%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN349+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 : n003.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 09:37:39 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 191 ( 65 ~; 89 |; 27 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 60 ( 0 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_17_5,conjecture,
? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
file('theBenchmark.p',church_46_17_5) ).
fof(church_46_17_5_neg,negated_conjecture,
~ ? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
inference(assume_negation,[status(cth)],[church_46_17_5]) ).
fof(nnf_1,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ~ big_f(X4,X2)
| ( ( ~ big_f(X3,X4)
| ( ( ~ big_f(X4,X3)
| ~ big_f(X1,X4) )
& ( big_f(X4,X3)
| big_f(X1,X4) ) ) )
& ( big_f(X3,X4)
| ( ( ~ big_f(X4,X3)
| big_f(X1,X4) )
& ( big_f(X4,X3)
| ~ big_f(X1,X4) ) ) ) ) )
& ( big_f(X4,X2)
| ( ( ~ big_f(X3,X4)
| ( ( ~ big_f(X4,X3)
| big_f(X1,X4) )
& ( big_f(X4,X3)
| ~ big_f(X1,X4) ) ) )
& ( big_f(X3,X4)
| ( ( ~ big_f(X4,X3)
| ~ big_f(X1,X4) )
& ( big_f(X4,X3)
| big_f(X1,X4) ) ) ) ) )
& ( ~ big_f(X2,X4)
| big_f(X1,X4) )
& ( big_f(X2,X4)
| ~ big_f(X1,X4) ) ),
inference(fof_nnf,[status(thm)],[church_46_17_5_neg]) ).
fof(sk_church_46_17_5_neg_sk,plain,
! [X1,X3] :
( ( ~ big_f(sK0(X1,X3),sK1(X1))
| ( ( ~ big_f(X3,sK0(X1,X3))
| ( ( ~ big_f(sK0(X1,X3),X3)
| ~ big_f(X1,sK0(X1,X3)) )
& ( big_f(sK0(X1,X3),X3)
| big_f(X1,sK0(X1,X3)) ) ) )
& ( big_f(X3,sK0(X1,X3))
| ( ( ~ big_f(sK0(X1,X3),X3)
| big_f(X1,sK0(X1,X3)) )
& ( big_f(sK0(X1,X3),X3)
| ~ big_f(X1,sK0(X1,X3)) ) ) ) ) )
& ( big_f(sK0(X1,X3),sK1(X1))
| ( ( ~ big_f(X3,sK0(X1,X3))
| ( ( ~ big_f(sK0(X1,X3),X3)
| big_f(X1,sK0(X1,X3)) )
& ( big_f(sK0(X1,X3),X3)
| ~ big_f(X1,sK0(X1,X3)) ) ) )
& ( big_f(X3,sK0(X1,X3))
| ( ( ~ big_f(sK0(X1,X3),X3)
| ~ big_f(X1,sK0(X1,X3)) )
& ( big_f(sK0(X1,X3),X3)
| big_f(X1,sK0(X1,X3)) ) ) ) ) )
& ( ~ big_f(sK1(X1),sK0(X1,X3))
| big_f(X1,sK0(X1,X3)) )
& ( big_f(sK1(X1),sK0(X1,X3))
| ~ big_f(X1,sK0(X1,X3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK1(X1)),skolemize(X4,sK0(X1,X3))],[nnf_1]) ).
fof(sk_church_46_17_5_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| ~ big_f(VAR_1,sK0(VAR_0,VAR_1))
| ~ big_f(sK0(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| ~ big_f(VAR_1,sK0(VAR_0,VAR_1))
| big_f(sK0(VAR_0,VAR_1),VAR_1)
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| big_f(VAR_1,sK0(VAR_0,VAR_1))
| ~ big_f(sK0(VAR_0,VAR_1),VAR_1)
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| big_f(VAR_1,sK0(VAR_0,VAR_1))
| big_f(sK0(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| ~ big_f(VAR_1,sK0(VAR_0,VAR_1))
| ~ big_f(sK0(VAR_0,VAR_1),VAR_1)
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| ~ big_f(VAR_1,sK0(VAR_0,VAR_1))
| big_f(sK0(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| big_f(VAR_1,sK0(VAR_0,VAR_1))
| ~ big_f(sK0(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0(VAR_0,VAR_1),sK1(VAR_0))
| big_f(VAR_1,sK0(VAR_0,VAR_1))
| big_f(sK0(VAR_0,VAR_1),VAR_1)
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK1(VAR_0),sK0(VAR_0,VAR_1))
| big_f(VAR_0,sK0(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK1(VAR_0),sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,sK0(VAR_0,VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_17_5_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_f(sK1(A),sK0(A,B))
| ~ big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_5_neg]) ).
cnf(c_3,negated_conjecture,
( ~ big_f(sK1(A),sK0(A,B))
| big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_5_neg]) ).
cnf(c_4,negated_conjecture,
( big_f(sK0(A,B),sK1(A))
| big_f(B,sK0(A,B))
| big_f(sK0(A,B),B)
| big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_5_neg]) ).
cnf(c_6,negated_conjecture,
( big_f(sK0(A,B),sK1(A))
| ~ big_f(B,sK0(A,B))
| big_f(sK0(A,B),B)
| ~ big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_5_neg]) ).
cnf(c_9,negated_conjecture,
( ~ big_f(sK0(A,B),sK1(A))
| big_f(B,sK0(A,B))
| ~ big_f(sK0(A,B),B)
| big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_5_neg]) ).
cnf(c_11,negated_conjecture,
( ~ big_f(sK0(A,B),sK1(A))
| ~ big_f(B,sK0(A,B))
| ~ big_f(sK0(A,B),B)
| ~ big_f(A,sK0(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_5_neg]) ).
cnf(c_13,plain,
( big_f(sK1(A),sK0(A,sK1(A)))
| big_f(sK0(A,sK1(A)),sK1(A))
| big_f(A,sK0(A,sK1(A))) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_15,plain,
( ~ big_f(sK1(A),sK0(A,sK1(A)))
| big_f(sK0(A,sK1(A)),sK1(A))
| ~ big_f(A,sK0(A,sK1(A))) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_17,plain,
( big_f(sK1(A),sK0(A,sK1(A)))
| ~ big_f(sK0(A,sK1(A)),sK1(A))
| big_f(A,sK0(A,sK1(A))) ),
inference(factor,[status(thm)],[c_9]) ).
cnf(c_19,plain,
( ~ big_f(sK1(A),sK0(A,sK1(A)))
| ~ big_f(sK0(A,sK1(A)),sK1(A))
| ~ big_f(A,sK0(A,sK1(A))) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_27,plain,
( big_f(sK1(A),sK0(A,sK1(A)))
| big_f(A,sK0(A,sK1(A)))
| big_f(sK1(A),sK0(A,sK1(A)))
| big_f(A,sK0(A,sK1(A))) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_28,plain,
( big_f(sK1(A),sK0(A,sK1(A)))
| big_f(sK1(A),sK0(A,sK1(A)))
| big_f(A,sK0(A,sK1(A))) ),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_20,plain,
( big_f(sK1(A),sK0(A,sK1(A)))
| big_f(A,sK0(A,sK1(A))) ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_29,negated_conjecture,
( big_f(A,sK0(A,sK1(A)))
| big_f(A,sK0(A,sK1(A))) ),
inference(resolve,[status(thm)],[c_20,c_3]) ).
cnf(c_21,negated_conjecture,
big_f(A,sK0(A,sK1(A))),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_22,plain,
( ~ big_f(sK1(A),sK0(A,sK1(A)))
| ~ big_f(sK0(A,sK1(A)),sK1(A)) ),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_23,plain,
( ~ big_f(sK1(A),sK0(A,sK1(A)))
| big_f(sK0(A,sK1(A)),sK1(A)) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_24,plain,
big_f(sK1(A),sK0(A,sK1(A))),
inference(resolve,[status(thm)],[c_21,c_2]) ).
cnf(c_25,plain,
big_f(sK0(A,sK1(A)),sK1(A)),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_30,plain,
~ big_f(sK1(A),sK0(A,sK1(A))),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN349+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 17:38:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3413502 was started by sandbox on n003,
% 0.14/0.36 % Sat Sep 26 17:38:54 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 18.
% 0.14/0.39 % Level of proof is 7.
% 0.14/0.39 % Maximum clause weight is 21.000.
% 0.14/0.39 % Given clauses 21.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------