%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG091+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n001.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 08:55:08 AM UTC 2026
% Result : Theorem 121.95s 127.22s
% Output : Proof 121.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 51 unt; 2 def)
% Number of atoms : 418 ( 90 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 515 ( 191 ~; 186 |; 131 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 181 ( 0 sgn 122 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSSum,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSSum) ).
fof(mDefIdeal,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('theBenchmark.p',m__870) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('theBenchmark.p',m__994) ).
fof(m__1021,hypothesis,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('theBenchmark.p',m__1021) ).
fof(m__1061,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('theBenchmark.p',m__1061) ).
fof(m__1098,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('theBenchmark.p',m__1098) ).
fof(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
file('theBenchmark.p',m__) ).
fof(f_22_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtpldt1(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
| ( ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0) ) )
& ( ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSSum]) ).
fof(f_22_2,plain,
! [U_45,U_44] :
( ! [U_43] :
( ( U_43 = sdtpldt1(U_45,U_44)
| ? [U_42] :
( ( ~ aElementOf0(U_42,U_43)
& ? [U_41,U_40] :
( sdtpldt0(U_41,U_40) = U_42
& aElementOf0(U_40,U_44)
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39,U_38] :
( sdtpldt0(U_39,U_38) != U_42
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_42,U_43) ) )
| ~ aSet0(U_43) )
& ( ( ! [U_37] :
( ( aElementOf0(U_37,U_43)
| ! [U_36,U_35] :
( sdtpldt0(U_36,U_35) != U_37
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45) ) )
& ( ? [U_34,U_33] :
( sdtpldt0(U_34,U_33) = U_37
& aElementOf0(U_33,U_44)
& aElementOf0(U_34,U_45) )
| ~ aElementOf0(U_37,U_43) ) )
& aSet0(U_43) )
| U_43 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ? [U_34] :
( ? [U_33] :
( sdtpldt0(U_34,U_33) = U_46
& aElementOf0(U_33,U_44) )
& aElementOf0(U_34,U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( ? [U_33] :
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),U_33) = U_46
& aElementOf0(U_33,U_44) )
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3(U_45,U_44,U_50,U_46))],[f_22_3]) ).
fof(f_22_5,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4(U_45,U_44,U_50,U_46))],[f_22_4]) ).
fof(f_22_6,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_48,sK5(U_45,U_44,U_51))],[f_22_5]) ).
fof(f_22_7,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = sK6(U_45,U_44,U_51)
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6(U_45,U_44,U_51))],[f_22_6]) ).
fof(f_22_8,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& ? [U_40] :
( sdtpldt0(sK7(U_45,U_44,U_51),U_40) = sK6(U_45,U_44,U_51)
& aElementOf0(U_40,U_44) )
& aElementOf0(sK7(U_45,U_44,U_51),U_45) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7(U_45,U_44,U_51))],[f_22_7]) ).
fof(f_22_9,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
& aElementOf0(sK8(U_45,U_44,U_51),U_44)
& aElementOf0(sK7(U_45,U_44,U_51),U_45) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_40,sK8(U_45,U_44,U_51))],[f_22_8]) ).
cnf(f_22_14,plain,
( aElementOf0(U_47,U_50)
| sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
fof(f_24_1,plain,
! [W0] :
( ( aIdeal0(W0)
| ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(fof_nnf,[status(thm)],[mDefIdeal]) ).
fof(f_24_2,plain,
! [U_69] :
( ( aIdeal0(U_69)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_69)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_69)
& aElementOf0(U_66,U_69) ) )
& aElementOf0(U_68,U_69) )
| ~ aSet0(U_69) )
& ( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_69)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_69)
| ~ aElementOf0(U_63,U_69) ) )
| ~ aElementOf0(U_65,U_69) )
& aSet0(U_69) )
| ~ aIdeal0(U_69) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(U_68,U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(sK11(U_71),U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_68,sK11(U_71))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_66,sK12(U_71))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
& aElement0(sK13(U_71)) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_67,sK13(U_71))],[f_24_5]) ).
cnf(f_24_7,plain,
( aSet0(U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
fof(f_25_1,plain,
( aIdeal0(xJ)
& aIdeal0(xI) ),
inference(fof_nnf,[status(thm)],[m__870]) ).
cnf(f_25_2,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_29_1,plain,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(fof_nnf,[status(thm)],[m__994]) ).
cnf(f_29_2,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(fof_nnf,[status(thm)],[m__1021]) ).
cnf(f_30_2,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(clausify,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_nnf,[status(thm)],[m__1061]) ).
cnf(f_31_2,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(fof_nnf,[status(thm)],[m__1098]) ).
cnf(f_32_2,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_33_2,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(clausify,[status(thm)],[f_33_3]) ).
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_7,axiom,
( sdtpldt1(Eq_x_0,Eq_x_1) = sdtpldt1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(start,[status(thm),parent(0:0)],[f_33_4]) ).
cnf(t2,plain,
( ~ aSet0(xJ)
| sdtpldt1(xI,xJ) != sdtpldt1(xI,xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(xx,xy)
| ~ aSet0(xI)
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(extension,[status(thm),parent(t1:1)],[f_22_14]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aIdeal0(xI)
| aSet0(xI) ),
inference(extension,[status(thm),parent(t2:2)],[f_24_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aIdeal0(xI),
inference(extension,[status(thm),parent(t4:2)],[f_25_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn))
| sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xx,xy) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(extension,[status(thm),parent(t8:2)],[f_31_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(extension,[status(thm),parent(t2:4)],[f_29_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(extension,[status(thm),parent(t2:5)],[f_29_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
cnf(t16,plain,
( xJ != xJ
| xI != xI
| sdtpldt1(xI,xJ) = sdtpldt1(xI,xJ) ),
inference(extension,[status(thm),parent(t2:6)],[equality_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:6]) ).
cnf(t18,plain,
xI = xI,
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
xJ = xJ,
inference(extension,[status(thm),parent(t16:3)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( ~ aIdeal0(xJ)
| aSet0(xJ) ),
inference(extension,[status(thm),parent(t2:7)],[f_24_7]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:7]) ).
cnf(t24,plain,
aIdeal0(xJ),
inference(extension,[status(thm),parent(t22:2)],[f_25_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ aSet0(xJ)
| sdtpldt1(xI,xJ) != sdtpldt1(xI,xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) != sdtasdt0(xz,xx)
| ~ aSet0(xI)
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(extension,[status(thm),parent(t1:2)],[f_22_14]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t1:2]) ).
cnf(t28,plain,
( ~ aIdeal0(xI)
| aSet0(xI) ),
inference(extension,[status(thm),parent(t26:2)],[f_24_7]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
aIdeal0(xI),
inference(extension,[status(thm),parent(t28:2)],[f_25_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( sdtasdt0(xz,xx) != sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl))
| sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) = sdtasdt0(xz,xx) ),
inference(extension,[status(thm),parent(t26:3)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(extension,[status(thm),parent(t32:2)],[f_32_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(extension,[status(thm),parent(t26:4)],[f_30_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t26:4]) ).
cnf(t38,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(extension,[status(thm),parent(t26:5)],[f_30_2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t26:5]) ).
cnf(t40,plain,
( xJ != xJ
| xI != xI
| sdtpldt1(xI,xJ) = sdtpldt1(xI,xJ) ),
inference(extension,[status(thm),parent(t26:6)],[equality_7]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t26:6]) ).
cnf(t42,plain,
xI = xI,
inference(extension,[status(thm),parent(t40:2)],[equality_1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
xJ = xJ,
inference(extension,[status(thm),parent(t40:3)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
( ~ aIdeal0(xJ)
| aSet0(xJ) ),
inference(extension,[status(thm),parent(t26:7)],[f_24_7]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t26:7]) ).
cnf(t48,plain,
aIdeal0(xJ),
inference(extension,[status(thm),parent(t46:2)],[f_25_3]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG091+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 19 20:56:30 UTC 2026
% 0.08/5.36 % CPUTime :
% 121.95/127.22 % SZS status Theorem for theBenchmark
% 121.95/127.22 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------