%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN080+1 : TPTP v9.3.1. Released v7.3.0.
% 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 08:19:23 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 18 ~; 12 |; 35 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 79 ( 18 sgn 14 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
file('theBenchmark.p',axiom_2a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('theBenchmark.p',axiom_4a) ).
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(xplustwoidy,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& id(Y3,Y2) ),
file('theBenchmark.p',xplustwoidy) ).
fof(xplustwoidy_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& id(Y3,Y2) ),
inference(assume_negation,[status(cth)],[xplustwoidy]) ).
cnf(c_29,plain,
( id(B,A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(nnf_13,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(sk_axiom_2a,plain,
! [X2,X9] :
( r4(X2,X9,sK1(X2,X9))
& r3(sK1(X2,X9),X2,sK2(X2,X9))
& r4(X2,sK0(X2,X9),sK5(X2,X9))
& r2(X9,sK0(X2,X9))
& id(sK5(X2,X9),sK2(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK2,sK0,sK1]),skolemize(Y2,sK2(X2,X9)),skolemize(Y3,sK5(X2,X9)),skolemize(Y14,sK0(X2,X9)),skolemize(Y6,sK1(X2,X9))],[nnf_13]) ).
cnf(c_45,plain,
r2(A,sK0(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
cnf(c_47,plain,
r3(sK1(A,B),A,sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
fof(nnf_15,plain,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(sk_axiom_4a,plain,
! [X4] :
( r3(X4,sK6(X4),sK3(X4))
& r1(sK6(X4))
& id(sK3(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK6]),skolemize(Y9,sK3(X4)),skolemize(Y16,sK6(X4))],[nnf_15]) ).
cnf(c_50,plain,
id(sK3(A),A),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
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(sK4(X5))
& id(sK8(X5),sK4(X5))
& r4(X5,sK7(X5),sK8(X5))
& r1(sK7(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK4]),skolemize(Y8,sK8(X5)),skolemize(Y17,sK7(X5)),skolemize(Y18,sK4(X5))],[nnf_16]) ).
cnf(c_56,plain,
r1(sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| ~ r3(C,D,A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[xplustwoidy_neg]) ).
cnf(c_134,plain,
id(A,sK3(A)),
inference(resolve,[status(thm)],[c_50,c_29]) ).
cnf(c_213,negated_conjecture,
( ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,A)
| ~ id(sK2(A,B),C) ),
inference(resolve,[status(thm)],[c_62,c_47]) ).
cnf(c_214,negated_conjecture,
( ~ r2(E,B)
| ~ r1(E)
| ~ id(sK2(sK0(A,B),C),D) ),
inference(resolve,[status(thm)],[c_213,c_45]) ).
cnf(c_215,negated_conjecture,
( ~ r2(sK4(E),B)
| ~ id(sK2(sK0(A,B),C),D) ),
inference(resolve,[status(thm)],[c_214,c_56]) ).
cnf(c_211,negated_conjecture,
~ id(sK2(sK0(A,sK0(B,sK4(C))),D),E),
inference(resolve,[status(thm)],[c_215,c_45]) ).
cnf(c_212,plain,
$false,
inference(resolve,[status(thm)],[c_211,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN080+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 04:30:52 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 820777 was started by sandbox on n004,
% 0.08/0.37 % Sat Sep 26 04:30:52 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 14.
% 0.08/0.39 % Level of proof is 3.
% 0.08/0.39 % Maximum clause weight is 35.000.
% 0.08/0.39 % Given clauses 43.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------