%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN069+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:29:29 PM UTC 2026
% Result : Theorem 6.84s 1.38s
% Output : Proof 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 19 unt; 0 def)
% Number of atoms : 101 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 107 ( 49 ~; 30 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 68 ( 1 sgn 34 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f0,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X19] :
( ( ~ id(X19,sk0)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c3,plain,
( ~ id(X1,sk0)
| r1(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,axiom,
ifeq(id(X0,sk0),true,r1(X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h3,plain,
r1(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi8]) ).
fof(f7,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('/export/starexec/sandbox2/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]) ).
fof(f14,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f14_nnf,plain,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X4] :
( r3(X4,sk13(X4),sk12(X4))
& r1(sk13(X4))
& id(sk12(X4),X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f14_nnf]) ).
cnf(c46,plain,
id(sk12(X0),X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi30,axiom,
id(sk12(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(h7,plain,
r1(sk12(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi30,h3]) ).
fof(f18,conjecture,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& id(Y1,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneidone) ).
fof(f18_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& id(Y1,Y1) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
! [Y1] :
( ! [Y2] :
( ~ r2(Y2,Y1)
| ~ r1(Y2) )
| ~ id(Y1,Y1) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [Y1,Y2] :
( ~ r2(Y2,Y1)
| ~ r1(Y2)
| ~ id(Y1,Y1) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c58,plain,
( ~ r2(X1,X0)
| ~ r1(X1)
| ~ id(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(id(X0,X0),true,ifeq(r1(X1),true,ifeq(r2(X1,X0),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,hi8,h7,h2]) ).
cnf(t624,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('/export/starexec/sandbox2/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c57,c58]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t624]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN069+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.39 % Computer : n015.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Thu Sep 24 05:57:42 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.84/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.84/1.38 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------