%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN059+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 09:36:54 AM UTC 2026
% Result : Theorem 0.09s 5.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 3
% Syntax : Number of formulae : 84 ( 18 unt; 0 def)
% Number of atoms : 306 ( 0 equ)
% Maximal formula atoms : 60 ( 3 avg)
% Number of connectives : 337 ( 115 ~; 179 |; 35 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 59 ( 14 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel29_1,axiom,
? [X] : big_f(X),
file('theBenchmark.p',pel29_1) ).
fof(pel29_2,axiom,
? [Y] : big_g(Y),
file('theBenchmark.p',pel29_2) ).
fof(pel29,conjecture,
( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
file('theBenchmark.p',pel29) ).
fof(pel29_neg,negated_conjecture,
~ ( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
inference(assume_negation,[status(cth)],[pel29]) ).
fof(nnf_1,plain,
? [X] : big_f(X),
inference(fof_nnf,[status(thm)],[pel29_1]) ).
fof(sk_pel29_1,plain,
big_f(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_1]) ).
cnf(c_4,plain,
big_f(sK0),
inference(split_conjunct,[status(thm)],[sk_pel29_1]) ).
fof(nnf_2,plain,
? [Y] : big_g(Y),
inference(fof_nnf,[status(thm)],[pel29_2]) ).
fof(sk_pel29_2,plain,
big_g(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1)],[nnf_2]) ).
cnf(c_5,plain,
big_g(sK1),
inference(split_conjunct,[status(thm)],[sk_pel29_2]) ).
fof(nnf_3,plain,
( ( ? [W,Y] :
( ( ~ big_j(Y)
| ~ big_h(W) )
& big_g(Y)
& big_f(W) )
| ? [U] :
( ~ big_j(U)
& big_g(U) )
| ? [X] :
( ~ big_h(X)
& big_f(X) ) )
& ( ! [X2,X3] :
( ( big_j(X3)
& big_h(X2) )
| ~ big_g(X3)
| ~ big_f(X2) )
| ( ! [X1] :
( big_j(X1)
| ~ big_g(X1) )
& ! [X0] :
( big_h(X0)
| ~ big_f(X0) ) ) ) ),
inference(fof_nnf,[status(thm)],[pel29_neg]) ).
fof(sk_pel29_neg_sk,plain,
( ( ( ( ~ big_j(sK5)
| ~ big_h(sK4) )
& big_g(sK5)
& big_f(sK4) )
| ( ~ big_j(sK3)
& big_g(sK3) )
| ( ~ big_h(sK2)
& big_f(sK2) ) )
& ( ! [X2,X3] :
( ( big_j(X3)
& big_h(X2) )
| ~ big_g(X3)
| ~ big_f(X2) )
| ( ! [X1] :
( big_j(X1)
| ~ big_g(X1) )
& ! [X0] :
( big_h(X0)
| ~ big_f(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X,sK2),skolemize(U,sK3),skolemize(W,sK4),skolemize(Y,sK5)],[nnf_3]) ).
fof(sk_pel29_neg,plain,
( ( ~ big_j(sK5)
| ~ big_h(sK4)
| ~ big_j(sK3)
| ~ big_h(sK2) )
& ( big_g(sK5)
| ~ big_j(sK3)
| ~ big_h(sK2) )
& ( big_f(sK4)
| ~ big_j(sK3)
| ~ big_h(sK2) )
& ( ~ big_j(sK5)
| ~ big_h(sK4)
| big_g(sK3)
| ~ big_h(sK2) )
& ( big_g(sK5)
| big_g(sK3)
| ~ big_h(sK2) )
& ( big_f(sK4)
| big_g(sK3)
| ~ big_h(sK2) )
& ( ~ big_j(sK5)
| ~ big_h(sK4)
| ~ big_j(sK3)
| big_f(sK2) )
& ( big_g(sK5)
| ~ big_j(sK3)
| big_f(sK2) )
& ( big_f(sK4)
| ~ big_j(sK3)
| big_f(sK2) )
& ( ~ big_j(sK5)
| ~ big_h(sK4)
| big_g(sK3)
| big_f(sK2) )
& ( big_g(sK5)
| big_g(sK3)
| big_f(sK2) )
& ( big_f(sK4)
| big_g(sK3)
| big_f(sK2) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_j(VAR_2)
| ~ big_g(VAR_2)
| ~ big_f(VAR_1)
| big_j(VAR_0)
| ~ big_g(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_h(VAR_1)
| ~ big_g(VAR_2)
| ~ big_f(VAR_1)
| big_j(VAR_0)
| ~ big_g(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_j(VAR_2)
| ~ big_g(VAR_2)
| ~ big_f(VAR_1)
| big_h(VAR_0)
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_h(VAR_1)
| ~ big_g(VAR_2)
| ~ big_f(VAR_1)
| big_h(VAR_0)
| ~ big_f(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel29_neg_sk]) ).
cnf(c_6,negated_conjecture,
( big_h(B)
| ~ big_g(C)
| ~ big_f(B)
| big_h(A)
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_9,negated_conjecture,
( big_j(C)
| ~ big_g(C)
| ~ big_f(B)
| big_j(A)
| ~ big_g(A) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_10,negated_conjecture,
( big_f(sK4)
| big_g(sK3)
| big_f(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_11,negated_conjecture,
( big_g(sK5)
| big_g(sK3)
| big_f(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_12,negated_conjecture,
( ~ big_j(sK5)
| ~ big_h(sK4)
| big_g(sK3)
| big_f(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_13,negated_conjecture,
( big_f(sK4)
| ~ big_j(sK3)
| big_f(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_14,negated_conjecture,
( big_g(sK5)
| ~ big_j(sK3)
| big_f(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_15,negated_conjecture,
( ~ big_j(sK5)
| ~ big_h(sK4)
| ~ big_j(sK3)
| big_f(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_16,negated_conjecture,
( big_f(sK4)
| big_g(sK3)
| ~ big_h(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_17,negated_conjecture,
( big_g(sK5)
| big_g(sK3)
| ~ big_h(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_18,negated_conjecture,
( ~ big_j(sK5)
| ~ big_h(sK4)
| big_g(sK3)
| ~ big_h(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_19,negated_conjecture,
( big_f(sK4)
| ~ big_j(sK3)
| ~ big_h(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_20,negated_conjecture,
( big_g(sK5)
| ~ big_j(sK3)
| ~ big_h(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_21,negated_conjecture,
( ~ big_j(sK5)
| ~ big_h(sK4)
| ~ big_j(sK3)
| ~ big_h(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel29_neg]) ).
cnf(c_75,plain,
( big_h(A)
| ~ big_g(B)
| big_h(A)
| ~ big_f(A) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_22,plain,
( ~ big_g(B)
| big_h(A)
| ~ big_f(A) ),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_76,plain,
( big_j(A)
| ~ big_f(B)
| big_j(A)
| ~ big_g(A) ),
inference(factor,[status(thm)],[c_9]) ).
cnf(c_23,plain,
( ~ big_f(B)
| big_j(A)
| ~ big_g(A) ),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_26,plain,
( big_h(A)
| ~ big_f(A) ),
inference(resolve,[status(thm)],[c_22,c_5]) ).
cnf(c_27,plain,
( big_g(sK3)
| big_f(sK2)
| ~ big_f(A)
| big_j(sK5) ),
inference(resolve,[status(thm)],[c_23,c_11]) ).
cnf(c_28,plain,
( big_f(sK4)
| big_f(sK2)
| ~ big_f(A)
| big_j(sK3) ),
inference(resolve,[status(thm)],[c_23,c_10]) ).
cnf(c_32,plain,
( big_g(sK3)
| big_f(sK2)
| big_j(sK5) ),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_33,plain,
( big_f(sK4)
| big_f(sK2)
| big_j(sK3) ),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_77,negated_conjecture,
( ~ big_h(sK4)
| big_g(sK3)
| big_f(sK2)
| big_g(sK3)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_32,c_12]) ).
cnf(c_78,negated_conjecture,
( ~ big_h(sK4)
| big_g(sK3)
| big_g(sK3)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_37,negated_conjecture,
( ~ big_h(sK4)
| big_g(sK3)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_79,negated_conjecture,
( big_f(sK4)
| big_f(sK2)
| big_f(sK4)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_33,c_13]) ).
cnf(c_80,negated_conjecture,
( big_f(sK4)
| big_f(sK4)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_41,negated_conjecture,
( big_f(sK4)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_42,plain,
( big_h(sK4)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_41,c_26]) ).
cnf(c_81,plain,
( big_f(sK2)
| big_g(sK3)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_37,c_42]) ).
cnf(c_43,plain,
( big_g(sK3)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_44,plain,
( ~ big_f(A)
| big_j(sK3)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_43,c_23]) ).
cnf(c_82,plain,
( big_f(sK2)
| big_j(sK3)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_44,c_41]) ).
cnf(c_45,plain,
( big_j(sK3)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,negated_conjecture,
( big_g(sK5)
| big_f(sK2)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_45,c_14]) ).
cnf(c_47,negated_conjecture,
( big_g(sK5)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_48,plain,
( ~ big_f(A)
| big_j(sK5)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_47,c_23]) ).
cnf(c_84,plain,
( big_f(sK2)
| big_j(sK5)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_48,c_41]) ).
cnf(c_49,plain,
( big_j(sK5)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,negated_conjecture,
( ~ big_h(sK4)
| ~ big_j(sK3)
| big_f(sK2)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_49,c_15]) ).
cnf(c_51,negated_conjecture,
( ~ big_h(sK4)
| ~ big_j(sK3)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_86,plain,
( big_f(sK2)
| ~ big_h(sK4)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_51,c_45]) ).
cnf(c_52,plain,
( ~ big_h(sK4)
| big_f(sK2) ),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
( big_f(sK2)
| big_f(sK2) ),
inference(resolve,[status(thm)],[c_52,c_42]) ).
cnf(c_53,plain,
big_f(sK2),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_54,plain,
big_h(sK2),
inference(resolve,[status(thm)],[c_53,c_26]) ).
cnf(c_55,negated_conjecture,
( ~ big_j(sK5)
| ~ big_h(sK4)
| ~ big_j(sK3) ),
inference(resolve,[status(thm)],[c_54,c_21]) ).
cnf(c_56,negated_conjecture,
( big_g(sK5)
| ~ big_j(sK3) ),
inference(resolve,[status(thm)],[c_54,c_20]) ).
cnf(c_57,negated_conjecture,
( big_f(sK4)
| ~ big_j(sK3) ),
inference(resolve,[status(thm)],[c_54,c_19]) ).
cnf(c_58,negated_conjecture,
( ~ big_j(sK5)
| ~ big_h(sK4)
| big_g(sK3) ),
inference(resolve,[status(thm)],[c_54,c_18]) ).
cnf(c_59,negated_conjecture,
( big_g(sK5)
| big_g(sK3) ),
inference(resolve,[status(thm)],[c_54,c_17]) ).
cnf(c_60,negated_conjecture,
( big_f(sK4)
| big_g(sK3) ),
inference(resolve,[status(thm)],[c_54,c_16]) ).
cnf(c_61,plain,
( ~ big_f(A)
| big_j(sK5)
| big_g(sK3) ),
inference(resolve,[status(thm)],[c_59,c_23]) ).
cnf(c_62,plain,
( ~ big_f(A)
| big_j(sK3)
| big_f(sK4) ),
inference(resolve,[status(thm)],[c_60,c_23]) ).
cnf(c_63,plain,
( big_j(sK5)
| big_g(sK3) ),
inference(resolve,[status(thm)],[c_61,c_53]) ).
cnf(c_88,negated_conjecture,
( ~ big_h(sK4)
| big_g(sK3)
| big_g(sK3) ),
inference(resolve,[status(thm)],[c_63,c_58]) ).
cnf(c_64,negated_conjecture,
( ~ big_h(sK4)
| big_g(sK3) ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_65,plain,
( big_j(sK3)
| big_f(sK4) ),
inference(resolve,[status(thm)],[c_62,c_53]) ).
cnf(c_89,negated_conjecture,
( big_f(sK4)
| big_f(sK4) ),
inference(resolve,[status(thm)],[c_65,c_57]) ).
cnf(c_66,negated_conjecture,
big_f(sK4),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_67,plain,
big_h(sK4),
inference(resolve,[status(thm)],[c_66,c_26]) ).
cnf(c_68,negated_conjecture,
big_g(sK3),
inference(resolve,[status(thm)],[c_67,c_64]) ).
cnf(c_69,negated_conjecture,
( ~ big_j(sK5)
| ~ big_j(sK3) ),
inference(resolve,[status(thm)],[c_67,c_55]) ).
cnf(c_70,plain,
( ~ big_f(A)
| big_j(sK3) ),
inference(resolve,[status(thm)],[c_68,c_23]) ).
cnf(c_71,plain,
big_j(sK3),
inference(resolve,[status(thm)],[c_70,c_66]) ).
cnf(c_72,negated_conjecture,
~ big_j(sK5),
inference(resolve,[status(thm)],[c_71,c_69]) ).
cnf(c_73,negated_conjecture,
big_g(sK5),
inference(resolve,[status(thm)],[c_71,c_56]) ).
cnf(c_90,negated_conjecture,
( ~ big_f(A)
| ~ big_g(sK5) ),
inference(resolve,[status(thm)],[c_23,c_72]) ).
cnf(c_91,negated_conjecture,
~ big_g(sK5),
inference(resolve,[status(thm)],[c_90,c_66]) ).
cnf(c_74,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_73,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN059+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n009.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 17:08:20 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 683196 was started by sandbox on n009,
% 0.09/5.37 % Sat Sep 26 17:08:20 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.38
% 0.09/5.38 % SZS status Theorem for theBenchmark
% 0.09/5.38
% 0.09/5.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.38 % Length of proof is 59.
% 0.09/5.38 % Level of proof is 26.
% 0.09/5.38 % Maximum clause weight is 10.000.
% 0.09/5.38 % Given clauses 54.
% 0.09/5.38
% 0.09/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------