%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:37:35 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 211 ( 75 ~; 73 |; 41 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 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 : 72 ( 0 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_4,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('theBenchmark.p',church_46_14_4) ).
fof(church_46_14_4_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(assume_negation,[status(cth)],[church_46_14_4]) ).
fof(nnf_1,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(fof_nnf,[status(thm)],[church_46_14_4_neg]) ).
fof(sk_church_46_14_4_neg_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(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_church_46_14_4_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_1,VAR_0)
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),VAR_1)
| big_f(VAR_1,VAR_0)
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_1,VAR_0)
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),VAR_1)
| big_f(VAR_1,VAR_0)
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_1,VAR_0),sK0(VAR_1,VAR_0))
| big_f(VAR_1,VAR_0)
| ~ 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_f(sK0(VAR_1,VAR_0),sK0(VAR_1,VAR_0))
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ big_f(VAR_1,sK0(VAR_0,VAR_1))
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(VAR_1,sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),VAR_0)
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),VAR_0)
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(VAR_0,sK0(VAR_0,VAR_1))
| ~ big_f(VAR_1,VAR_0)
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_f(VAR_1,sK0(VAR_1,VAR_0))
| big_f(VAR_0,VAR_1) )
& ! [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_4_neg_sk]) ).
cnf(c_3,negated_conjecture,
( big_f(B,sK0(B,A))
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_f(A,sK0(A,B))
| ~ big_f(B,A)
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_5,negated_conjecture,
( big_f(sK0(A,B),A)
| ~ big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_7,negated_conjecture,
( big_f(B,sK0(A,B))
| ~ big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_11,negated_conjecture,
( ~ big_f(sK0(B,A),sK0(B,A))
| big_f(B,A)
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_14,negated_conjecture,
( ~ big_f(sK0(A,B),B)
| big_f(B,A)
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_15,negated_conjecture,
( ~ big_f(sK0(A,B),B)
| ~ big_f(B,A)
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_4_neg]) ).
cnf(c_16,plain,
( ~ big_f(A,sK0(A,A))
| ~ big_f(A,A) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_17,plain,
( ~ big_f(sK0(A,A),A)
| big_f(A,A) ),
inference(factor,[status(thm)],[c_14]) ).
cnf(c_18,plain,
( ~ big_f(sK0(A,A),A)
| ~ big_f(A,A) ),
inference(factor,[status(thm)],[c_15]) ).
cnf(c_21,plain,
( big_f(sK0(A,B),sK0(sK0(A,B),A))
| ~ big_f(B,A)
| ~ big_f(A,B) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_22,plain,
( big_f(sK0(A,A),sK0(sK0(A,A),A))
| ~ big_f(A,A) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_23,plain,
( big_f(B,A)
| big_f(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_58,plain,
( big_f(A,A)
| big_f(A,A) ),
inference(resolve,[status(thm)],[c_23,c_17]) ).
cnf(c_39,plain,
big_f(A,A),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_42,plain,
big_f(sK0(A,A),sK0(sK0(A,A),A)),
inference(resolve,[status(thm)],[c_39,c_22]) ).
cnf(c_43,plain,
~ big_f(sK0(A,A),A),
inference(resolve,[status(thm)],[c_39,c_18]) ).
cnf(c_44,plain,
~ big_f(A,sK0(A,A)),
inference(resolve,[status(thm)],[c_39,c_16]) ).
cnf(c_45,negated_conjecture,
( big_f(B,A)
| ~ big_f(A,B) ),
inference(resolve,[status(thm)],[c_39,c_11]) ).
cnf(c_59,negated_conjecture,
( ~ big_f(sK0(sK0(A,A),A),A)
| big_f(A,sK0(A,A)) ),
inference(resolve,[status(thm)],[c_14,c_43]) ).
cnf(c_50,negated_conjecture,
~ big_f(sK0(sK0(A,A),A),A),
inference(resolve,[status(thm)],[c_59,c_44]) ).
cnf(c_53,negated_conjecture,
~ big_f(A,sK0(sK0(A,A),A)),
inference(resolve,[status(thm)],[c_45,c_50]) ).
cnf(c_60,negated_conjecture,
~ big_f(sK0(A,A),sK0(sK0(A,A),A)),
inference(resolve,[status(thm)],[c_7,c_53]) ).
cnf(c_57,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_42,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 17:34:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3252410 was started by sandbox on n013,
% 0.10/0.36 % Sat Sep 26 17:34:37 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 22.
% 0.13/0.38 % Level of proof is 7.
% 0.13/0.38 % Maximum clause weight is 15.000.
% 0.13/0.38 % Given clauses 27.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------