%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUN080+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 08:53:50 AM UTC 2026
% Result : Theorem 1.24s 1.54s
% Output : Proof 1.31s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('NUM009+0.ax',axiom_1) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
file('NUM009+0.ax',axiom_2) ).
fof(axiom_3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
file('NUM009+0.ax',axiom_3) ).
fof(axiom_4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ id(X18,Y23)
& ~ r4(X16,X17,X18) )
| ( r4(X16,X17,X18)
& id(X18,Y23) ) ),
file('NUM009+0.ax',axiom_4) ).
fof(axiom_5,axiom,
! [X20] : id(X20,X20),
file('NUM009+0.ax',axiom_5) ).
fof(axiom_6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('NUM009+0.ax',axiom_6) ).
fof(axiom_7,axiom,
! [X23,X24,X25] :
( ~ id(X24,X25)
| id(X23,X25)
| ~ id(X23,X24) ),
file('NUM009+0.ax',axiom_7) ).
fof(axiom_8,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('NUM009+0.ax',axiom_8) ).
fof(axiom_9,axiom,
! [X28,X29,X30,X31] :
( ( r2(X30,X31)
& r2(X28,X29) )
| ( ~ r2(X30,X31)
& ~ r2(X28,X29) )
| ~ id(X29,X31)
| ~ id(X28,X30) ),
file('NUM009+0.ax',axiom_9) ).
fof(axiom_10,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ( r3(X35,X36,X37)
& r3(X32,X33,X34) )
| ( ~ r3(X35,X36,X37)
& ~ r3(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
file('NUM009+0.ax',axiom_10) ).
fof(axiom_11,axiom,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
file('NUM009+0.ax',axiom_11) ).
fof(axiom_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('NUM009+0.ax',axiom_1a) ).
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
file('NUM009+0.ax',axiom_2a) ).
fof(axiom_3a,axiom,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
file('NUM009+0.ax',axiom_3a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('NUM009+0.ax',axiom_4a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('NUM009+0.ax',axiom_5a) ).
fof(axiom_6a,axiom,
! [X6] :
( ? [Y1,Y11] :
( r2(Y1,Y11)
& id(X6,Y11) )
| ? [Y19] :
( r1(Y19)
& id(X6,Y19) ) ),
file('NUM009+0.ax',axiom_6a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('NUM009+0.ax',axiom_7a) ).
fof(xplustwoidy,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& id(Y3,Y2) ),
file('theBenchmark.p',xplustwoidy) ).
fof(f_1_1,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
inference(fof_nnf,[status(thm)],[axiom_1]) ).
fof(f_1_2,plain,
? [U_1] :
! [U_0] :
( ( ~ id(U_0,U_1)
& ~ r1(U_0) )
| ( r1(U_0)
& id(U_0,U_1) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_0] :
( ( ~ id(U_0,sK1)
& ~ r1(U_0) )
| ( r1(U_0)
& id(U_0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ r1(U_0)
| id(U_0,sK1) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ id(U_0,sK1)
| id(U_0,sK1) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( ~ r1(U_0)
| r1(U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_7,plain,
( ~ id(U_0,sK1)
| r1(U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(f_2_2,plain,
! [U_4] :
? [U_3] :
! [U_2] :
( ( ~ id(U_2,U_3)
& ~ r2(U_4,U_2) )
| ( r2(U_4,U_2)
& id(U_2,U_3) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_4,U_2] :
( ( ~ id(U_2,sK2(U_4))
& ~ r2(U_4,U_2) )
| ( r2(U_4,U_2)
& id(U_2,sK2(U_4)) ) ),
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)
| id(U_2,sK2(U_4)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ id(U_2,sK2(U_4))
| id(U_2,sK2(U_4)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( ~ r2(U_4,U_2)
| r2(U_4,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_7,plain,
( ~ id(U_2,sK2(U_4))
| r2(U_4,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(f_3_2,plain,
! [U_8,U_7] :
? [U_6] :
! [U_5] :
( ( ~ id(U_5,U_6)
& ~ r3(U_8,U_7,U_5) )
| ( r3(U_8,U_7,U_5)
& id(U_5,U_6) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_8,U_7,U_5] :
( ( ~ id(U_5,sK3(U_8,U_7))
& ~ r3(U_8,U_7,U_5) )
| ( r3(U_8,U_7,U_5)
& id(U_5,sK3(U_8,U_7)) ) ),
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)
| id(U_5,sK3(U_8,U_7)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( ~ id(U_5,sK3(U_8,U_7))
| id(U_5,sK3(U_8,U_7)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,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_7,plain,
( ~ id(U_5,sK3(U_8,U_7))
| r3(U_8,U_7,U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ id(X18,Y23)
& ~ r4(X16,X17,X18) )
| ( r4(X16,X17,X18)
& id(X18,Y23) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(f_4_2,plain,
! [U_12,U_11] :
? [U_10] :
! [U_9] :
( ( ~ id(U_9,U_10)
& ~ r4(U_12,U_11,U_9) )
| ( r4(U_12,U_11,U_9)
& id(U_9,U_10) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_12,U_11,U_9] :
( ( ~ id(U_9,sK4(U_12,U_11))
& ~ r4(U_12,U_11,U_9) )
| ( r4(U_12,U_11,U_9)
& id(U_9,sK4(U_12,U_11)) ) ),
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)
| id(U_9,sK4(U_12,U_11)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ id(U_9,sK4(U_12,U_11))
| id(U_9,sK4(U_12,U_11)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,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_7,plain,
( ~ id(U_9,sK4(U_12,U_11))
| r4(U_12,U_11,U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X20] : id(X20,X20),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(f_5_2,plain,
! [U_13] : id(U_13,U_13),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
id(U_13,U_13),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(f_6_2,plain,
! [U_15,U_14] :
( id(U_14,U_15)
| ~ id(U_15,U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( id(U_14,U_15)
| ~ id(U_15,U_14) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [X23,X24,X25] :
( ~ id(X24,X25)
| id(X23,X25)
| ~ id(X23,X24) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(f_7_2,plain,
! [U_18,U_17,U_16] :
( ~ id(U_17,U_16)
| id(U_18,U_16)
| ~ id(U_18,U_17) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_18,U_17] :
( ! [U_16] :
( ~ id(U_17,U_16)
| id(U_18,U_16) )
| ~ id(U_18,U_17) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ~ id(U_17,U_16)
| id(U_18,U_16)
| ~ id(U_18,U_17) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
inference(fof_nnf,[status(thm)],[axiom_8]) ).
fof(f_8_2,plain,
! [U_20,U_19] :
( ( r1(U_19)
& r1(U_20) )
| ( ~ r1(U_19)
& ~ r1(U_20) )
| ~ id(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( r1(U_20)
| ~ r1(U_20)
| ~ id(U_20,U_19) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( r1(U_19)
| ~ r1(U_20)
| ~ id(U_20,U_19) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( r1(U_20)
| ~ r1(U_19)
| ~ id(U_20,U_19) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_6,plain,
( r1(U_19)
| ~ r1(U_19)
| ~ id(U_20,U_19) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [X28,X29,X30,X31] :
( ( r2(X30,X31)
& r2(X28,X29) )
| ( ~ r2(X30,X31)
& ~ r2(X28,X29) )
| ~ id(X29,X31)
| ~ id(X28,X30) ),
inference(fof_nnf,[status(thm)],[axiom_9]) ).
fof(f_9_2,plain,
! [U_24,U_23,U_22,U_21] :
( ( r2(U_22,U_21)
& r2(U_24,U_23) )
| ( ~ r2(U_22,U_21)
& ~ r2(U_24,U_23) )
| ~ id(U_23,U_21)
| ~ id(U_24,U_22) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_24,U_23,U_22] :
( ! [U_21] :
( ( r2(U_22,U_21)
& r2(U_24,U_23) )
| ( ~ r2(U_22,U_21)
& ~ r2(U_24,U_23) )
| ~ id(U_23,U_21) )
| ~ id(U_24,U_22) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( r2(U_24,U_23)
| ~ r2(U_24,U_23)
| ~ id(U_23,U_21)
| ~ id(U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( r2(U_22,U_21)
| ~ r2(U_24,U_23)
| ~ id(U_23,U_21)
| ~ id(U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( r2(U_24,U_23)
| ~ r2(U_22,U_21)
| ~ id(U_23,U_21)
| ~ id(U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( r2(U_22,U_21)
| ~ r2(U_22,U_21)
| ~ id(U_23,U_21)
| ~ id(U_24,U_22) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( r3(X35,X36,X37)
& r3(X32,X33,X34) )
| ( ~ r3(X35,X36,X37)
& ~ r3(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
inference(fof_nnf,[status(thm)],[axiom_10]) ).
fof(f_10_2,plain,
! [U_30,U_29,U_28,U_27,U_26,U_25] :
( ( r3(U_27,U_26,U_25)
& r3(U_30,U_29,U_28) )
| ( ~ r3(U_27,U_26,U_25)
& ~ r3(U_30,U_29,U_28) )
| ~ id(U_28,U_25)
| ~ id(U_29,U_26)
| ~ id(U_30,U_27) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_30,U_29,U_28,U_27] :
( ! [U_26] :
( ! [U_25] :
( ( r3(U_27,U_26,U_25)
& r3(U_30,U_29,U_28) )
| ( ~ r3(U_27,U_26,U_25)
& ~ r3(U_30,U_29,U_28) )
| ~ id(U_28,U_25) )
| ~ id(U_29,U_26) )
| ~ id(U_30,U_27) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( r3(U_30,U_29,U_28)
| ~ r3(U_30,U_29,U_28)
| ~ id(U_28,U_25)
| ~ id(U_29,U_26)
| ~ id(U_30,U_27) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( r3(U_27,U_26,U_25)
| ~ r3(U_30,U_29,U_28)
| ~ id(U_28,U_25)
| ~ id(U_29,U_26)
| ~ id(U_30,U_27) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( r3(U_30,U_29,U_28)
| ~ r3(U_27,U_26,U_25)
| ~ id(U_28,U_25)
| ~ id(U_29,U_26)
| ~ id(U_30,U_27) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( r3(U_27,U_26,U_25)
| ~ r3(U_27,U_26,U_25)
| ~ id(U_28,U_25)
| ~ id(U_29,U_26)
| ~ id(U_30,U_27) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
inference(fof_nnf,[status(thm)],[axiom_11]) ).
fof(f_11_2,plain,
! [U_36,U_35,U_34,U_33,U_32,U_31] :
( ( r4(U_33,U_32,U_31)
& r4(U_36,U_35,U_34) )
| ( ~ r4(U_33,U_32,U_31)
& ~ r4(U_36,U_35,U_34) )
| ~ id(U_34,U_31)
| ~ id(U_35,U_32)
| ~ id(U_36,U_33) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_36,U_35,U_34,U_33] :
( ! [U_32] :
( ! [U_31] :
( ( r4(U_33,U_32,U_31)
& r4(U_36,U_35,U_34) )
| ( ~ r4(U_33,U_32,U_31)
& ~ r4(U_36,U_35,U_34) )
| ~ id(U_34,U_31) )
| ~ id(U_35,U_32) )
| ~ id(U_36,U_33) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( r4(U_36,U_35,U_34)
| ~ r4(U_36,U_35,U_34)
| ~ id(U_34,U_31)
| ~ id(U_35,U_32)
| ~ id(U_36,U_33) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( r4(U_33,U_32,U_31)
| ~ r4(U_36,U_35,U_34)
| ~ id(U_34,U_31)
| ~ id(U_35,U_32)
| ~ id(U_36,U_33) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( r4(U_36,U_35,U_34)
| ~ r4(U_33,U_32,U_31)
| ~ id(U_34,U_31)
| ~ id(U_35,U_32)
| ~ id(U_36,U_33) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( r4(U_33,U_32,U_31)
| ~ r4(U_33,U_32,U_31)
| ~ id(U_34,U_31)
| ~ id(U_35,U_32)
| ~ id(U_36,U_33) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(f_12_2,plain,
! [U_42,U_41] :
? [U_40] :
( ? [U_39] :
( r3(U_42,U_41,U_39)
& r2(U_39,U_40) )
& ? [U_38] :
( ? [U_37] :
( r3(U_42,U_37,U_38)
& r2(U_41,U_37) )
& id(U_38,U_40) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_42,U_41] :
( ? [U_39] :
( r3(U_42,U_41,U_39)
& r2(U_39,sK5(U_42,U_41)) )
& ? [U_38] :
( ? [U_37] :
( r3(U_42,U_37,U_38)
& r2(U_41,U_37) )
& id(U_38,sK5(U_42,U_41)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_40,sK5(U_42,U_41))],[f_12_2]) ).
fof(f_12_4,plain,
! [U_42,U_41] :
( ? [U_39] :
( r3(U_42,U_41,U_39)
& r2(U_39,sK5(U_42,U_41)) )
& ? [U_37] :
( r3(U_42,U_37,sK6(U_42,U_41))
& r2(U_41,U_37) )
& id(sK6(U_42,U_41),sK5(U_42,U_41)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_38,sK6(U_42,U_41))],[f_12_3]) ).
fof(f_12_5,plain,
! [U_42,U_41] :
( ? [U_39] :
( r3(U_42,U_41,U_39)
& r2(U_39,sK5(U_42,U_41)) )
& r3(U_42,sK7(U_42,U_41),sK6(U_42,U_41))
& r2(U_41,sK7(U_42,U_41))
& id(sK6(U_42,U_41),sK5(U_42,U_41)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_37,sK7(U_42,U_41))],[f_12_4]) ).
fof(f_12_6,plain,
! [U_42,U_41] :
( r3(U_42,U_41,sK8(U_42,U_41))
& r2(sK8(U_42,U_41),sK5(U_42,U_41))
& r3(U_42,sK7(U_42,U_41),sK6(U_42,U_41))
& r2(U_41,sK7(U_42,U_41))
& id(sK6(U_42,U_41),sK5(U_42,U_41)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_39,sK8(U_42,U_41))],[f_12_5]) ).
cnf(f_12_7,plain,
id(sK6(U_42,U_41),sK5(U_42,U_41)),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,plain,
r2(U_41,sK7(U_42,U_41)),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,plain,
r3(U_42,sK7(U_42,U_41),sK6(U_42,U_41)),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_10,plain,
r2(sK8(U_42,U_41),sK5(U_42,U_41)),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_11,plain,
r3(U_42,U_41,sK8(U_42,U_41)),
inference(clausify,[status(thm)],[f_12_6]) ).
fof(f_13_1,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(f_13_2,plain,
! [U_48,U_47] :
? [U_46] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,U_46) )
& ? [U_44] :
( ? [U_43] :
( r4(U_48,U_43,U_44)
& r2(U_47,U_43) )
& id(U_44,U_46) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_48,U_47] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,sK9(U_48,U_47)) )
& ? [U_44] :
( ? [U_43] :
( r4(U_48,U_43,U_44)
& r2(U_47,U_43) )
& id(U_44,sK9(U_48,U_47)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_46,sK9(U_48,U_47))],[f_13_2]) ).
fof(f_13_4,plain,
! [U_48,U_47] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,sK9(U_48,U_47)) )
& ? [U_43] :
( r4(U_48,U_43,sK10(U_48,U_47))
& r2(U_47,U_43) )
& id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10(U_48,U_47))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_48,U_47] :
( ? [U_45] :
( r4(U_48,U_47,U_45)
& r3(U_45,U_48,sK9(U_48,U_47)) )
& r4(U_48,sK11(U_48,U_47),sK10(U_48,U_47))
& r2(U_47,sK11(U_48,U_47))
& id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_43,sK11(U_48,U_47))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_48,U_47] :
( r4(U_48,U_47,sK12(U_48,U_47))
& r3(sK12(U_48,U_47),U_48,sK9(U_48,U_47))
& r4(U_48,sK11(U_48,U_47),sK10(U_48,U_47))
& r2(U_47,sK11(U_48,U_47))
& id(sK10(U_48,U_47),sK9(U_48,U_47)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_45,sK12(U_48,U_47))],[f_13_5]) ).
cnf(f_13_7,plain,
id(sK10(U_48,U_47),sK9(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,plain,
r2(U_47,sK11(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,plain,
r4(U_48,sK11(U_48,U_47),sK10(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,plain,
r3(sK12(U_48,U_47),U_48,sK9(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,plain,
r4(U_48,U_47,sK12(U_48,U_47)),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_1,plain,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_3a]) ).
fof(f_14_2,plain,
! [U_52,U_51] :
( id(U_52,U_51)
| ! [U_50] :
( ~ r2(U_51,U_50)
| ! [U_49] :
( ~ r2(U_52,U_49)
| ~ id(U_49,U_50) ) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( id(U_52,U_51)
| ~ r2(U_51,U_50)
| ~ r2(U_52,U_49)
| ~ id(U_49,U_50) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(f_15_2,plain,
! [U_55] :
? [U_54] :
( ? [U_53] :
( r3(U_55,U_53,U_54)
& r1(U_53) )
& id(U_54,U_55) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_55] :
( ? [U_53] :
( r3(U_55,U_53,sK13(U_55))
& r1(U_53) )
& id(sK13(U_55),U_55) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_54,sK13(U_55))],[f_15_2]) ).
fof(f_15_4,plain,
! [U_55] :
( r3(U_55,sK14(U_55),sK13(U_55))
& r1(sK14(U_55))
& id(sK13(U_55),U_55) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_53,sK14(U_55))],[f_15_3]) ).
cnf(f_15_5,plain,
id(sK13(U_55),U_55),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
r1(sK14(U_55)),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
r3(U_55,sK14(U_55),sK13(U_55)),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(f_16_2,plain,
! [U_59] :
? [U_58] :
( ? [U_57] :
( r1(U_57)
& id(U_58,U_57) )
& ? [U_56] :
( r4(U_59,U_56,U_58)
& r1(U_56) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_59] :
( ? [U_57] :
( r1(U_57)
& id(sK15(U_59),U_57) )
& ? [U_56] :
( r4(U_59,U_56,sK15(U_59))
& r1(U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_58,sK15(U_59))],[f_16_2]) ).
fof(f_16_4,plain,
! [U_59] :
( ? [U_57] :
( r1(U_57)
& id(sK15(U_59),U_57) )
& r4(U_59,sK16(U_59),sK15(U_59))
& r1(sK16(U_59)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_56,sK16(U_59))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_59] :
( r1(sK17(U_59))
& id(sK15(U_59),sK17(U_59))
& r4(U_59,sK16(U_59),sK15(U_59))
& r1(sK16(U_59)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_57,sK17(U_59))],[f_16_4]) ).
cnf(f_16_6,plain,
r1(sK16(U_59)),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
r4(U_59,sK16(U_59),sK15(U_59)),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
id(sK15(U_59),sK17(U_59)),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
r1(sK17(U_59)),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_1,plain,
! [X6] :
( ? [Y1,Y11] :
( r2(Y1,Y11)
& id(X6,Y11) )
| ? [Y19] :
( r1(Y19)
& id(X6,Y19) ) ),
inference(fof_nnf,[status(thm)],[axiom_6a]) ).
fof(f_17_2,plain,
! [U_63] :
( ? [U_62,U_61] :
( r2(U_62,U_61)
& id(U_63,U_61) )
| ? [U_60] :
( r1(U_60)
& id(U_63,U_60) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_63] :
( ? [U_62,U_61] :
( r2(U_62,U_61)
& id(U_63,U_61) )
| ( r1(sK18(U_63))
& id(U_63,sK18(U_63)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_60,sK18(U_63))],[f_17_2]) ).
fof(f_17_4,plain,
! [U_63] :
( ? [U_61] :
( r2(sK19(U_63),U_61)
& id(U_63,U_61) )
| ( r1(sK18(U_63))
& id(U_63,sK18(U_63)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_62,sK19(U_63))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_63] :
( ( r2(sK19(U_63),sK20(U_63))
& id(U_63,sK20(U_63)) )
| ( r1(sK18(U_63))
& id(U_63,sK18(U_63)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_61,sK20(U_63))],[f_17_4]) ).
cnf(f_17_6,plain,
( id(U_63,sK20(U_63))
| id(U_63,sK18(U_63)) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( r2(sK19(U_63),sK20(U_63))
| id(U_63,sK18(U_63)) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( id(U_63,sK20(U_63))
| r1(sK18(U_63)) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( r2(sK19(U_63),sK20(U_63))
| r1(sK18(U_63)) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_1,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
inference(fof_nnf,[status(thm)],[axiom_7a]) ).
fof(f_18_2,plain,
! [U_66,U_65] :
( ~ r2(U_66,U_65)
| ! [U_64] :
( ~ r1(U_64)
| ~ id(U_64,U_65) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ r2(U_66,U_65)
| ~ r1(U_64)
| ~ id(U_64,U_65) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& id(Y3,Y2) ),
inference(negate,[status(cth)],[xplustwoidy]) ).
fof(f_19_2,negated_conjecture,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ~ r2(Y6,Y5)
| ~ r1(Y6) )
| ~ r2(Y5,Y4) )
| ~ r3(Y1,Y4,Y3) )
| ~ id(Y3,Y2) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
! [U_72,U_71,U_70] :
( ! [U_69] :
( ! [U_68] :
( ! [U_67] :
( ~ r2(U_67,U_68)
| ~ r1(U_67) )
| ~ r2(U_68,U_69) )
| ~ r3(U_72,U_69,U_70) )
| ~ id(U_70,U_71) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
! [U_68,U_70,U_71,U_72,U_67,U_69] :
( ~ r2(U_67,U_68)
| ~ r1(U_67)
| ~ r2(U_68,U_69)
| ~ r3(U_72,U_69,U_70)
| ~ id(U_70,U_71) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,negated_conjecture,
( ~ r2(U_67,U_68)
| ~ r1(U_67)
| ~ r2(U_68,U_69)
| ~ r3(U_72,U_69,U_70)
| ~ id(U_70,U_71) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_1_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_5]) ).
cnf(f_1_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_6]) ).
cnf(f_2_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_5]) ).
cnf(f_2_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_6]) ).
cnf(f_3_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_5]) ).
cnf(f_3_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_6]) ).
cnf(f_4_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_5]) ).
cnf(f_4_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_6]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_8_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_6]) ).
cnf(f_9_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_4]) ).
cnf(f_9_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_7]) ).
cnf(f_10_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_4]) ).
cnf(f_10_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_7]) ).
cnf(f_11_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_4]) ).
cnf(f_11_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_7]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN080+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.38 % Computer : n017.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Sat Sep 19 19:29:40 UTC 2026
% 0.08/0.38 % CPUTime :
% 1.24/1.54 % SZS status Theorem for theBenchmark
% 1.24/1.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------