%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 09:39:12 AM UTC 2026
% Result : Theorem 0.15s 5.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 86 ( 26 ~; 32 |; 20 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 79 ( 5 sgn 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm400,conjecture,
( ! [X,Y] : q(X,Y)
| ( ( ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y,Z] :
( ( q(Y,Z)
& q(X,Y) )
=> q(X,Z) )
& ! [X,Y,Z] :
( ( p(Y,Z)
& p(X,Y) )
=> p(X,Z) ) )
=> ! [X,Y] : p(X,Y) ) ),
file('theBenchmark.p',thm400) ).
fof(thm400_neg,negated_conjecture,
~ ( ! [X,Y] : q(X,Y)
| ( ( ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y,Z] :
( ( q(Y,Z)
& q(X,Y) )
=> q(X,Z) )
& ! [X,Y,Z] :
( ( p(Y,Z)
& p(X,Y) )
=> p(X,Z) ) )
=> ! [X,Y] : p(X,Y) ) ),
inference(assume_negation,[status(cth)],[thm400]) ).
fof(nnf_1,plain,
( ? [X,Y] : ~ q(X,Y)
& ? [X9,X10] : ~ p(X9,X10)
& ! [X7,X8] :
( q(X7,X8)
| p(X7,X8) )
& ! [X5,X6] :
( q(X6,X5)
| ~ q(X5,X6) )
& ! [X3,X4,Z] :
( q(X3,Z)
| ~ q(X4,Z)
| ~ q(X3,X4) )
& ! [X0,X1,X2] :
( p(X0,X2)
| ~ p(X1,X2)
| ~ p(X0,X1) ) ),
inference(fof_nnf,[status(thm)],[thm400_neg]) ).
fof(sk_thm400_neg,plain,
( ~ q(sK2,sK3)
& ~ p(sK0,sK1)
& ! [X7,X8] :
( q(X7,X8)
| p(X7,X8) )
& ! [X5,X6] :
( q(X6,X5)
| ~ q(X5,X6) )
& ! [X3,X4,Z] :
( q(X3,Z)
| ~ q(X4,Z)
| ~ q(X3,X4) )
& ! [X0,X1,X2] :
( p(X0,X2)
| ~ p(X1,X2)
| ~ p(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X9,sK0),skolemize(X10,sK1),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( p(A,C)
| ~ p(B,C)
| ~ p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_thm400_neg]) ).
cnf(c_3,negated_conjecture,
( q(A,C)
| ~ q(B,C)
| ~ q(A,B) ),
inference(split_conjunct,[status(thm)],[sk_thm400_neg]) ).
cnf(c_4,negated_conjecture,
( q(B,A)
| ~ q(A,B) ),
inference(split_conjunct,[status(thm)],[sk_thm400_neg]) ).
cnf(c_5,negated_conjecture,
( q(A,B)
| p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_thm400_neg]) ).
cnf(c_6,negated_conjecture,
~ p(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thm400_neg]) ).
cnf(c_7,negated_conjecture,
~ q(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_thm400_neg]) ).
cnf(c_8,plain,
( p(C,B)
| ~ p(C,A)
| q(A,B) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_10,plain,
q(sK0,sK1),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_11,negated_conjecture,
~ q(sK3,sK2),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_12,plain,
( q(C,A)
| p(C,B)
| q(A,B) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_13,plain,
q(sK1,sK0),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_16,plain,
( q(A,sK0)
| ~ q(A,sK1) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_21,plain,
( q(sK0,A)
| q(A,sK1) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_24,plain,
( q(A,sK0)
| q(sK0,A) ),
inference(resolve,[status(thm)],[c_21,c_16]) ).
cnf(c_39,negated_conjecture,
( q(A,sK0)
| q(A,sK0) ),
inference(resolve,[status(thm)],[c_24,c_4]) ).
cnf(c_32,negated_conjecture,
q(A,sK0),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_40,negated_conjecture,
( q(sK0,A)
| q(sK0,A) ),
inference(resolve,[status(thm)],[c_24,c_4]) ).
cnf(c_33,negated_conjecture,
q(sK0,A),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_41,negated_conjecture,
( q(B,A)
| ~ q(sK0,A) ),
inference(resolve,[status(thm)],[c_32,c_3]) ).
cnf(c_37,negated_conjecture,
q(A,B),
inference(resolve,[status(thm)],[c_33,c_41]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n004.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Sat Sep 26 18:21:57 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.59 % Process 2340905 was started by sandbox on n004,
% 0.10/5.59 % Sat Sep 26 18:21:57 2026
% 0.10/5.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.59
% 0.10/5.59 % From the command line: assign(max_seconds, 300).
% 0.15/5.61
% 0.15/5.61 % SZS status Theorem for theBenchmark
% 0.15/5.61
% 0.15/5.61 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.61 % Length of proof is 19.
% 0.15/5.61 % Level of proof is 8.
% 0.15/5.61 % Maximum clause weight is 9.000.
% 0.15/5.61 % Given clauses 21.
% 0.15/5.61
% 0.15/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------