%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:19:18 AM UTC 2026
% Result : Theorem 23.08s 3.71s
% Output : CNFRefutation 23.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 184 ( 78 ~; 58 |; 48 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 139 ( 6 sgn 40 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_5,axiom,
! [X20] : id(X20,X20),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('theBenchmark.p',axiom_6) ).
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_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('theBenchmark.p',axiom_1a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('theBenchmark.p',axiom_4a) ).
fof(zeroplusoneidone,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y4,Y2,Y1)
& r1(Y4) ) ) ),
file('theBenchmark.p',zeroplusoneidone) ).
fof(zeroplusoneidone_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y4,Y2,Y1)
& r1(Y4) ) ) ),
inference(assume_negation,[status(cth)],[zeroplusoneidone]) ).
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]) ).
fof(nnf_3,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X13,X14,X15] :
( ( ~ id(X15,sK1(X13,X14))
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,sK1(X13,X14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y22,sK1(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ id(VAR_2,sK1(VAR_0,VAR_1))
| r3(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ r3(VAR_1,VAR_2,VAR_0)
| id(VAR_0,sK1(VAR_1,VAR_2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_24,plain,
( ~ r3(B,C,A)
| id(A,sK1(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_28,plain,
id(A,A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_29,plain,
( id(B,A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_31,plain,
( r1(B)
| ~ r1(A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_32,plain,
( r1(A)
| ~ r1(B)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_36,plain,
( r3(A,C,E)
| ~ r3(B,D,F)
| ~ id(E,F)
| ~ id(C,D)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
fof(nnf_12,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(sk_axiom_1a,plain,
! [X1,X8] :
( r3(X1,X8,sK5(X1,X8))
& r2(sK5(X1,X8),sK3(X1,X8))
& r3(X1,sK4(X1,X8),sK2(X1,X8))
& r2(X8,sK4(X1,X8))
& id(sK2(X1,X8),sK3(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(Y4,sK3(X1,X8)),skolemize(Y5,sK2(X1,X8)),skolemize(Y15,sK4(X1,X8)),skolemize(Y7,sK5(X1,X8))],[nnf_12]) ).
cnf(c_39,plain,
id(sK2(A,B),sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_40,plain,
r2(A,sK4(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_41,plain,
r3(A,sK4(A,B),sK2(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_42,plain,
r2(sK5(A,B),sK3(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_43,plain,
r3(A,B,sK5(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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,sK7(X4),sK6(X4))
& r1(sK7(X4))
& id(sK6(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(Y9,sK6(X4)),skolemize(Y16,sK7(X4))],[nnf_15]) ).
cnf(c_50,plain,
id(sK6(A),A),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_51,plain,
r1(sK7(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_52,plain,
r3(A,sK7(A),sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_62,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ id(C,E)
| ~ r2(D,B)
| ~ r1(D)
| ~ r3(A,B,C)
| ~ r1(A) ),
inference(clausify,[status(thm)],[zeroplusoneidone_neg]) ).
cnf(c_77,plain,
( ~ r2(E,D)
| ~ r1(E)
| ~ id(C,D)
| ~ r2(A,B)
| ~ r3(A,B,C)
| ~ r1(A) ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_90,plain,
r1(sK0),
inference(resolve,[status(thm)],[c_28,c_21]) ).
cnf(c_107,plain,
id(sK5(A,B),sK1(A,B)),
inference(resolve,[status(thm)],[c_43,c_24]) ).
cnf(c_139,plain,
id(A,sK6(A)),
inference(resolve,[status(thm)],[c_50,c_29]) ).
cnf(c_144,plain,
id(sK7(A),sK0),
inference(resolve,[status(thm)],[c_51,c_20]) ).
cnf(c_15473,plain,
( ~ r2(D,C)
| ~ r1(D)
| ~ id(B,C)
| ~ r2(sK0,A)
| ~ r3(sK0,A,B) ),
inference(resolve,[status(thm)],[c_77,c_90]) ).
cnf(c_15474,plain,
( ~ r2(C,B)
| ~ r1(C)
| ~ id(sK2(sK0,A),B)
| ~ r2(sK0,sK4(sK0,A)) ),
inference(resolve,[status(thm)],[c_15473,c_41]) ).
cnf(c_15475,plain,
( ~ r2(B,A)
| ~ r1(B)
| ~ id(sK2(sK0,sK0),A) ),
inference(resolve,[status(thm)],[c_15474,c_40]) ).
cnf(c_15476,plain,
( ~ r2(A,sK3(sK0,sK0))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_15475,c_39]) ).
cnf(c_3372,plain,
~ r1(sK5(sK0,sK0)),
inference(resolve,[status(thm)],[c_15476,c_42]) ).
cnf(c_14218,plain,
id(sK0,sK7(A)),
inference(resolve,[status(thm)],[c_144,c_29]) ).
cnf(c_15477,plain,
( r1(sK5(A,B))
| ~ r1(sK1(A,B)) ),
inference(resolve,[status(thm)],[c_32,c_107]) ).
cnf(c_14530,plain,
~ r1(sK1(sK0,sK0)),
inference(resolve,[status(thm)],[c_15477,c_3372]) ).
cnf(c_15478,plain,
( r1(A)
| ~ id(sK0,A) ),
inference(resolve,[status(thm)],[c_31,c_90]) ).
cnf(c_14540,plain,
~ id(sK0,sK1(sK0,sK0)),
inference(resolve,[status(thm)],[c_15478,c_14530]) ).
cnf(c_15276,plain,
~ r3(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_24,c_14540]) ).
cnf(c_15479,plain,
( r3(A,sK0,C)
| ~ r3(B,sK7(E),D)
| ~ id(C,D)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_36,c_14218]) ).
cnf(c_15480,plain,
( r3(A,sK0,D)
| ~ r3(B,sK7(C),sK6(D))
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_15479,c_139]) ).
cnf(c_15481,plain,
( r3(A,sK0,B)
| ~ id(A,B) ),
inference(resolve,[status(thm)],[c_15480,c_52]) ).
cnf(c_15482,plain,
~ id(sK0,sK0),
inference(resolve,[status(thm)],[c_15481,c_15276]) ).
cnf(c_15472,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_15482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 04:28:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 611507 was started by sandbox on n020,
% 0.11/0.38 % Sat Sep 26 04:28:34 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 23.08/3.71
% 23.08/3.71 % SZS status Theorem for theBenchmark
% 23.08/3.71
% 23.08/3.71 % Proof 1 at 2.75 (+ 0.55) seconds.
% 23.08/3.71 % Length of proof is 37.
% 23.08/3.71 % Level of proof is 7.
% 23.08/3.71 % Maximum clause weight is 24.000.
% 23.08/3.71 % Given clauses 163.
% 23.08/3.71
% 23.08/3.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------