%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 : Thu Sep 24 08:53:51 AM UTC 2026
% Result : Theorem 0.33s 0.58s
% Output : Proof 0.33s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('NUM008+0.ax',axiom_1) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('NUM008+0.ax',axiom_2) ).
fof(axiom_3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('NUM008+0.ax',axiom_3) ).
fof(axiom_4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
file('NUM008+0.ax',axiom_4) ).
fof(axiom_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('NUM008+0.ax',axiom_1a) ).
fof(axiom_2a,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('NUM008+0.ax',axiom_2a) ).
fof(axiom_3a,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('NUM008+0.ax',axiom_3a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('NUM008+0.ax',axiom_4a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('NUM008+0.ax',axiom_5a) ).
fof(axiom_6a,axiom,
! [X6] :
( ? [Y1,Y11] :
( X6 = Y11
& r2(Y1,Y11) )
| ? [Y19] :
( X6 = Y19
& r1(Y19) ) ),
file('NUM008+0.ax',axiom_6a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('NUM008+0.ax',axiom_7a) ).
fof(xplustwoeqy,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& Y3 = Y2 ),
file('theBenchmark.p',xplustwoeqy) ).
fof(f_1_1,plain,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
inference(fof_nnf,[status(thm)],[axiom_1]) ).
fof(f_1_2,plain,
? [U_1] :
! [U_0] :
( ( U_0 = U_1
& r1(U_0) )
| ( U_0 != U_1
& ~ r1(U_0) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_0] :
( ( U_0 = sK1
& r1(U_0) )
| ( U_0 != sK1
& ~ r1(U_0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_1_2]) ).
cnf(f_1_4,plain,
( r1(U_0)
| ~ r1(U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( U_0 = sK1
| ~ r1(U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( r1(U_0)
| U_0 != sK1 ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_7,plain,
( U_0 = sK1
| U_0 != sK1 ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(f_2_2,plain,
! [U_4] :
? [U_3] :
! [U_2] :
( ( U_2 = U_3
& r2(U_4,U_2) )
| ( U_2 != U_3
& ~ r2(U_4,U_2) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_4,U_2] :
( ( U_2 = sK2(U_4)
& r2(U_4,U_2) )
| ( U_2 != sK2(U_4)
& ~ r2(U_4,U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2(U_4))],[f_2_2]) ).
cnf(f_2_4,plain,
( r2(U_4,U_2)
| ~ r2(U_4,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( U_2 = sK2(U_4)
| ~ r2(U_4,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( r2(U_4,U_2)
| U_2 != sK2(U_4) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_7,plain,
( U_2 = sK2(U_4)
| U_2 != sK2(U_4) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(f_3_2,plain,
! [U_8,U_7] :
? [U_6] :
! [U_5] :
( ( U_5 = U_6
& r3(U_8,U_7,U_5) )
| ( U_5 != U_6
& ~ r3(U_8,U_7,U_5) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_8,U_7,U_5] :
( ( U_5 = sK3(U_8,U_7)
& r3(U_8,U_7,U_5) )
| ( U_5 != sK3(U_8,U_7)
& ~ r3(U_8,U_7,U_5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_6,sK3(U_8,U_7))],[f_3_2]) ).
cnf(f_3_4,plain,
( r3(U_8,U_7,U_5)
| ~ r3(U_8,U_7,U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( U_5 = sK3(U_8,U_7)
| ~ r3(U_8,U_7,U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( r3(U_8,U_7,U_5)
| U_5 != sK3(U_8,U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( U_5 = sK3(U_8,U_7)
| U_5 != sK3(U_8,U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(f_4_2,plain,
! [U_12,U_11] :
? [U_10] :
! [U_9] :
( ( U_9 = U_10
& r4(U_12,U_11,U_9) )
| ( U_9 != U_10
& ~ r4(U_12,U_11,U_9) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_12,U_11,U_9] :
( ( U_9 = sK4(U_12,U_11)
& r4(U_12,U_11,U_9) )
| ( U_9 != sK4(U_12,U_11)
& ~ r4(U_12,U_11,U_9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_10,sK4(U_12,U_11))],[f_4_2]) ).
cnf(f_4_4,plain,
( r4(U_12,U_11,U_9)
| ~ r4(U_12,U_11,U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( U_9 = sK4(U_12,U_11)
| ~ r4(U_12,U_11,U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( r4(U_12,U_11,U_9)
| U_9 != sK4(U_12,U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( U_9 = sK4(U_12,U_11)
| U_9 != sK4(U_12,U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(f_5_2,plain,
! [U_18,U_17] :
? [U_16] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,U_16) )
& ? [U_14] :
( U_14 = U_16
& ? [U_13] :
( r3(U_18,U_13,U_14)
& r2(U_17,U_13) ) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_18,U_17] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,sK5(U_18,U_17)) )
& ? [U_14] :
( U_14 = sK5(U_18,U_17)
& ? [U_13] :
( r3(U_18,U_13,U_14)
& r2(U_17,U_13) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_16,sK5(U_18,U_17))],[f_5_2]) ).
fof(f_5_4,plain,
! [U_18,U_17] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,sK5(U_18,U_17)) )
& sK6(U_18,U_17) = sK5(U_18,U_17)
& ? [U_13] :
( r3(U_18,U_13,sK6(U_18,U_17))
& r2(U_17,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6(U_18,U_17))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_18,U_17] :
( ? [U_15] :
( r3(U_18,U_17,U_15)
& r2(U_15,sK5(U_18,U_17)) )
& sK6(U_18,U_17) = sK5(U_18,U_17)
& r3(U_18,sK7(U_18,U_17),sK6(U_18,U_17))
& r2(U_17,sK7(U_18,U_17)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_13,sK7(U_18,U_17))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_18,U_17] :
( r3(U_18,U_17,sK8(U_18,U_17))
& r2(sK8(U_18,U_17),sK5(U_18,U_17))
& sK6(U_18,U_17) = sK5(U_18,U_17)
& r3(U_18,sK7(U_18,U_17),sK6(U_18,U_17))
& r2(U_17,sK7(U_18,U_17)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_15,sK8(U_18,U_17))],[f_5_5]) ).
cnf(f_5_7,plain,
r2(U_17,sK7(U_18,U_17)),
inference(clausify,[status(thm)],[f_5_6]) ).
cnf(f_5_8,plain,
r3(U_18,sK7(U_18,U_17),sK6(U_18,U_17)),
inference(clausify,[status(thm)],[f_5_6]) ).
cnf(f_5_9,plain,
sK6(U_18,U_17) = sK5(U_18,U_17),
inference(clausify,[status(thm)],[f_5_6]) ).
cnf(f_5_10,plain,
r2(sK8(U_18,U_17),sK5(U_18,U_17)),
inference(clausify,[status(thm)],[f_5_6]) ).
cnf(f_5_11,plain,
r3(U_18,U_17,sK8(U_18,U_17)),
inference(clausify,[status(thm)],[f_5_6]) ).
fof(f_6_1,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(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(f_6_2,plain,
! [U_24,U_23] :
? [U_22] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,U_22) )
& ? [U_20] :
( U_20 = U_22
& ? [U_19] :
( r4(U_24,U_19,U_20)
& r2(U_23,U_19) ) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_24,U_23] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,sK9(U_24,U_23)) )
& ? [U_20] :
( U_20 = sK9(U_24,U_23)
& ? [U_19] :
( r4(U_24,U_19,U_20)
& r2(U_23,U_19) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_22,sK9(U_24,U_23))],[f_6_2]) ).
fof(f_6_4,plain,
! [U_24,U_23] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,sK9(U_24,U_23)) )
& sK10(U_24,U_23) = sK9(U_24,U_23)
& ? [U_19] :
( r4(U_24,U_19,sK10(U_24,U_23))
& r2(U_23,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_20,sK10(U_24,U_23))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_24,U_23] :
( ? [U_21] :
( r4(U_24,U_23,U_21)
& r3(U_21,U_24,sK9(U_24,U_23)) )
& sK10(U_24,U_23) = sK9(U_24,U_23)
& r4(U_24,sK11(U_24,U_23),sK10(U_24,U_23))
& r2(U_23,sK11(U_24,U_23)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_19,sK11(U_24,U_23))],[f_6_4]) ).
fof(f_6_6,plain,
! [U_24,U_23] :
( r4(U_24,U_23,sK12(U_24,U_23))
& r3(sK12(U_24,U_23),U_24,sK9(U_24,U_23))
& sK10(U_24,U_23) = sK9(U_24,U_23)
& r4(U_24,sK11(U_24,U_23),sK10(U_24,U_23))
& r2(U_23,sK11(U_24,U_23)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_21,sK12(U_24,U_23))],[f_6_5]) ).
cnf(f_6_7,plain,
r2(U_23,sK11(U_24,U_23)),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_8,plain,
r4(U_24,sK11(U_24,U_23),sK10(U_24,U_23)),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_9,plain,
sK10(U_24,U_23) = sK9(U_24,U_23),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_10,plain,
r3(sK12(U_24,U_23),U_24,sK9(U_24,U_23)),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_11,plain,
r4(U_24,U_23,sK12(U_24,U_23)),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_7_1,plain,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_3a]) ).
fof(f_7_2,plain,
! [U_28,U_27] :
( U_28 = U_27
| ! [U_26] :
( ~ r2(U_27,U_26)
| ! [U_25] :
( U_25 != U_26
| ~ r2(U_28,U_25) ) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( U_28 = U_27
| ~ r2(U_27,U_26)
| U_25 != U_26
| ~ r2(U_28,U_25) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(f_8_2,plain,
! [U_31] :
? [U_30] :
( U_30 = U_31
& ? [U_29] :
( r3(U_31,U_29,U_30)
& r1(U_29) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_31] :
( sK13(U_31) = U_31
& ? [U_29] :
( r3(U_31,U_29,sK13(U_31))
& r1(U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_30,sK13(U_31))],[f_8_2]) ).
fof(f_8_4,plain,
! [U_31] :
( sK13(U_31) = U_31
& r3(U_31,sK14(U_31),sK13(U_31))
& r1(sK14(U_31)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_29,sK14(U_31))],[f_8_3]) ).
cnf(f_8_5,plain,
r1(sK14(U_31)),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
r3(U_31,sK14(U_31),sK13(U_31)),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
sK13(U_31) = U_31,
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(f_9_2,plain,
! [U_35] :
? [U_34] :
( ? [U_33] :
( U_34 = U_33
& r1(U_33) )
& ? [U_32] :
( r4(U_35,U_32,U_34)
& r1(U_32) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_35] :
( ? [U_33] :
( sK15(U_35) = U_33
& r1(U_33) )
& ? [U_32] :
( r4(U_35,U_32,sK15(U_35))
& r1(U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_34,sK15(U_35))],[f_9_2]) ).
fof(f_9_4,plain,
! [U_35] :
( ? [U_33] :
( sK15(U_35) = U_33
& r1(U_33) )
& r4(U_35,sK16(U_35),sK15(U_35))
& r1(sK16(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_32,sK16(U_35))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_35] :
( sK15(U_35) = sK17(U_35)
& r1(sK17(U_35))
& r4(U_35,sK16(U_35),sK15(U_35))
& r1(sK16(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_33,sK17(U_35))],[f_9_4]) ).
cnf(f_9_6,plain,
r1(sK16(U_35)),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
r4(U_35,sK16(U_35),sK15(U_35)),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
r1(sK17(U_35)),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
sK15(U_35) = sK17(U_35),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,plain,
! [X6] :
( ? [Y1,Y11] :
( X6 = Y11
& r2(Y1,Y11) )
| ? [Y19] :
( X6 = Y19
& r1(Y19) ) ),
inference(fof_nnf,[status(thm)],[axiom_6a]) ).
fof(f_10_2,plain,
! [U_39] :
( ? [U_38,U_37] :
( U_39 = U_37
& r2(U_38,U_37) )
| ? [U_36] :
( U_39 = U_36
& r1(U_36) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_39] :
( ? [U_38,U_37] :
( U_39 = U_37
& r2(U_38,U_37) )
| ( U_39 = sK18(U_39)
& r1(sK18(U_39)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_36,sK18(U_39))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_39] :
( ? [U_37] :
( U_39 = U_37
& r2(sK19(U_39),U_37) )
| ( U_39 = sK18(U_39)
& r1(sK18(U_39)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_38,sK19(U_39))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_39] :
( ( U_39 = sK20(U_39)
& r2(sK19(U_39),sK20(U_39)) )
| ( U_39 = sK18(U_39)
& r1(sK18(U_39)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_37,sK20(U_39))],[f_10_4]) ).
cnf(f_10_6,plain,
( r2(sK19(U_39),sK20(U_39))
| r1(sK18(U_39)) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( U_39 = sK20(U_39)
| r1(sK18(U_39)) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( r2(sK19(U_39),sK20(U_39))
| U_39 = sK18(U_39) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( U_39 = sK20(U_39)
| U_39 = sK18(U_39) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(fof_nnf,[status(thm)],[axiom_7a]) ).
fof(f_11_2,plain,
! [U_42,U_41] :
( ~ r2(U_42,U_41)
| ! [U_40] :
( U_40 != U_41
| ~ r1(U_40) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( ~ r2(U_42,U_41)
| U_40 != U_41
| ~ r1(U_40) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& Y3 = Y2 ),
inference(negate,[status(cth)],[xplustwoeqy]) ).
fof(f_12_2,negated_conjecture,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ~ r2(Y6,Y5)
| ~ r1(Y6) )
| ~ r2(Y5,Y4) )
| ~ r3(Y1,Y4,Y3) )
| Y3 != Y2 ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
! [U_48,U_47,U_46] :
( ! [U_45] :
( ! [U_44] :
( ! [U_43] :
( ~ r2(U_43,U_44)
| ~ r1(U_43) )
| ~ r2(U_44,U_45) )
| ~ r3(U_48,U_45,U_46) )
| U_46 != U_47 ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
! [U_43,U_45,U_44,U_46,U_47,U_48] :
( ~ r2(U_43,U_44)
| ~ r1(U_43)
| ~ r2(U_44,U_45)
| ~ r3(U_48,U_45,U_46)
| U_46 != U_47 ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,negated_conjecture,
( ~ r2(U_43,U_44)
| ~ r1(U_43)
| ~ r2(U_44,U_45)
| ~ r3(U_48,U_45,U_46)
| U_46 != U_47 ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_1_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_7]) ).
cnf(f_2_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_4]) ).
cnf(f_2_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_7]) ).
cnf(f_3_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_4]) ).
cnf(f_3_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_7]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_4_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( r1(Eq_y_0)
| ~ r1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( r2(Eq_y_0,Eq_y_1)
| ~ r2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( r3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( r4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.37 % Computer : n019.cluster.edu
% 0.07/0.37 % Model : x86_64 x86_64
% 0.07/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.37 % Memory : 8046.5625MB
% 0.07/0.37 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Sat Sep 19 19:34:50 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.33/0.58 % SZS status Theorem for theBenchmark
% 0.33/0.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------