%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN082+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 : n012.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 02:29:32 PM UTC 2026
% Result : Theorem 2.48s 0.72s
% Output : Proof 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 32 unt; 0 def)
% Number of atoms : 173 ( 56 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 161 ( 56 ~; 34 |; 71 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 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 : 163 ( 16 sgn 55 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox2/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]) ).
fof(f7,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox2/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]) ).
cnf(p43,plain,
sk13(X0) = sk0,
inference(resolution,[status(thm)],[c1,c27]) ).
cnf(c28,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p45,plain,
r3(X0,sk0,sk12(X0)),
inference(demodulation,[status(thm)],[p43,c28]) ).
cnf(p72,plain,
X0 = sk2(X0,sk0),
inference(resolution,[status(thm)],[c9,p45]) ).
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(p73,plain,
sk7(X0,X1) = sk2(X0,X1),
inference(resolution,[status(thm)],[c9,c20]) ).
cnf(p91,plain,
sk2(X0,sk0) = X0,
inference(superposition,[status(thm)],[p72,p73]) ).
fof(f3,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
file('/export/starexec/sandbox2/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]) ).
fof(f8,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox2/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(p46,plain,
sk15(X0) = sk0,
inference(resolution,[status(thm)],[c1,c30]) ).
cnf(c31,plain,
r4(X0,sk15(X0),sk14(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p47,plain,
r4(X0,sk0,sk14(X0)),
inference(demodulation,[status(thm)],[p46,c31]) ).
cnf(p92,plain,
sk0 = sk3(X0,sk0),
inference(resolution,[status(thm)],[c13,p47]) ).
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/sandbox2/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(p93,plain,
sk11(X0,X1) = sk3(X0,X1),
inference(resolution,[status(thm)],[c13,c25]) ).
cnf(p122,plain,
sk3(X0,sk0) = sk0,
inference(superposition,[status(thm)],[p92,p93]) ).
cnf(c24,plain,
r3(sk11(X0,X1),X0,sk8(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p94,plain,
r3(sk3(X0,X1),X0,sk8(X0,X1)),
inference(demodulation,[status(thm)],[p93,c24]) ).
cnf(p140,plain,
r3(sk0,X0,sk8(X0,sk0)),
inference(superposition,[status(thm)],[p122,p94]) ).
cnf(p141,plain,
sk8(X0,sk0) = sk2(sk0,X0),
inference(resolution,[status(thm)],[p140,c9]) ).
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(c5,plain,
( X2 = sk1(X0)
| ~ r2(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c21,plain,
r2(X1,sk10(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p60,plain,
sk10(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c5,c21]) ).
cnf(c22,plain,
r4(X0,sk10(X0,X1),sk9(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p61,plain,
r4(X0,sk1(X1),sk9(X0,X1)),
inference(demodulation,[status(thm)],[p60,c22]) ).
fof(f11,conjecture,
? [Y1,Y2] :
( ? [Y5] :
( Y2 = Y5
& r1(Y5) )
& ? [Y3] :
( ? [Y4] :
( r2(Y4,Y3)
& r1(Y4) )
& r4(Y1,Y3,Y2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xtimesoneeqzero) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1,Y2] :
( ? [Y5] :
( Y2 = Y5
& r1(Y5) )
& ? [Y3] :
( ? [Y4] :
( r2(Y4,Y3)
& r1(Y4) )
& r4(Y1,Y3,Y2) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1,Y2] :
( ! [Y5] :
( Y2 != Y5
| ~ r1(Y5) )
| ! [Y3] :
( ! [Y4] :
( ~ r2(Y4,Y3)
| ~ r1(Y4) )
| ~ r4(Y1,Y3,Y2) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y1,Y3,Y2,Y4,Y5] :
( Y2 != Y5
| ~ r1(Y5)
| ~ r2(Y4,Y3)
| ~ r1(Y4)
| ~ r4(Y1,Y3,Y2) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( X1 != X4
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r4(X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p41,plain,
( ~ r1(X2)
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r4(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(p80,plain,
( ~ r1(sk8(X2,X1))
| ~ r2(X0,sk1(X1))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p61,p41]) ).
cnf(p44,plain,
r1(sk0),
inference(demodulation,[status(thm)],[p43,c27]) ).
cnf(p84,plain,
( ~ r1(sk8(X1,X0))
| ~ r2(sk0,sk1(X0)) ),
inference(resolution,[status(thm)],[p80,p44]) ).
cnf(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p57,plain,
sk6(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c5,c16]) ).
cnf(p58,plain,
r2(X0,sk1(X0)),
inference(demodulation,[status(thm)],[p57,c16]) ).
cnf(p85,plain,
~ r1(sk8(X0,sk0)),
inference(resolution,[status(thm)],[p84,p58]) ).
cnf(p142,plain,
~ r1(sk2(sk0,X0)),
inference(demodulation,[status(thm)],[p141,p85]) ).
cnf(p145,plain,
~ r1(sk0),
inference(superposition,[status(thm)],[p91,p142]) ).
cnf(p146,plain,
$false,
inference(resolution,[status(thm)],[p145,p44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN082+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 05:58:56 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.48/0.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.48/0.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------