%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN087+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:19:24 AM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 101 ( 43 ~; 32 |; 26 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 68 ( 10 sgn 17 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_5,axiom,
! [X20] : id(X20,X20),
file('theBenchmark.p',axiom_5) ).
fof(axiom_8,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_11,axiom,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
file('theBenchmark.p',axiom_11) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(zerotimeszeroeqzero,conjecture,
? [Y1] :
( ? [Y3] :
( r1(Y3)
& id(Y1,Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
file('theBenchmark.p',zerotimeszeroeqzero) ).
fof(zerotimeszeroeqzero_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( r1(Y3)
& id(Y1,Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
inference(assume_negation,[status(cth)],[zerotimeszeroeqzero]) ).
fof(nnf_1,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
inference(fof_nnf,[status(thm)],[axiom_1]) ).
fof(sk_axiom_1_sk,plain,
! [X19] :
( ( ~ id(X19,sK0)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y24,sK0)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( ~ id(VAR_0,sK0)
| r1(VAR_0) )
& ! [VAR_0] :
( ~ r1(VAR_0)
| id(VAR_0,sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_20,plain,
( ~ r1(A)
| id(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_21,plain,
( ~ id(A,sK0)
| r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_28,plain,
id(A,A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_32,plain,
( r1(A)
| ~ r1(B)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_37,plain,
( r4(B,D,F)
| ~ r4(A,C,E)
| ~ id(E,F)
| ~ id(C,D)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_11]) ).
fof(nnf_16,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(sk_axiom_5a,plain,
! [X5] :
( r1(sK3(X5))
& id(sK2(X5),sK3(X5))
& r4(X5,sK1(X5),sK2(X5))
& r1(sK1(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(Y8,sK2(X5)),skolemize(Y17,sK1(X5)),skolemize(Y18,sK3(X5))],[nnf_16]) ).
cnf(c_53,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_54,plain,
r4(A,sK1(A),sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_55,plain,
id(sK2(A),sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_56,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r1(C)
| ~ id(B,C)
| ~ r4(A,A,B)
| ~ r1(A) ),
inference(clausify,[status(thm)],[zerotimeszeroeqzero_neg]) ).
cnf(c_77,plain,
( ~ id(B,A)
| ~ r4(A,A,B)
| ~ r1(A) ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_85,plain,
r1(sK0),
inference(resolve,[status(thm)],[c_28,c_21]) ).
cnf(c_143,plain,
id(sK1(A),sK0),
inference(resolve,[status(thm)],[c_53,c_20]) ).
cnf(c_569,plain,
( r1(sK2(A))
| ~ r1(sK3(A)) ),
inference(resolve,[status(thm)],[c_55,c_32]) ).
cnf(c_147,plain,
r1(sK2(A)),
inference(resolve,[status(thm)],[c_56,c_569]) ).
cnf(c_570,plain,
( ~ id(A,sK0)
| ~ r4(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_77,c_85]) ).
cnf(c_289,plain,
~ r4(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_570,c_28]) ).
cnf(c_367,plain,
id(sK2(A),sK0),
inference(resolve,[status(thm)],[c_147,c_20]) ).
cnf(c_571,plain,
( r4(sK0,B,D)
| ~ r4(sK1(E),A,C)
| ~ id(C,D)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_37,c_143]) ).
cnf(c_572,plain,
( r4(sK0,sK0,B)
| ~ r4(sK1(C),sK1(D),A)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_571,c_143]) ).
cnf(c_573,plain,
( r4(sK0,sK0,B)
| ~ id(sK2(sK1(A)),B) ),
inference(resolve,[status(thm)],[c_572,c_54]) ).
cnf(c_574,plain,
~ id(sK2(sK1(A)),sK0),
inference(resolve,[status(thm)],[c_573,c_289]) ).
cnf(c_568,plain,
$false,
inference(resolve,[status(thm)],[c_367,c_574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN087+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 04:34:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2038297 was started by sandbox2 on n003,
% 0.09/0.37 % Sat Sep 26 04:34:08 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.45
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45
% 0.09/0.45 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.45 % Length of proof is 23.
% 0.09/0.45 % Level of proof is 4.
% 0.09/0.45 % Maximum clause weight is 22.000.
% 0.09/0.45 % Given clauses 83.
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------