Sep 26 17:35:27 UTC 2026
% 0.10/5.78 % CPUTime :
% 0.10/5.79 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.79 % Process 1849858 was started by sandbox2 on n019,
% 0.10/5.79 % Sat Sep 26 17:35:27 2026
% 0.10/5.79 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.79
% 0.10/5.79 % From the command line: assign(max_seconds, 300).
% 0.14/5.80
% 0.14/5.80 % SZS status Theorem for theBenchmark
% 0.14/5.80
% 0.14/5.80 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.80 % Length of proof is 24.
% 0.14/5.80 % Level of proof is 15.
% 0.14/5.80 % Maximum clause weight is 37.000.
% 0.14/5.80 % Given clauses 24.
% 0.14/5.80
% 0.14/5.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------