%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN069-1 : 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 : n011.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 09:36:57 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.68s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 8 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 163 ( 83 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_5,axiom,
big_f(a),
file('theBenchmark.p',clause_5) ).
cnf(c_1,plain,
big_f(a),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( big_k(VAR_1)
| ~ big_h(VAR_0,VAR_1)
| ~ big_g(VAR_1)
| ~ big_j(VAR_0,f(VAR_0))
| ~ big_f(VAR_0) ),
file('theBenchmark.p',clause_3) ).
cnf(c_2,plain,
( big_k(B)
| ~ big_h(A,B)
| ~ big_g(B)
| ~ big_j(A,f(A))
| ~ big_f(A) ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_2,axiom,
! [VAR_0,VAR_1] :
( big_k(VAR_1)
| ~ big_h(VAR_0,VAR_1)
| ~ big_g(VAR_1)
| big_h(VAR_0,f(VAR_0))
| ~ big_f(VAR_0) ),
file('theBenchmark.p',clause_2) ).
cnf(c_3,plain,
( big_k(B)
| ~ big_h(A,B)
| ~ big_g(B)
| big_h(A,f(A))
| ~ big_f(A) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( big_k(VAR_1)
| ~ big_h(VAR_0,VAR_1)
| ~ big_g(VAR_1)
| big_g(f(VAR_0))
| ~ big_f(VAR_0) ),
file('theBenchmark.p',clause_1) ).
cnf(c_4,plain,
( big_k(B)
| ~ big_h(A,B)
| ~ big_g(B)
| big_g(f(A))
| ~ big_f(A) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_8,axiom,
! [VAR_0] :
( big_g(g(VAR_0))
| ~ big_f(VAR_0) ),
file('theBenchmark.p',clause_8) ).
cnf(c_5,plain,
( big_g(g(A))
| ~ big_f(A) ),
inference(clausify,[status(thm)],[clause_8]) ).
fof(clause_9,axiom,
! [VAR_0] :
( big_h(VAR_0,g(VAR_0))
| ~ big_f(VAR_0) ),
file('theBenchmark.p',clause_9) ).
cnf(c_6,plain,
( big_h(A,g(A))
| ~ big_f(A) ),
inference(clausify,[status(thm)],[clause_9]) ).
fof(clause_4,axiom,
! [VAR_0] :
( ~ big_k(VAR_0)
| ~ big_l(VAR_0) ),
file('theBenchmark.p',clause_4) ).
cnf(c_7,plain,
( ~ big_k(A)
| ~ big_l(A) ),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_8,plain,
( big_k(A)
| ~ big_h(a,A)
| ~ big_g(A)
| ~ big_j(a,f(a)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
( big_k(A)
| ~ big_h(a,A)
| ~ big_g(A)
| big_h(a,f(a)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
( big_k(A)
| ~ big_h(a,A)
| ~ big_g(A)
| big_g(f(a)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(clause_7,axiom,
! [VAR_0] :
( big_j(a,VAR_0)
| ~ big_h(a,VAR_0)
| ~ big_g(VAR_0) ),
file('theBenchmark.p',clause_7) ).
cnf(c_11,plain,
( big_j(a,A)
| ~ big_h(a,A)
| ~ big_g(A) ),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_12,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| ~ big_j(a,f(a))
| ~ big_l(A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
fof(clause_6,axiom,
! [VAR_0] :
( big_l(VAR_0)
| ~ big_h(a,VAR_0) ),
file('theBenchmark.p',clause_6) ).
cnf(c_13,plain,
( big_l(A)
| ~ big_h(a,A) ),
inference(clausify,[status(thm)],[clause_6]) ).
cnf(c_14,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| ~ big_l(A)
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_15,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| big_h(a,f(a))
| ~ big_l(A) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_16,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| big_g(f(a))
| ~ big_l(A) ),
inference(resolve,[status(thm)],[c_7,c_10]) ).
cnf(c_17,plain,
( ~ big_h(a,A)
| ~ big_h(a,A)
| ~ big_g(A)
| big_g(f(a)) ),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_18,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| big_g(f(a)) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_19,plain,
( ~ big_h(a,A)
| ~ big_h(a,A)
| ~ big_g(A)
| big_h(a,f(a)) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_20,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| big_h(a,f(a)) ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_21,plain,
( ~ big_h(a,A)
| ~ big_g(A)
| ~ big_h(a,f(a))
| ~ big_g(f(a))
| ~ big_h(a,A) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_22,plain,
( ~ big_g(A)
| ~ big_h(a,f(a))
| ~ big_g(f(a))
| ~ big_h(a,A) ),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_23,plain,
big_g(g(a)),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_24,plain,
big_h(a,g(a)),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_31,plain,
( ~ big_h(a,f(a))
| ~ big_g(f(a))
| ~ big_h(a,g(a)) ),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_27,plain,
( ~ big_h(a,f(a))
| ~ big_g(f(a)) ),
inference(resolve,[status(thm)],[c_24,c_31]) ).
cnf(c_32,plain,
( ~ big_h(a,g(a))
| big_h(a,f(a)) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_28,plain,
big_h(a,f(a)),
inference(resolve,[status(thm)],[c_32,c_24]) ).
cnf(c_33,plain,
( ~ big_h(a,g(a))
| big_g(f(a)) ),
inference(resolve,[status(thm)],[c_18,c_23]) ).
cnf(c_29,plain,
big_g(f(a)),
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_34,plain,
~ big_h(a,f(a)),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_30,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.65 % Computer : n011.cluster.edu
% 0.17/5.65 % Model : x86_64 x86_64
% 0.17/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.65 % Memory : 8046.5625MB
% 0.17/5.65 % OS : Linux 6.8.0-71-generic
% 0.17/5.65 % CPULimit : 300
% 0.17/5.65 % WCLimit : 300
% 0.17/5.65 % DateTime : Sat Sep 26 17:09:05 UTC 2026
% 0.17/5.66 % CPUTime :
% 0.17/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.66 % Process 1117436 was started by sandbox on n011,
% 0.17/5.66 % Sat Sep 26 17:09:05 2026
% 0.17/5.66 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.66
% 0.17/5.66 % From the command line: assign(max_seconds, 300).
% 0.17/5.68
% 0.17/5.68 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.68
% 0.17/5.68 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/5.68 % Length of proof is 28.
% 0.17/5.68 % Level of proof is 7.
% 0.17/5.68 % Maximum clause weight is 12.000.
% 0.17/5.68 % Given clauses 5.
% 0.17/5.68
% 0.17/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------