%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:19:19 AM UTC 2026
% Result : Theorem 0.16s 10.79s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 147 ( 62 ~; 49 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 123 ( 14 sgn 26 !; 26 ?)
% 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_10,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ( r3(X35,X36,X37)
& r3(X32,X33,X34) )
| ( ~ r3(X35,X36,X37)
& ~ r3(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
file('theBenchmark.p',axiom_10) ).
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_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(fermattothepoweroftwoid,conjecture,
? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( r4(Y2,Y2,Y5)
& id(Y4,Y5) ) ),
file('theBenchmark.p',fermattothepoweroftwoid) ).
fof(fermattothepoweroftwoid_neg,negated_conjecture,
~ ? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( r4(Y2,Y2,Y5)
& id(Y4,Y5) ) ),
inference(assume_negation,[status(cth)],[fermattothepoweroftwoid]) ).
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_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_35,plain,
( r3(B,D,F)
| ~ r3(A,C,E)
| ~ id(E,F)
| ~ id(C,D)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
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_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,sK2(X4),sK1(X4))
& r1(sK2(X4))
& id(sK1(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(Y9,sK1(X4)),skolemize(Y16,sK2(X4))],[nnf_15]) ).
cnf(c_50,plain,
id(sK1(A),A),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_51,plain,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_52,plain,
r3(A,sK2(A),sK1(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(sK5(X5))
& id(sK4(X5),sK5(X5))
& r4(X5,sK3(X5),sK4(X5))
& r1(sK3(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(Y8,sK4(X5)),skolemize(Y17,sK3(X5)),skolemize(Y18,sK5(X5))],[nnf_16]) ).
cnf(c_53,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_54,plain,
r4(A,sK3(A),sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_55,plain,
id(sK4(A),sK5(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_56,plain,
r1(sK5(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r3(V6,E,A)
| ~ r4(F,F,V6)
| ~ r4(D,D,E)
| ~ r4(C,C,B)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[fermattothepoweroftwoid_neg]) ).
cnf(c_77,plain,
( ~ r3(E,B,A)
| ~ r4(D,D,E)
| ~ r4(C,C,B)
| ~ id(A,B) ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_84,plain,
( ~ r3(B,B,A)
| ~ r4(C,C,B)
| ~ id(A,B) ),
inference(factor,[status(thm)],[c_77]) ).
cnf(c_332,plain,
id(sK2(A),sK0),
inference(resolve,[status(thm)],[c_51,c_20]) ).
cnf(c_359,plain,
id(sK3(A),sK0),
inference(resolve,[status(thm)],[c_53,c_20]) ).
cnf(c_4775,plain,
( r1(sK4(A))
| ~ r1(sK5(A)) ),
inference(resolve,[status(thm)],[c_55,c_32]) ).
cnf(c_382,plain,
r1(sK4(A)),
inference(resolve,[status(thm)],[c_56,c_4775]) ).
cnf(c_1801,plain,
id(sK4(A),sK0),
inference(resolve,[status(thm)],[c_382,c_20]) ).
cnf(c_4776,plain,
( r3(E,B,D)
| ~ r3(E,A,C)
| ~ id(C,D)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_35,c_28]) ).
cnf(c_4777,plain,
( r3(C,sK0,B)
| ~ r3(C,sK2(D),A)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_4776,c_332]) ).
cnf(c_4778,plain,
( r3(A,sK0,C)
| ~ r3(A,sK2(B),sK1(C)) ),
inference(resolve,[status(thm)],[c_4777,c_50]) ).
cnf(c_3549,plain,
r3(A,sK0,A),
inference(resolve,[status(thm)],[c_4778,c_52]) ).
cnf(c_4779,plain,
( ~ r3(B,B,B)
| ~ r4(A,A,B) ),
inference(resolve,[status(thm)],[c_84,c_28]) ).
cnf(c_3810,plain,
~ r4(A,A,sK0),
inference(resolve,[status(thm)],[c_4779,c_3549]) ).
cnf(c_4780,plain,
( r4(sK0,B,D)
| ~ r4(sK3(E),A,C)
| ~ id(C,D)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_37,c_359]) ).
cnf(c_4781,plain,
( r4(sK0,sK0,B)
| ~ r4(sK3(C),sK3(D),A)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_4780,c_359]) ).
cnf(c_4782,plain,
( r4(sK0,sK0,B)
| ~ id(sK4(sK3(A)),B) ),
inference(resolve,[status(thm)],[c_4781,c_54]) ).
cnf(c_4783,plain,
~ id(sK4(sK3(A)),sK0),
inference(resolve,[status(thm)],[c_4782,c_3810]) ).
cnf(c_4774,plain,
$false,
inference(resolve,[status(thm)],[c_1801,c_4783]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n016.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 26 04:33:27 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 4181366 was started by sandbox on n016,
% 0.11/10.39 % Sat Sep 26 04:33:27 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.39
% 0.11/10.39 % From the command line: assign(max_seconds, 300).
% 0.16/10.79
% 0.16/10.79 % SZS status Theorem for theBenchmark
% 0.16/10.79
% 0.16/10.79 % Proof 1 at 0.24 (+ 0.09) seconds.
% 0.16/10.79 % Length of proof is 30.
% 0.16/10.79 % Level of proof is 5.
% 0.16/10.79 % Maximum clause weight is 24.000.
% 0.16/10.79 % Given clauses 93.
% 0.16/10.79
% 0.16/10.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------