%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN328-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:37:34 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 6 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 97 ( 40 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 42 ( 5 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause3,axiom,
! [VAR_0] :
( f(VAR_0)
| ~ g(y(VAR_0)) ),
file('theBenchmark.p',clause3) ).
cnf(c_1,plain,
( f(A)
| ~ g(y(A)) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause1,axiom,
! [VAR_0] :
( ~ f(VAR_0)
| g(y(VAR_0))
| ~ f(y(VAR_0)) ),
file('theBenchmark.p',clause1) ).
cnf(c_2,plain,
( ~ f(A)
| g(y(A))
| ~ f(y(A)) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause4,axiom,
! [VAR_0] :
( ~ g(VAR_0)
| h(y(VAR_0))
| ~ f(y(VAR_0)) ),
file('theBenchmark.p',clause4) ).
cnf(c_3,plain,
( ~ g(A)
| h(y(A))
| ~ f(y(A)) ),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause5,axiom,
! [VAR_0] :
( g(VAR_0)
| f(y(VAR_0)) ),
file('theBenchmark.p',clause5) ).
cnf(c_4,plain,
( g(A)
| f(y(A)) ),
inference(clausify,[status(thm)],[clause5]) ).
fof(clause6,axiom,
! [VAR_0] :
( g(VAR_0)
| ~ h(y(VAR_0)) ),
file('theBenchmark.p',clause6) ).
cnf(c_5,plain,
( g(A)
| ~ h(y(A)) ),
inference(clausify,[status(thm)],[clause6]) ).
fof(clause9,axiom,
! [VAR_0] :
( h(VAR_0)
| g(y(VAR_0))
| ~ f(y(VAR_0)) ),
file('theBenchmark.p',clause9) ).
cnf(c_7,plain,
( h(A)
| g(y(A))
| ~ f(y(A)) ),
inference(clausify,[status(thm)],[clause9]) ).
fof(clause11,axiom,
! [VAR_0] :
( ~ h(z(VAR_0))
| ~ g(z(VAR_0))
| ~ f(z(VAR_0)) ),
file('theBenchmark.p',clause11) ).
cnf(c_8,plain,
( ~ h(z(A))
| ~ g(z(A))
| ~ f(z(A)) ),
inference(clausify,[status(thm)],[clause11]) ).
cnf(c_10,plain,
( ~ h(y(z(A)))
| ~ h(z(A))
| ~ f(z(A)) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_11,plain,
( f(A)
| h(A)
| ~ f(y(A)) ),
inference(resolve,[status(thm)],[c_7,c_1]) ).
cnf(c_15,plain,
( f(A)
| ~ h(y(y(A))) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_16,plain,
( f(A)
| f(y(y(A))) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_17,plain,
( ~ f(A)
| ~ f(y(A))
| h(y(y(A)))
| ~ f(y(y(A))) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(clause10,axiom,
! [VAR_0] :
( h(VAR_0)
| ~ h(y(VAR_0)) ),
file('theBenchmark.p',clause10) ).
cnf(c_18,plain,
( h(A)
| ~ h(y(A)) ),
inference(clausify,[status(thm)],[clause10]) ).
fof(clause2,axiom,
! [VAR_0] :
( f(VAR_0)
| f(y(VAR_0)) ),
file('theBenchmark.p',clause2) ).
cnf(c_20,plain,
( f(A)
| f(y(A)) ),
inference(clausify,[status(thm)],[clause2]) ).
cnf(c_65,plain,
( f(A)
| h(A)
| f(A) ),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_21,plain,
( h(A)
| f(A) ),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_22,plain,
( h(A)
| f(y(A)) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_24,plain,
( f(A)
| f(y(y(y(A)))) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_30,plain,
( ~ f(y(A))
| ~ f(y(y(A)))
| h(y(y(y(A))))
| f(A) ),
inference(resolve,[status(thm)],[c_24,c_17]) ).
cnf(c_66,plain,
( f(A)
| ~ f(y(A))
| h(y(y(y(A))))
| f(A) ),
inference(resolve,[status(thm)],[c_30,c_16]) ).
cnf(c_49,plain,
( ~ f(y(A))
| h(y(y(y(A))))
| f(A) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_67,plain,
( f(A)
| h(y(y(y(A))))
| f(A) ),
inference(resolve,[status(thm)],[c_49,c_20]) ).
cnf(c_53,plain,
( h(y(y(y(A))))
| f(A) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_54,plain,
( h(y(y(A)))
| f(A) ),
inference(resolve,[status(thm)],[c_53,c_18]) ).
cnf(c_68,plain,
( f(A)
| f(A) ),
inference(resolve,[status(thm)],[c_54,c_15]) ).
cnf(c_57,plain,
f(A),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
( ~ f(A)
| ~ f(y(A))
| h(y(y(A))) ),
inference(resolve,[status(thm)],[c_57,c_17]) ).
cnf(c_70,plain,
( ~ f(A)
| h(y(y(A))) ),
inference(resolve,[status(thm)],[c_57,c_69]) ).
cnf(c_58,plain,
h(y(y(A))),
inference(resolve,[status(thm)],[c_57,c_70]) ).
cnf(c_60,plain,
( ~ h(y(z(A)))
| ~ h(z(A)) ),
inference(resolve,[status(thm)],[c_57,c_10]) ).
cnf(c_61,plain,
h(y(A)),
inference(resolve,[status(thm)],[c_58,c_18]) ).
cnf(c_62,plain,
~ h(z(A)),
inference(resolve,[status(thm)],[c_61,c_60]) ).
cnf(c_63,plain,
h(A),
inference(resolve,[status(thm)],[c_61,c_18]) ).
cnf(c_64,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN328-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 17:30:04 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1266986 was started by sandbox2 on n017,
% 0.13/0.36 % Sat Sep 26 17:30:04 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/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 Unsatisfiable 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 28.
% 0.13/0.38 % Level of proof is 13.
% 0.13/0.38 % Maximum clause weight is 14.000.
% 0.13/0.38 % Given clauses 35.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------