%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN345+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 : n004.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 09:37:38 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 5 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 126 ( 40 ~; 46 |; 20 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 9 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_16_4,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( ( ( big_f(X1,X2,Y1)
=> big_f(Y2,Y1,Z) )
=> ( big_f(X1,X1,X2)
=> big_f(X1,X2,X2) ) )
=> ( ( ( big_f(X2,Y1,Y2)
=> big_f(Y1,Z,Z) )
=> ( big_f(X1,X2,X2)
=> big_f(X1,X1,X2) ) )
=> ( big_f(Y1,Y2,Z)
=> ( ( big_f(X1,X1,X2)
<=> big_f(X1,X2,X2) )
& big_f(X2,X2,Y1) ) ) ) ),
file('theBenchmark.p',church_46_16_4) ).
fof(church_46_16_4_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( ( ( big_f(X1,X2,Y1)
=> big_f(Y2,Y1,Z) )
=> ( big_f(X1,X1,X2)
=> big_f(X1,X2,X2) ) )
=> ( ( ( big_f(X2,Y1,Y2)
=> big_f(Y1,Z,Z) )
=> ( big_f(X1,X2,X2)
=> big_f(X1,X1,X2) ) )
=> ( big_f(Y1,Y2,Z)
=> ( ( big_f(X1,X1,X2)
<=> big_f(X1,X2,X2) )
& big_f(X2,X2,Y1) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_16_4]) ).
fof(nnf_1,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( ~ big_f(X1,X2,X2)
| ~ big_f(X1,X1,X2) )
& ( big_f(X1,X2,X2)
| big_f(X1,X1,X2) ) )
| ~ big_f(X2,X2,Y1) )
& big_f(Y1,Y2,Z)
& ( big_f(X1,X1,X2)
| ~ big_f(X1,X2,X2)
| ( ~ big_f(Y1,Z,Z)
& big_f(X2,Y1,Y2) ) )
& ( big_f(X1,X2,X2)
| ~ big_f(X1,X1,X2)
| ( ~ big_f(Y2,Y1,Z)
& big_f(X1,X2,Y1) ) ) ),
inference(fof_nnf,[status(thm)],[church_46_16_4_neg]) ).
fof(sk_church_46_16_4_neg_sk,plain,
! [Y1,Y2] :
( ( ( ( ~ big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1) )
& ( big_f(sK0,sK1,sK1)
| big_f(sK0,sK0,sK1) ) )
| ~ big_f(sK1,sK1,Y1) )
& big_f(Y1,Y2,sK2(Y1,Y2))
& ( big_f(sK0,sK0,sK1)
| ~ big_f(sK0,sK1,sK1)
| ( ~ big_f(Y1,sK2(Y1,Y2),sK2(Y1,Y2))
& big_f(sK1,Y1,Y2) ) )
& ( big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1)
| ( ~ big_f(Y2,Y1,sK2(Y1,Y2))
& big_f(sK0,sK1,Y1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(Z,sK2(Y1,Y2))],[nnf_1]) ).
fof(sk_church_46_16_4_neg,plain,
( ! [VAR_0] :
( ~ big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1)
| ~ big_f(sK1,sK1,VAR_0) )
& ! [VAR_0] :
( big_f(sK0,sK1,sK1)
| big_f(sK0,sK0,sK1)
| ~ big_f(sK1,sK1,VAR_0) )
& ! [VAR_0,VAR_1] : big_f(VAR_0,VAR_1,sK2(VAR_0,VAR_1))
& ! [VAR_0,VAR_1] :
( big_f(sK0,sK0,sK1)
| ~ big_f(sK0,sK1,sK1)
| ~ big_f(VAR_0,sK2(VAR_0,VAR_1),sK2(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK0,sK0,sK1)
| ~ big_f(sK0,sK1,sK1)
| big_f(sK1,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1)
| ~ big_f(VAR_0,VAR_1,sK2(VAR_1,VAR_0)) )
& ! [VAR_0] :
( big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1)
| big_f(sK0,sK1,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_16_4_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1)
| big_f(sK0,sK1,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_16_4_neg]) ).
cnf(c_4,negated_conjecture,
( big_f(sK0,sK0,sK1)
| ~ big_f(sK0,sK1,sK1)
| big_f(sK1,A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_16_4_neg]) ).
cnf(c_5,negated_conjecture,
( big_f(sK0,sK0,sK1)
| ~ big_f(sK0,sK1,sK1)
| ~ big_f(A,sK2(A,B),sK2(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_16_4_neg]) ).
cnf(c_6,negated_conjecture,
big_f(A,B,sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_church_46_16_4_neg]) ).
cnf(c_7,negated_conjecture,
( big_f(sK0,sK1,sK1)
| big_f(sK0,sK0,sK1)
| ~ big_f(sK1,sK1,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_16_4_neg]) ).
cnf(c_8,negated_conjecture,
( ~ big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1)
| ~ big_f(sK1,sK1,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_16_4_neg]) ).
cnf(c_9,plain,
( ~ big_f(sK0,sK0,sK1)
| big_f(sK0,sK1,sK1) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_10,plain,
( big_f(sK0,sK1,sK1)
| big_f(sK0,sK0,sK1) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_11,plain,
( ~ big_f(sK0,sK1,sK1)
| ~ big_f(sK0,sK0,sK1) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_17,negated_conjecture,
( big_f(sK0,sK0,sK1)
| ~ big_f(A,sK2(A,B),sK2(A,B))
| big_f(sK0,sK0,sK1) ),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_12,negated_conjecture,
( ~ big_f(A,sK2(A,B),sK2(A,B))
| big_f(sK0,sK0,sK1) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_18,negated_conjecture,
( big_f(sK0,sK0,sK1)
| big_f(sK1,A,B)
| big_f(sK0,sK0,sK1) ),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_13,negated_conjecture,
( big_f(sK1,A,B)
| big_f(sK0,sK0,sK1) ),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_19,plain,
( big_f(sK0,sK0,sK1)
| big_f(sK0,sK0,sK1) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_14,plain,
big_f(sK0,sK0,sK1),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_15,plain,
~ big_f(sK0,sK1,sK1),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_20,plain,
~ big_f(sK0,sK0,sK1),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_16,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN345+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n004.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 17:36:21 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2251997 was started by sandbox2 on n004,
% 0.16/0.44 % Sat Sep 26 17:36:21 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 15.
% 0.16/0.46 % Level of proof is 6.
% 0.16/0.46 % Maximum clause weight is 16.000.
% 0.16/0.46 % Given clauses 10.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------