%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN354+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 : n008.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 09:37:40 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 118 ( 39 ~; 41 |; 22 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 20 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_20_1,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(Y1,Y2)
& big_f(X2,Y1)
& big_f(X1,Y1) ) ) ) ) ),
file('theBenchmark.p',church_46_20_1) ).
fof(church_46_20_1_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(Y1,Y2)
& big_f(X2,Y1)
& big_f(X1,Y1) ) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_20_1]) ).
fof(nnf_1,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(X2,Y1)
| ~ big_f(X1,Y1) )
& ( ~ big_g(Y1,Z)
| big_g(X2,Z) )
& ( big_g(Y1,Z)
| ~ big_g(X2,Z) )
& ( big_f(X2,Y2)
| ~ big_f(Y1,Y2)
| ( ( ~ big_g(Y2,Z)
| ~ big_g(X2,Z) )
& ( big_g(Y2,Z)
| big_g(X2,Z) ) ) )
& big_g(X1,X2)
& big_f(X1,X2) ),
inference(fof_nnf,[status(thm)],[church_46_20_1_neg]) ).
fof(sk_church_46_20_1_neg_sk,plain,
! [Y1,Y2] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(sK1,Y1)
| ~ big_f(sK0,Y1) )
& ( ~ big_g(Y1,sK2(Y1,Y2))
| big_g(sK1,sK2(Y1,Y2)) )
& ( big_g(Y1,sK2(Y1,Y2))
| ~ big_g(sK1,sK2(Y1,Y2)) )
& ( big_f(sK1,Y2)
| ~ big_f(Y1,Y2)
| ( ( ~ big_g(Y2,sK2(Y1,Y2))
| ~ big_g(sK1,sK2(Y1,Y2)) )
& ( big_g(Y2,sK2(Y1,Y2))
| big_g(sK1,sK2(Y1,Y2)) ) ) )
& big_g(sK0,sK1)
& big_f(sK0,sK1) ),
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_20_1_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_f(VAR_0,VAR_1)
| ~ big_f(sK1,VAR_0)
| ~ big_f(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ big_g(VAR_0,sK2(VAR_0,VAR_1))
| big_g(sK1,sK2(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_0,sK2(VAR_0,VAR_1))
| ~ big_g(sK1,sK2(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK1,VAR_1)
| ~ big_f(VAR_0,VAR_1)
| ~ big_g(VAR_1,sK2(VAR_0,VAR_1))
| ~ big_g(sK1,sK2(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK1,VAR_1)
| ~ big_f(VAR_0,VAR_1)
| big_g(VAR_1,sK2(VAR_0,VAR_1))
| big_g(sK1,sK2(VAR_0,VAR_1)) )
& big_g(sK0,sK1)
& big_f(sK0,sK1) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_20_1_neg_sk]) ).
cnf(c_2,negated_conjecture,
big_f(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_church_46_20_1_neg]) ).
cnf(c_4,negated_conjecture,
( big_f(sK1,B)
| ~ big_f(A,B)
| big_g(B,sK2(A,B))
| big_g(sK1,sK2(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_20_1_neg]) ).
cnf(c_5,negated_conjecture,
( big_f(sK1,B)
| ~ big_f(A,B)
| ~ big_g(B,sK2(A,B))
| ~ big_g(sK1,sK2(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_20_1_neg]) ).
cnf(c_8,negated_conjecture,
( ~ big_f(A,B)
| ~ big_f(sK1,A)
| ~ big_f(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_20_1_neg]) ).
cnf(c_17,plain,
( ~ big_f(sK1,sK1)
| ~ big_f(sK0,sK1) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_12,negated_conjecture,
~ big_f(sK1,sK1),
inference(resolve,[status(thm)],[c_2,c_17]) ).
cnf(c_18,negated_conjecture,
( big_f(sK1,sK1)
| big_g(sK1,sK2(sK0,sK1))
| big_g(sK1,sK2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_19,negated_conjecture,
( big_f(sK1,sK1)
| big_g(sK1,sK2(sK0,sK1)) ),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_15,negated_conjecture,
big_g(sK1,sK2(sK0,sK1)),
inference(resolve,[status(thm)],[c_12,c_19]) ).
cnf(c_20,negated_conjecture,
( big_f(sK1,sK1)
| ~ big_g(sK1,sK2(sK0,sK1))
| ~ big_g(sK1,sK2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_21,negated_conjecture,
( big_f(sK1,sK1)
| ~ big_g(sK1,sK2(sK0,sK1)) ),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
big_f(sK1,sK1),
inference(resolve,[status(thm)],[c_15,c_21]) ).
cnf(c_16,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_12,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN354+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 : n008.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 17:37:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4168014 was started by sandbox on n008,
% 0.10/0.37 % Sat Sep 26 17:37:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 8.
% 0.10/0.38 % Level of proof is 4.
% 0.10/0.38 % Maximum clause weight is 16.000.
% 0.10/0.38 % Given clauses 4.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------