%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN074-1 : TPTP v9.3.1. Released v1.0.0.
% 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 09:36:58 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 6 unt; 0 def)
% Number of atoms : 75 ( 47 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 77 ( 36 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = a
| ~ big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( A = a
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[clause_1]) ).
cnf(c_2,plain,
( a = A
| ~ big_f(A,B) ),
inference(copy,[status(thm)],[c_1]) ).
fof(clause_2,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = b
| ~ big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_2) ).
cnf(c_3,plain,
( B = b
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[clause_2]) ).
cnf(c_4,plain,
( b = B
| ~ big_f(A,B) ),
inference(copy,[status(thm)],[c_3]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( big_f(VAR_0,VAR_1)
| VAR_1 != b
| VAR_0 != a ),
file('theBenchmark.p',clause_3) ).
cnf(c_5,plain,
( big_f(A,B)
| B != b
| A != a ),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_63,plain,
( big_f(A,B)
| B != b
| a != A ),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_6,plain,
( big_f(A,B)
| b != B
| a != A ),
inference(copy,[status(thm)],[c_63]) ).
fof(clause_8,axiom,
! [VAR_0,VAR_1] :
( f(VAR_1) = VAR_1
| big_f(f(VAR_1),VAR_0)
| VAR_0 != g(VAR_1) ),
file('theBenchmark.p',clause_8) ).
cnf(c_15,plain,
( f(B) = B
| big_f(f(B),A)
| A != g(B) ),
inference(clausify,[status(thm)],[clause_8]) ).
cnf(c_16,plain,
( f(A) = A
| big_f(f(A),B)
| g(A) != B ),
inference(copy,[status(thm)],[c_15]) ).
fof(clause_10,axiom,
! [VAR_0,VAR_1] :
( h(VAR_0,VAR_1) = VAR_1
| big_f(f(VAR_0),h(VAR_0,VAR_1))
| f(VAR_0) != VAR_0 ),
file('theBenchmark.p',clause_10) ).
cnf(c_19,plain,
( h(A,B) = B
| big_f(f(A),h(A,B))
| f(A) != A ),
inference(clausify,[status(thm)],[clause_10]) ).
fof(clause_11,axiom,
! [VAR_0,VAR_1] :
( ~ big_f(f(VAR_0),h(VAR_0,VAR_1))
| h(VAR_0,VAR_1) != VAR_1
| f(VAR_0) != VAR_0 ),
file('theBenchmark.p',clause_11) ).
cnf(c_20,plain,
( ~ big_f(f(A),h(A,B))
| h(A,B) != B
| f(A) != A ),
inference(clausify,[status(thm)],[clause_11]) ).
cnf(c_23,plain,
( big_f(a,A)
| b != A ),
inference(xxres,[status(thm)],[c_6]) ).
cnf(c_26,plain,
( f(A) = A
| big_f(f(A),g(A)) ),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_27,plain,
big_f(a,b),
inference(xxres,[status(thm)],[c_23]) ).
cnf(c_64,plain,
( a = f(A)
| f(A) = A ),
inference(resolve,[status(thm)],[c_26,c_2]) ).
cnf(c_29,plain,
( f(A) = a
| f(A) = A ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_30,plain,
f(a) = a,
inference(factor,[status(thm)],[c_29]) ).
cnf(c_65,plain,
( h(a,A) = A
| big_f(f(a),h(a,A)) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_31,plain,
( h(a,A) = A
| big_f(a,h(a,A)) ),
inference(paramod,[status(thm)],[c_30,c_65]) ).
cnf(c_66,plain,
( ~ big_f(a,h(a,A))
| h(a,A) != A
| f(a) != a ),
inference(paramod,[status(thm)],[c_30,c_20]) ).
cnf(c_67,plain,
( ~ big_f(a,h(a,A))
| h(a,A) != A
| a != a ),
inference(paramod,[status(thm)],[c_30,c_66]) ).
cnf(c_34,plain,
( ~ big_f(a,h(a,A))
| h(a,A) != A ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_68,plain,
( b = h(a,A)
| h(a,A) = A ),
inference(resolve,[status(thm)],[c_31,c_4]) ).
cnf(c_60,plain,
( h(a,A) = b
| h(a,A) = A ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_61,plain,
h(a,b) = b,
inference(factor,[status(thm)],[c_60]) ).
cnf(c_69,plain,
~ big_f(a,h(a,b)),
inference(resolve,[status(thm)],[c_34,c_61]) ).
cnf(c_70,plain,
~ big_f(a,b),
inference(paramod,[status(thm)],[c_61,c_69]) ).
cnf(c_62,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN074-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 17:12:25 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1535581 was started by sandbox on n026,
% 0.11/0.37 % Sat Sep 26 17:12:25 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % 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 0.01 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 20.
% 0.15/0.39 % Level of proof is 8.
% 0.15/0.39 % Maximum clause weight is 15.000.
% 0.15/0.39 % Given clauses 26.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------