%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN075-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 6 unt; 0 def)
% Number of atoms : 83 ( 54 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 90 ( 42 ~; 48 |; 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 : 58 ( 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_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_34,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_34]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1] :
( f(VAR_1) = VAR_1
| VAR_0 != g(VAR_1)
| ~ big_f(VAR_0,f(VAR_1)) ),
file('theBenchmark.p',clause_4) ).
cnf(c_7,plain,
( f(B) = B
| A != g(B)
| ~ big_f(A,f(B)) ),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_8,plain,
( f(B) = B
| g(B) != A
| ~ big_f(A,f(B)) ),
inference(copy,[status(thm)],[c_7]) ).
fof(clause_6,axiom,
! [VAR_0,VAR_1] :
( f(VAR_1) = VAR_1
| big_f(VAR_0,f(VAR_1))
| VAR_0 != g(VAR_1) ),
file('theBenchmark.p',clause_6) ).
cnf(c_10,plain,
( f(B) = B
| big_f(A,f(B))
| A != g(B) ),
inference(clausify,[status(thm)],[clause_6]) ).
cnf(c_11,plain,
( f(A) = A
| big_f(B,f(A))
| g(A) != B ),
inference(copy,[status(thm)],[c_10]) ).
fof(clause_9,axiom,
! [VAR_0,VAR_1] :
( h(VAR_0,VAR_1) = VAR_1
| big_f(h(VAR_0,VAR_1),f(VAR_0))
| f(VAR_0) != VAR_0 ),
file('theBenchmark.p',clause_9) ).
cnf(c_16,plain,
( h(A,B) = B
| big_f(h(A,B),f(A))
| f(A) != A ),
inference(clausify,[status(thm)],[clause_9]) ).
fof(clause_10,axiom,
! [VAR_0,VAR_1] :
( ~ big_f(h(VAR_0,VAR_1),f(VAR_0))
| h(VAR_0,VAR_1) != VAR_1
| f(VAR_0) != VAR_0 ),
file('theBenchmark.p',clause_10) ).
cnf(c_17,plain,
( ~ big_f(h(A,B),f(A))
| h(A,B) != B
| f(A) != A ),
inference(clausify,[status(thm)],[clause_10]) ).
cnf(c_19,plain,
( big_f(a,A)
| b != A ),
inference(xxres,[status(thm)],[c_6]) ).
cnf(c_21,plain,
( f(A) = A
| big_f(g(A),f(A)) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_23,plain,
big_f(a,b),
inference(xxres,[status(thm)],[c_19]) ).
cnf(c_35,plain,
( f(A) = A
| g(A) != g(A)
| f(A) = A ),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_36,plain,
( f(A) = A
| f(A) = A ),
inference(copy,[status(thm)],[c_35]) ).
cnf(c_24,plain,
f(A) = A,
inference(copy,[status(thm)],[c_36]) ).
cnf(c_37,plain,
( ~ big_f(h(A,B),f(A))
| h(A,B) != B
| A != A ),
inference(paramod,[status(thm)],[c_24,c_17]) ).
cnf(c_38,plain,
( ~ big_f(h(A,B),A)
| h(A,B) != B
| A != A ),
inference(paramod,[status(thm)],[c_24,c_37]) ).
cnf(c_27,plain,
( ~ big_f(h(A,B),A)
| h(A,B) != B ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_39,plain,
( h(A,B) = B
| big_f(h(A,B),f(A))
| A != A ),
inference(paramod,[status(thm)],[c_24,c_16]) ).
cnf(c_40,plain,
( h(A,B) = B
| big_f(h(A,B),A)
| A != A ),
inference(paramod,[status(thm)],[c_24,c_39]) ).
cnf(c_28,plain,
( h(A,B) = B
| big_f(h(A,B),A) ),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_41,plain,
( a = h(A,B)
| h(A,B) = B ),
inference(resolve,[status(thm)],[c_28,c_2]) ).
cnf(c_30,plain,
( h(A,B) = a
| h(A,B) = B ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_31,plain,
h(A,a) = a,
inference(factor,[status(thm)],[c_30]) ).
cnf(c_42,plain,
~ big_f(h(A,a),A),
inference(resolve,[status(thm)],[c_27,c_31]) ).
cnf(c_32,plain,
~ big_f(a,A),
inference(paramod,[status(thm)],[c_31,c_42]) ).
cnf(c_33,plain,
$false,
inference(resolve,[status(thm)],[c_32,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:09:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3223684 was started by sandbox2 on n013,
% 0.08/0.36 % Sat Sep 26 17:09:06 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.37
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.37
% 0.14/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.37 % Length of proof is 20.
% 0.14/0.37 % Level of proof is 8.
% 0.14/0.37 % Maximum clause weight is 15.000.
% 0.14/0.37 % Given clauses 18.
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------