%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN056+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 : n015.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 09:36:53 AM UTC 2026
% Result : Theorem 0.08s 5.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 6 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 174 ( 73 ~; 78 |; 14 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 55 ( 10 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel26_1,axiom,
( ? [X] : big_p(X)
<=> ? [Y] : big_q(Y) ),
file('theBenchmark.p',pel26_1) ).
fof(pel26_2,axiom,
! [X,Y] :
( ( big_q(Y)
& big_p(X) )
=> ( big_r(X)
<=> big_s(Y) ) ),
file('theBenchmark.p',pel26_2) ).
fof(pel26,conjecture,
( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
file('theBenchmark.p',pel26) ).
fof(pel26_neg,negated_conjecture,
~ ( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
inference(assume_negation,[status(cth)],[pel26]) ).
fof(nnf_1,plain,
( ( ! [Y] : ~ big_q(Y)
| ? [X] : big_p(X) )
& ( ? [X1] : big_q(X1)
| ! [X0] : ~ big_p(X0) ) ),
inference(fof_nnf,[status(thm)],[pel26_1]) ).
fof(sk_pel26_1_sk,plain,
( ( ! [Y] : ~ big_q(Y)
| big_p(sK0) )
& ( big_q(sK1)
| ! [X0] : ~ big_p(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X1,sK1),skolemize(X,sK0)],[nnf_1]) ).
fof(sk_pel26_1,plain,
( ! [VAR_0] :
( ~ big_q(VAR_0)
| big_p(sK0) )
& ! [VAR_0] :
( big_q(sK1)
| ~ big_p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel26_1_sk]) ).
cnf(c_4,plain,
( ~ big_q(A)
| big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel26_1]) ).
cnf(c_5,plain,
( big_q(sK1)
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_pel26_1]) ).
cnf(c_6,plain,
( big_s(B)
| ~ big_r(A)
| ~ big_q(B)
| ~ big_p(A) ),
inference(clausify,[status(thm)],[pel26_2]) ).
cnf(c_7,plain,
( ~ big_s(B)
| big_r(A)
| ~ big_q(B)
| ~ big_p(A) ),
inference(clausify,[status(thm)],[pel26_2]) ).
fof(nnf_3,plain,
( ( ? [Y] :
( ~ big_s(Y)
& big_q(Y) )
| ? [X] :
( ~ big_r(X)
& big_p(X) ) )
& ( ! [X1] :
( big_s(X1)
| ~ big_q(X1) )
| ! [X0] :
( big_r(X0)
| ~ big_p(X0) ) ) ),
inference(fof_nnf,[status(thm)],[pel26_neg]) ).
fof(sk_pel26_neg_sk,plain,
( ( ( ~ big_s(sK3)
& big_q(sK3) )
| ( ~ big_r(sK2)
& big_p(sK2) ) )
& ( ! [X1] :
( big_s(X1)
| ~ big_q(X1) )
| ! [X0] :
( big_r(X0)
| ~ big_p(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_3]) ).
fof(sk_pel26_neg,plain,
( ( ~ big_s(sK3)
| ~ big_r(sK2) )
& ( big_q(sK3)
| ~ big_r(sK2) )
& ( ~ big_s(sK3)
| big_p(sK2) )
& ( big_q(sK3)
| big_p(sK2) )
& ! [VAR_0,VAR_1] :
( big_s(VAR_1)
| ~ big_q(VAR_1)
| big_r(VAR_0)
| ~ big_p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel26_neg_sk]) ).
cnf(c_8,negated_conjecture,
( big_s(B)
| ~ big_q(B)
| big_r(A)
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_pel26_neg]) ).
cnf(c_9,negated_conjecture,
( big_q(sK3)
| big_p(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel26_neg]) ).
cnf(c_10,negated_conjecture,
( ~ big_s(sK3)
| big_p(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel26_neg]) ).
cnf(c_11,plain,
( ~ big_q(B)
| big_s(A)
| ~ big_r(sK0)
| ~ big_q(A) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_13,negated_conjecture,
( ~ big_q(B)
| big_s(A)
| ~ big_q(A)
| big_r(sK0) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_15,negated_conjecture,
( ~ big_s(A)
| big_r(sK2)
| ~ big_q(A)
| big_q(sK3) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_17,negated_conjecture,
( ~ big_s(A)
| big_r(sK2)
| ~ big_q(A)
| ~ big_s(sK3) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_18,negated_conjecture,
( ~ big_s(sK3)
| ~ big_r(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel26_neg]) ).
cnf(c_19,negated_conjecture,
( big_q(sK3)
| ~ big_r(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel26_neg]) ).
cnf(c_20,negated_conjecture,
( ~ big_s(A)
| ~ big_q(A)
| big_q(sK3)
| big_q(sK3) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_21,negated_conjecture,
( ~ big_s(A)
| ~ big_q(A)
| big_q(sK3) ),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
( ~ big_s(A)
| ~ big_q(A)
| ~ big_s(sK3)
| ~ big_s(sK3) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_23,negated_conjecture,
( ~ big_s(A)
| ~ big_q(A)
| ~ big_s(sK3) ),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_24,negated_conjecture,
( ~ big_q(D)
| big_s(C)
| ~ big_q(C)
| ~ big_q(B)
| big_s(A)
| ~ big_q(A) ),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_26,plain,
( big_q(sK1)
| ~ big_q(A) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_27,negated_conjecture,
( big_q(sK1)
| big_q(sK3) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_30,plain,
( ~ big_q(C)
| big_s(B)
| ~ big_q(B)
| big_s(A)
| ~ big_q(A) ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_39,plain,
( ~ big_q(B)
| big_s(A)
| big_s(A)
| ~ big_q(A) ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_32,plain,
( ~ big_q(B)
| big_s(A)
| ~ big_q(A) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_33,plain,
( big_s(A)
| ~ big_q(A) ),
inference(factor,[status(thm)],[c_32]) ).
cnf(c_40,negated_conjecture,
( big_q(sK1)
| big_q(sK1) ),
inference(resolve,[status(thm)],[c_27,c_26]) ).
cnf(c_34,negated_conjecture,
big_q(sK1),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_35,plain,
big_s(sK1),
inference(resolve,[status(thm)],[c_34,c_33]) ).
cnf(c_41,negated_conjecture,
( ~ big_q(sK1)
| ~ big_s(sK3) ),
inference(resolve,[status(thm)],[c_35,c_23]) ).
cnf(c_36,negated_conjecture,
~ big_s(sK3),
inference(resolve,[status(thm)],[c_34,c_41]) ).
cnf(c_42,negated_conjecture,
( ~ big_q(sK1)
| big_q(sK3) ),
inference(resolve,[status(thm)],[c_35,c_21]) ).
cnf(c_37,negated_conjecture,
big_q(sK3),
inference(resolve,[status(thm)],[c_34,c_42]) ).
cnf(c_43,plain,
big_s(sK3),
inference(resolve,[status(thm)],[c_37,c_33]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n015.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 17:10:50 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 353900 was started by sandbox on n015,
% 0.08/5.37 % Sat Sep 26 17:10:50 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 0.08/5.39
% 0.08/5.39 % SZS status Theorem for theBenchmark
% 0.08/5.39
% 0.08/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/5.39 % Length of proof is 31.
% 0.08/5.39 % Level of proof is 9.
% 0.08/5.39 % Maximum clause weight is 12.000.
% 0.08/5.39 % Given clauses 9.
% 0.08/5.39
% 0.08/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------