%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 02:29:27 PM UTC 2026
% Result : Theorem 6.07s 1.31s
% Output : Proof 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 17 unt; 0 def)
% Number of atoms : 94 ( 47 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 41 ~; 26 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 98 ( 2 sgn 40 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X11,X12] :
( ( X12 = sk1(X11)
& r2(X11,X12) )
| ( X12 != sk1(X11)
& ~ r2(X11,X12) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c6,plain,
( r2(X0,X2)
| X2 != sk1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
ifeq(X0,sk1(X1),r2(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(hi37,axiom,
or(X0,false) = X0,
introduced(definition) ).
cnf(h9,plain,
r2(V0,or(sk1(V0),false)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi37]) ).
fof(f2,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f2_nnf,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X13,X14,X15] :
( ( X15 = sk2(X13,X14)
& r3(X13,X14,X15) )
| ( X15 != sk2(X13,X14)
& ~ r3(X13,X14,X15) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f2_nnf]) ).
cnf(c9,plain,
( X3 = sk2(X0,X1)
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,axiom,
ifeq(r3(X0,X1,X2),true,X2,sk2(X0,X1)) = sk2(X0,X1),
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f4,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f4_nnf,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X8,X1] :
( r3(X1,X8,sk7(X1,X8))
& r2(sk7(X1,X8),sk4(X1,X8))
& sk5(X1,X8) = sk4(X1,X8)
& r3(X1,sk6(X1,X8),sk5(X1,X8))
& r2(X8,sk6(X1,X8)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f4_nnf]) ).
cnf(c20,plain,
r3(X0,X1,sk7(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi12,axiom,
r3(X0,X1,sk7(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h30,plain,
sk7(V0,V1) = sk2(V0,V1),
inference(hyper_resolution,[status(thm)],[hi4,hi12]) ).
fof(f11,conjecture,
! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( Y3 = Y2
& r3(X1,Y1,Y3) )
& ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbers) ).
fof(f11_neg,negated_conjecture,
~ ! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( Y3 = Y2
& r3(X1,Y1,Y3) )
& ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [X1] :
! [Y2,Y1] :
( ! [Y3] :
( Y3 != Y2
| ~ r3(X1,Y1,Y3) )
| ? [Y4] :
( Y1 = Y4
& r1(Y4) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y2,Y1,Y3] :
( Y3 != Y2
| ~ r3(sk20,Y1,Y3)
| ( Y1 = sk21(Y2,Y1)
& r1(sk21(Y2,Y1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21])],[f11_nnf]) ).
cnf(c40,plain,
( X4 != X1
| ~ r3(sk20,X2,X4)
| X2 = sk21(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi31,negated_conjecture,
ifeq(r3(sk20,X0,X1),true,ifeq(X1,X2,X0,sk21(X2,X0)),sk21(X2,X0)) = sk21(X2,X0),
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h31,plain,
V0 = sk21(sk2(sk20,V0),V0),
inference(hyper_resolution,[status(thm)],[hi31,hi12,h30]) ).
cnf(c39,plain,
( X4 != X1
| ~ r3(sk20,X2,X4)
| r1(sk21(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi30,negated_conjecture,
ifeq(r3(sk20,X0,X1),true,ifeq(X1,X2,r1(sk21(X2,X0)),true),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h32,plain,
r1(sk21(sk2(sk20,V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi30,hi12,h30]) ).
fof(f10,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f10_nnf,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y20,Y10,X7] :
( ~ r2(X7,Y10)
| Y20 != Y10
| ~ r1(Y20) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c38,plain,
( ~ r2(X0,X1)
| X2 != X1
| ~ r1(X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi32,axiom,
ifeq(r1(X0),true,ifeq(X0,X1,ifeq(r2(X2,X1),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi32,h32,h31,h9]) ).
cnf(t115,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t115]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 05:53:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.07/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.07/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------