%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN332-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 69 ( 37 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 47 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause2,axiom,
! [VAR_0,VAR_1] :
( f(VAR_1,z(VAR_1,VAR_0))
| f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause2) ).
cnf(c_2,plain,
( f(B,z(B,A))
| f(A,B) ),
inference(clausify,[status(thm)],[clause2]) ).
fof(clause3,axiom,
! [VAR_0,VAR_1] :
( ~ f(VAR_0,z(VAR_0,VAR_1))
| ~ f(VAR_1,VAR_0)
| ~ f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause3) ).
cnf(c_3,plain,
( ~ f(A,z(A,B))
| ~ f(B,A)
| ~ f(A,B) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause5,axiom,
! [VAR_0,VAR_1] :
( f(z(VAR_0,VAR_1),VAR_0)
| ~ f(VAR_0,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause5) ).
cnf(c_5,plain,
( f(z(A,B),A)
| ~ f(A,z(A,B)) ),
inference(clausify,[status(thm)],[clause5]) ).
fof(clause7,axiom,
! [VAR_0,VAR_1] :
( f(VAR_1,z(VAR_0,VAR_1))
| ~ f(VAR_0,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause7) ).
cnf(c_7,plain,
( f(B,z(A,B))
| ~ f(A,z(A,B)) ),
inference(clausify,[status(thm)],[clause7]) ).
fof(clause8,axiom,
! [VAR_0,VAR_1] :
( ~ f(z(VAR_1,VAR_0),z(VAR_1,VAR_0))
| f(VAR_1,VAR_0)
| ~ f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause8) ).
cnf(c_8,plain,
( ~ f(z(B,A),z(B,A))
| f(B,A)
| ~ f(A,B) ),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause13,axiom,
! [VAR_0,VAR_1] :
( ~ f(z(VAR_0,VAR_1),VAR_1)
| f(VAR_1,VAR_0)
| f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause13) ).
cnf(c_13,plain,
( ~ f(z(A,B),B)
| f(B,A)
| f(A,B) ),
inference(clausify,[status(thm)],[clause13]) ).
fof(clause14,axiom,
! [VAR_0,VAR_1] :
( ~ f(z(VAR_0,VAR_1),VAR_1)
| ~ f(VAR_1,VAR_0)
| ~ f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause14) ).
cnf(c_14,plain,
( ~ f(z(A,B),B)
| ~ f(B,A)
| ~ f(A,B) ),
inference(clausify,[status(thm)],[clause14]) ).
cnf(c_15,plain,
( ~ f(A,z(A,A))
| ~ f(A,A) ),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_16,plain,
( ~ f(z(A,A),A)
| f(A,A) ),
inference(factor,[status(thm)],[c_13]) ).
cnf(c_17,plain,
( ~ f(z(A,A),A)
| ~ f(A,A) ),
inference(factor,[status(thm)],[c_14]) ).
cnf(c_20,plain,
( f(z(A,B),z(z(A,B),A))
| ~ f(B,A)
| ~ f(A,B) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_21,plain,
( f(z(A,A),z(z(A,A),A))
| ~ f(A,A) ),
inference(factor,[status(thm)],[c_20]) ).
cnf(c_22,plain,
( f(B,A)
| f(z(A,B),A) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_57,plain,
( f(A,A)
| f(A,A) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_38,plain,
f(A,A),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_41,plain,
f(z(A,A),z(z(A,A),A)),
inference(resolve,[status(thm)],[c_38,c_21]) ).
cnf(c_42,plain,
~ f(z(A,A),A),
inference(resolve,[status(thm)],[c_38,c_17]) ).
cnf(c_43,plain,
~ f(A,z(A,A)),
inference(resolve,[status(thm)],[c_38,c_15]) ).
cnf(c_44,plain,
( f(B,A)
| ~ f(A,B) ),
inference(resolve,[status(thm)],[c_38,c_8]) ).
cnf(c_58,plain,
( ~ f(z(z(A,A),A),A)
| f(A,z(A,A)) ),
inference(resolve,[status(thm)],[c_13,c_42]) ).
cnf(c_49,plain,
~ f(z(z(A,A),A),A),
inference(resolve,[status(thm)],[c_58,c_43]) ).
cnf(c_52,plain,
~ f(A,z(z(A,A),A)),
inference(resolve,[status(thm)],[c_44,c_49]) ).
cnf(c_59,plain,
~ f(z(A,A),z(z(A,A),A)),
inference(resolve,[status(thm)],[c_7,c_52]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_41,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN332-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:37:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.37 % Process 1564239 was started by sandbox on n026,
% 0.15/0.37 % Sat Sep 26 17:37:56 2026
% 0.15/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 21.
% 0.15/0.39 % Level of proof is 6.
% 0.15/0.39 % Maximum clause weight is 15.000.
% 0.15/0.39 % Given clauses 27.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------