%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN386+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 : n012.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 09:37:46 AM UTC 2026
% Result : Theorem 0.02s 0.31s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 76 ( 24 ~; 19 |; 21 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 100 ( 6 sgn 56 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2138,conjecture,
( ( ! [E] :
? [D] :
! [A,B] :
( big_d(A,B,D)
=> ! [Y,Z] :
( ( big_f(B,Z)
& big_f(A,Y) )
=> big_d(Y,Z,E) ) )
& ? [X] :
! [E] :
? [N] :
! [W] :
( big_s(N,W)
=> big_d(W,X,E) )
& ! [X] :
? [Y] : big_f(X,Y) )
=> ? [Y] :
! [E] :
? [M] :
! [W] :
( big_s(M,W)
=> ! [Z] :
( big_f(W,Z)
=> big_d(Z,Y,E) ) ) ),
file('theBenchmark.p',x2138) ).
fof(x2138_neg,negated_conjecture,
~ ( ( ! [E] :
? [D] :
! [A,B] :
( big_d(A,B,D)
=> ! [Y,Z] :
( ( big_f(B,Z)
& big_f(A,Y) )
=> big_d(Y,Z,E) ) )
& ? [X] :
! [E] :
? [N] :
! [W] :
( big_s(N,W)
=> big_d(W,X,E) )
& ! [X] :
? [Y] : big_f(X,Y) )
=> ? [Y] :
! [E] :
? [M] :
! [W] :
( big_s(M,W)
=> ! [Z] :
( big_f(W,Z)
=> big_d(Z,Y,E) ) ) ),
inference(assume_negation,[status(cth)],[x2138]) ).
fof(nnf_1,plain,
( ! [Y] :
? [E] :
! [M] :
? [W] :
( ? [Z] :
( ~ big_d(Z,Y,E)
& big_f(W,Z) )
& big_s(M,W) )
& ! [X4] :
? [D] :
! [A,B] :
( ! [X5,X6] :
( big_d(X5,X6,X4)
| ~ big_f(B,X6)
| ~ big_f(A,X5) )
| ~ big_d(A,B,D) )
& ? [X] :
! [X2] :
? [N] :
! [X3] :
( big_d(X3,X,X2)
| ~ big_s(N,X3) )
& ! [X0] :
? [X1] : big_f(X0,X1) ),
inference(fof_nnf,[status(thm)],[x2138_neg]) ).
fof(sk_x2138_neg_sk,plain,
( ! [Y,M] :
( ~ big_d(sK3(Y,M),Y,sK4(Y))
& big_f(sK0(Y,M),sK3(Y,M))
& big_s(M,sK0(Y,M)) )
& ! [X4,A,B] :
( ! [X5,X6] :
( big_d(X5,X6,X4)
| ~ big_f(B,X6)
| ~ big_f(A,X5) )
| ~ big_d(A,B,sK5(X4)) )
& ! [X2,X3] :
( big_d(X3,sK2,X2)
| ~ big_s(sK1(X2),X3) )
& ! [X0] : big_f(X0,sK6(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK1,sK2,sK5,sK0,sK3,sK4]),skolemize(X1,sK6(X0)),skolemize(X,sK2),skolemize(N,sK1(X2)),skolemize(D,sK5(X4)),skolemize(E,sK4(Y)),skolemize(W,sK0(Y,M)),skolemize(Z,sK3(Y,M))],[nnf_1]) ).
fof(sk_x2138_neg,plain,
( ! [VAR_0,VAR_1] : ~ big_d(sK3(VAR_0,VAR_1),VAR_0,sK4(VAR_0))
& ! [VAR_0,VAR_1] : big_f(sK0(VAR_0,VAR_1),sK3(VAR_0,VAR_1))
& ! [VAR_0,VAR_1] : big_s(VAR_0,sK0(VAR_1,VAR_0))
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( big_d(VAR_3,VAR_4,VAR_2)
| ~ big_f(VAR_1,VAR_4)
| ~ big_f(VAR_0,VAR_3)
| ~ big_d(VAR_0,VAR_1,sK5(VAR_2)) )
& ! [VAR_0,VAR_1] :
( big_d(VAR_1,sK2,VAR_0)
| ~ big_s(sK1(VAR_0),VAR_1) )
& ! [VAR_0] : big_f(VAR_0,sK6(VAR_0)) ),
inference(cnf_transformation,[status(thm)],[sk_x2138_neg_sk]) ).
cnf(c_2,negated_conjecture,
big_s(A,sK0(B,A)),
inference(split_conjunct,[status(thm)],[sk_x2138_neg]) ).
cnf(c_3,negated_conjecture,
( big_d(B,sK2,A)
| ~ big_s(sK1(A),B) ),
inference(split_conjunct,[status(thm)],[sk_x2138_neg]) ).
cnf(c_4,negated_conjecture,
big_d(sK0(A,sK1(B)),sK2,B),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_5,negated_conjecture,
~ big_d(sK3(A,B),A,sK4(A)),
inference(split_conjunct,[status(thm)],[sk_x2138_neg]) ).
cnf(c_6,negated_conjecture,
big_f(sK0(A,B),sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_x2138_neg]) ).
cnf(c_7,negated_conjecture,
( big_d(D,E,C)
| ~ big_f(B,E)
| ~ big_f(A,D)
| ~ big_d(A,B,sK5(C)) ),
inference(split_conjunct,[status(thm)],[sk_x2138_neg]) ).
cnf(c_8,negated_conjecture,
big_f(A,sK6(A)),
inference(split_conjunct,[status(thm)],[sk_x2138_neg]) ).
cnf(c_12,negated_conjecture,
( big_d(C,D,B)
| ~ big_f(sK2,D)
| ~ big_f(sK0(A,sK1(sK5(B))),C) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_13,negated_conjecture,
( big_d(sK3(B,sK1(sK5(C))),A,C)
| ~ big_f(sK2,A) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_10,negated_conjecture,
big_d(sK3(A,sK1(sK5(B))),sK6(sK2),B),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN386+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 17:39:19 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 1150506 was started by sandbox on n012,
% 0.02/0.30 % Sat Sep 26 17:39:19 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.02/0.31
% 0.02/0.31 % SZS status Theorem for theBenchmark
% 0.02/0.31
% 0.02/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.31 % Length of proof is 10.
% 0.02/0.31 % Level of proof is 4.
% 0.02/0.31 % Maximum clause weight is 15.000.
% 0.02/0.31 % Given clauses 5.
% 0.02/0.31
% 0.02/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------