%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 : Fri Sep 25 02:29:26 PM UTC 2026
% Result : Theorem 18.20s 2.76s
% Output : Proof 18.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 25 unt; 0 def)
% Number of atoms : 108 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 107 ( 46 ~; 31 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 104 ( 3 sgn 40 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X12,X11] :
( ( ~ id(X12,sk1(X11))
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,sk1(X11)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c7,plain,
( ~ id(X2,sk1(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
ifeq(id(X0,sk1(X1)),true,r2(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f4,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f4_nnf,plain,
! [X20] : id(X20,X20),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X20] : id(X20,X20),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c16,plain,
id(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi8,axiom,
id(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h2,plain,
r2(V0,sk1(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi8]) ).
fof(f18,conjecture,
! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( r3(X1,Y1,Y3)
& id(Y3,Y2) )
& ! [Y4] :
( ~ r1(Y4)
| ~ id(Y1,Y4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(f18_neg,negated_conjecture,
~ ! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( r3(X1,Y1,Y3)
& id(Y3,Y2) )
& ! [Y4] :
( ~ r1(Y4)
| ~ id(Y1,Y4) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X1] :
! [Y2,Y1] :
( ! [Y3] :
( ~ r3(X1,Y1,Y3)
| ~ id(Y3,Y2) )
| ? [Y4] :
( r1(Y4)
& id(Y1,Y4) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [Y1,Y2,Y3] :
( ~ r3(sk20,Y1,Y3)
| ~ id(Y3,Y2)
| ( r1(sk21(Y2,Y1))
& id(Y1,sk21(Y2,Y1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21])],[f18_nnf]) ).
cnf(c59,plain,
( ~ r3(sk20,X2,X4)
| ~ id(X4,X1)
| r1(sk21(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(id(X0,X1),true,ifeq(r3(sk20,X2,X0),true,r1(sk21(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
fof(f11,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('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f11_nnf,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(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X1,X8] :
( r3(X1,X8,sk7(X1,X8))
& r2(sk7(X1,X8),sk4(X1,X8))
& r3(X1,sk6(X1,X8),sk5(X1,X8))
& r2(X8,sk6(X1,X8))
& id(sk5(X1,X8),sk4(X1,X8)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f11_nnf]) ).
cnf(c39,plain,
r3(X0,X1,sk7(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi23,axiom,
r3(X0,X1,sk7(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h20,plain,
r1(sk21(sk7(sk20,V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi42,hi8,hi23]) ).
cnf(c58,plain,
( ~ r3(sk20,X2,X4)
| ~ id(X4,X1)
| id(X2,sk21(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi41,negated_conjecture,
ifeq(id(X0,X1),true,ifeq(r3(sk20,X2,X0),true,id(X2,sk21(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h21,plain,
id(V0,sk21(sk7(sk20,V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi41,hi8,hi23]) ).
fof(f7,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f7_nnf,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c21,plain,
( r1(X0)
| ~ r1(X1)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi12,axiom,
ifeq(id(X0,X1),true,ifeq(r1(X1),true,r1(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h6954,plain,
r1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi12,h21,h20]) ).
cnf(c4,plain,
( ~ r2(X0,X2)
| id(X2,sk1(X0)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(r2(X0,X1),true,id(X1,sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c38,plain,
r2(sk7(X0,X1),sk4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi22,axiom,
r2(sk7(X0,X1),sk4(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h19,plain,
id(sk4(V0,V1),sk1(sk7(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi22]) ).
fof(f17,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f17_nnf,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [Y20,Y10,X7] :
( ~ r2(X7,Y10)
| ~ r1(Y20)
| ~ id(Y20,Y10) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c57,plain,
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi43,axiom,
ifeq(id(X0,X1),true,ifeq(r1(X0),true,ifeq(r2(X2,X1),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi43,h19,h6954,h2]) ).
cnf(t1834,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1834]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 05:54:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.20/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.20/2.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------