%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN943+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:43:25 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 88 ( 26 ~; 30 |; 24 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 29 ( 0 sgn 12 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [A] :
? [X,X2,X3,X4,Y] :
( ( ( s(A,Y)
=> p(Y) )
& ( e(X2)
=> ( c(f(X2))
| g(X2) ) )
& ( e(X)
=> ( s(X,f(X))
| g(X) ) )
& e(A)
& p(A) )
=> ( ( c(X4)
& p(X4) )
| ( g(X3)
& p(X3) ) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [A] :
? [X,X2,X3,X4,Y] :
( ( ( s(A,Y)
=> p(Y) )
& ( e(X2)
=> ( c(f(X2))
| g(X2) ) )
& ( e(X)
=> ( s(X,f(X))
| g(X) ) )
& e(A)
& p(A) )
=> ( ( c(X4)
& p(X4) )
| ( g(X3)
& p(X3) ) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p(X4) )
& ( ~ g(X3)
| ~ p(X3) )
& ( p(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p(A) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p(X4) )
& ( ~ g(X3)
| ~ p(X3) )
& ( p(Y)
| ~ s(sK0,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(sK0)
& p(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( ~ g(A)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( p(A)
| ~ s(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
p(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
( ~ c(A)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
e(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
( s(A,f(A))
| g(A)
| ~ e(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_8,negated_conjecture,
( c(f(A))
| g(A)
| ~ e(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_10,negated_conjecture,
( s(sK0,f(sK0))
| g(sK0) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_11,negated_conjecture,
( c(f(sK0))
| g(sK0) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_12,negated_conjecture,
~ g(sK0),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_15,negated_conjecture,
c(f(sK0)),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_16,negated_conjecture,
( ~ s(sK0,A)
| ~ c(A) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_17,negated_conjecture,
~ s(sK0,f(sK0)),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_20,negated_conjecture,
s(sK0,f(sK0)),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_21,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN943+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 18:46:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1420773 was started by sandbox2 on n017,
% 0.10/0.37 % Sat Sep 26 18:46:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 16.
% 0.10/0.38 % Level of proof is 5.
% 0.10/0.38 % Maximum clause weight is 4.000.
% 0.10/0.38 % Given clauses 0.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------