%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:29:30 PM UTC 2026
% Result : Theorem 18.58s 3.09s
% Output : Proof 18.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 41 unt; 0 def)
% Number of atoms : 248 ( 72 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 272 ( 109 ~; 82 |; 81 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 231 ( 9 sgn 63 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f7_nnf,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X4] :
( sk12(X4) = X4
& r3(X4,sk13(X4),sk12(X4))
& r1(sk13(X4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f7_nnf]) ).
cnf(c27,plain,
r1(sk13(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X19] :
( ( X19 = sk0
& r1(X19) )
| ( X19 != sk0
& ~ r1(X19) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( X1 = sk0
| ~ r1(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p213,plain,
sk13(X0) = sk0,
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(c28,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p214,plain,
r3(X0,sk0,sk12(X0)),
inference(demodulation,[status(thm)],[p213,c28]) ).
fof(f2,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('/export/starexec/sandbox/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(p475,plain,
X0 = sk2(X0,sk0),
inference(resolution,[status(thm)],[p214,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/sandbox/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(p170,plain,
sk7(X0,X1) = sk2(X0,X1),
inference(resolution,[status(thm)],[c20,c9]) ).
cnf(p809,plain,
sk2(X0,sk0) = X0,
inference(superposition,[status(thm)],[p475,p170]) ).
cnf(c19,plain,
r2(sk7(X0,X1),sk4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p171,plain,
r2(sk2(X0,X1),sk4(X0,X1)),
inference(demodulation,[status(thm)],[p170,c19]) ).
cnf(p1092,plain,
r2(X0,sk4(X0,sk0)),
inference(superposition,[status(thm)],[p809,p171]) ).
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox/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(c5,plain,
( X2 = sk1(X0)
| ~ r2(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p3599,plain,
sk4(X0,sk0) = sk1(X0),
inference(resolution,[status(thm)],[p1092,c5]) ).
fof(f8,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f8_nnf,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X5] :
( sk14(X5) = sk16(X5)
& r1(sk16(X5))
& r4(X5,sk15(X5),sk14(X5))
& r1(sk15(X5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f8_nnf]) ).
cnf(c30,plain,
r1(sk15(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p219,plain,
sk15(X0) = sk0,
inference(resolution,[status(thm)],[c30,c1]) ).
cnf(c31,plain,
r4(X0,sk15(X0),sk14(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p220,plain,
r4(X0,sk0,sk14(X0)),
inference(demodulation,[status(thm)],[p219,c31]) ).
fof(f3,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f3_nnf,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X16,X17,X18] :
( ( X18 = sk3(X16,X17)
& r4(X16,X17,X18) )
| ( X18 != sk3(X16,X17)
& ~ r4(X16,X17,X18) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f3_nnf]) ).
cnf(c13,plain,
( X3 = sk3(X0,X1)
| ~ r4(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p484,plain,
sk14(X0) = sk3(X0,sk0),
inference(resolution,[status(thm)],[p220,c13]) ).
fof(f5,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2a) ).
fof(f5_nnf,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X9,X2] :
( r4(X2,X9,sk11(X2,X9))
& r3(sk11(X2,X9),X2,sk8(X2,X9))
& sk9(X2,X9) = sk8(X2,X9)
& r4(X2,sk10(X2,X9),sk9(X2,X9))
& r2(X9,sk10(X2,X9)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10,sk11])],[f5_nnf]) ).
cnf(c25,plain,
r4(X0,X1,sk11(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p199,plain,
sk11(X0,X1) = sk3(X0,X1),
inference(resolution,[status(thm)],[c25,c13]) ).
cnf(p816,plain,
sk3(X0,sk0) = sk0,
inference(superposition,[status(thm)],[p484,p199]) ).
cnf(c24,plain,
r3(sk11(X0,X1),X0,sk8(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p196,plain,
sk8(X0,X1) = sk2(sk11(X0,X1),X0),
inference(resolution,[status(thm)],[c24,c9]) ).
cnf(p201,plain,
sk8(X0,X1) = sk2(sk3(X0,X1),X0),
inference(demodulation,[status(thm)],[p199,p196]) ).
cnf(p452,plain,
sk2(sk3(X0,X1),X0) = sk8(X0,X1),
inference(superposition,[status(thm)],[p201,p170]) ).
cnf(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p146,plain,
sk6(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(c17,plain,
r3(X0,sk6(X0,X1),sk5(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p147,plain,
r3(X0,sk1(X1),sk5(X0,X1)),
inference(demodulation,[status(thm)],[p146,c17]) ).
cnf(p396,plain,
sk4(X0,X1) = sk2(X0,sk1(X1)),
inference(resolution,[status(thm)],[p147,c9]) ).
cnf(p732,plain,
sk2(X0,sk1(X1)) = sk4(X0,X1),
inference(superposition,[status(thm)],[p396,p170]) ).
cnf(p1058,plain,
sk8(sk1(X0),X1) = sk4(sk3(sk1(X0),X1),X0),
inference(superposition,[status(thm)],[p452,p732]) ).
cnf(p2965,plain,
sk8(sk1(X0),sk0) = sk4(sk0,X0),
inference(superposition,[status(thm)],[p816,p1058]) ).
fof(f11,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r2(Y6,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r4(Y5,Y2,Y1) )
& ? [Y4] :
( ? [Y7] :
( r2(Y7,Y4)
& r1(Y7) )
& r2(Y4,Y2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',onetimestwoeqtwo) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r2(Y6,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r4(Y5,Y2,Y1) )
& ? [Y4] :
( ? [Y7] :
( r2(Y7,Y4)
& r1(Y7) )
& r2(Y4,Y2) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ! [Y9] :
( ~ r2(Y9,Y6)
| ~ r1(Y9) )
| ~ r2(Y6,Y3) )
| Y1 != Y3 )
| ! [Y2] :
( ! [Y5] :
( ! [Y8] :
( ~ r2(Y8,Y5)
| ~ r1(Y8) )
| ~ r4(Y5,Y2,Y1) )
| ! [Y4] :
( ! [Y7] :
( ~ r2(Y7,Y4)
| ~ r1(Y7) )
| ~ r2(Y4,Y2) ) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y4,Y2,Y7,Y5,Y1,Y8,Y3,Y6,Y9] :
( ~ r2(Y9,Y6)
| ~ r1(Y9)
| ~ r2(Y6,Y3)
| Y1 != Y3
| ~ r2(Y8,Y5)
| ~ r1(Y8)
| ~ r4(Y5,Y2,Y1)
| ~ r2(Y7,Y4)
| ~ r1(Y7)
| ~ r2(Y4,Y2) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| X0 != X6
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r4(X4,X1,X0)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p44,plain,
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| X4 != X5
| ~ r2(X2,X3)
| ~ r4(X3,X1,X4)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(factoring,[status(thm)],[c39]) ).
cnf(p327,plain,
( ~ r2(X2,X6)
| ~ r2(X6,X5)
| X4 != X5
| ~ r2(X2,X3)
| ~ r4(X3,X1,X4)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(factoring,[status(thm)],[p44]) ).
cnf(p578,plain,
( ~ r2(X2,X5)
| ~ r2(X5,X4)
| X3 != X4
| ~ r4(X0,X1,X3)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(factoring,[status(thm)],[p327]) ).
cnf(c6,plain,
( r2(X0,X2)
| X2 != sk1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p97,plain,
r2(X0,sk1(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(p626,plain,
( ~ r2(X0,X4)
| ~ r2(X4,X3)
| X2 != X3
| ~ r4(X1,sk1(X1),X2)
| ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p578,p97]) ).
cnf(c2,plain,
( r1(X1)
| X1 != sk0 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p76,plain,
r1(sk0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p628,plain,
( ~ r2(sk0,X3)
| ~ r2(X3,X2)
| X1 != X2
| ~ r4(X0,sk1(X0),X1)
| ~ r2(sk0,X0) ),
inference(resolution,[status(thm)],[p626,p76]) ).
cnf(p633,plain,
( ~ r2(sk0,X2)
| ~ r2(X2,X1)
| X0 != X1
| ~ r4(sk1(sk0),sk1(sk1(sk0)),X0) ),
inference(resolution,[status(thm)],[p628,p97]) ).
cnf(c21,plain,
r2(X1,sk10(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p186,plain,
sk10(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c21,c5]) ).
cnf(c22,plain,
r4(X0,sk10(X0,X1),sk9(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p187,plain,
r4(X0,sk1(X1),sk9(X0,X1)),
inference(demodulation,[status(thm)],[p186,c22]) ).
cnf(p635,plain,
( ~ r2(sk0,X1)
| ~ r2(X1,X0)
| sk8(sk1(sk0),sk1(sk0)) != X0 ),
inference(resolution,[status(thm)],[p633,p187]) ).
cnf(p2961,plain,
( ~ r2(sk0,X0)
| ~ r2(X0,sk4(sk8(sk1(sk0),sk0),sk0)) ),
inference(resolution,[status(thm)],[p1058,p635]) ).
cnf(p2967,plain,
( ~ r2(sk0,X0)
| ~ r2(X0,sk4(sk4(sk0,sk0),sk0)) ),
inference(demodulation,[status(thm)],[p2965,p2961]) ).
cnf(p2973,plain,
~ r2(sk0,sk4(sk0,sk0)),
inference(resolution,[status(thm)],[p2967,p171]) ).
cnf(p3603,plain,
~ r2(sk0,sk1(sk0)),
inference(demodulation,[status(thm)],[p3599,p2973]) ).
cnf(p3624,plain,
$false,
inference(resolution,[status(thm)],[p3603,p97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.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 05:51:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.58/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.58/3.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------