%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG099+2 : 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 : n011.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 08:55:10 AM UTC 2026
% Result : Theorem 208.52s 208.80s
% Output : Proof 208.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 125 ( 71 unt; 0 def)
% Number of atoms : 293 ( 52 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 281 ( 113 ~; 105 |; 53 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(m__1205,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__1205) ).
fof(m__1217,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('theBenchmark.p',m__1217) ).
fof(m__1294,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('theBenchmark.p',m__1294) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('theBenchmark.p',m__1319) ).
fof(m__1332,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('theBenchmark.p',m__1332) ).
fof(m__1409,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('theBenchmark.p',m__1409) ).
fof(m__,conjecture,
? [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(f_5_1,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB]) ).
fof(f_5_2,plain,
! [U_3,U_2] :
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_2,U_3] :
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB_02]) ).
fof(f_6_2,plain,
! [U_5,U_4] :
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_4,U_5] :
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_20_1,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mEOfElem]) ).
fof(f_20_2,plain,
! [U_28] :
( ! [U_27] :
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28) )
| ~ aSet0(U_28) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_28,U_27] :
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28)
| ~ aSet0(U_28) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28)
| ~ aSet0(U_28) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_28_1,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(fof_nnf,[status(thm)],[m__1205]) ).
fof(f_28_2,plain,
( aIdeal0(xJ)
& ! [U_84] :
( ( ! [U_83] :
( aElementOf0(sdtasdt0(U_83,U_84),xJ)
| ~ aElement0(U_83) )
& ! [U_82] :
( aElementOf0(sdtpldt0(U_84,U_82),xJ)
| ~ aElementOf0(U_82,xJ) ) )
| ~ aElementOf0(U_84,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [U_81] :
( ( ! [U_80] :
( aElementOf0(sdtasdt0(U_80,U_81),xI)
| ~ aElement0(U_80) )
& ! [U_79] :
( aElementOf0(sdtpldt0(U_81,U_79),xI)
| ~ aElementOf0(U_79,xI) ) )
| ~ aElementOf0(U_81,xI) )
& aSet0(xI) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_83,U_82,U_84] :
( aElementOf0(sdtasdt0(U_83,U_84),xJ)
| ~ aElement0(U_83)
| ~ sP25(U_83,U_82,U_84) )
& ! [U_83,U_82,U_84] :
( aElementOf0(sdtpldt0(U_84,U_82),xJ)
| ~ aElementOf0(U_82,xJ)
| ~ sP25(U_83,U_82,U_84) )
& ! [U_80,U_79,U_81] :
( aElementOf0(sdtasdt0(U_80,U_81),xI)
| ~ aElement0(U_80)
| ~ sP24(U_80,U_79,U_81) )
& ! [U_80,U_79,U_81] :
( aElementOf0(sdtpldt0(U_81,U_79),xI)
| ~ aElementOf0(U_79,xI)
| ~ sP24(U_80,U_79,U_81) )
& aIdeal0(xJ)
& ! [U_83,U_82,U_84] :
( sP25(U_83,U_82,U_84)
| ~ aElementOf0(U_84,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [U_80,U_79,U_81] :
( sP24(U_80,U_79,U_81)
| ~ aElementOf0(U_81,xI) )
& aSet0(xI) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25])],[f_28_2]) ).
cnf(f_28_4,plain,
aSet0(xI),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_7,plain,
aSet0(xJ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_30_1,plain,
( aElement0(xy)
& aElement0(xx) ),
inference(fof_nnf,[status(thm)],[m__1217]) ).
fof(f_30_2,plain,
( aElement0(xy)
& aElement0(xx) ),
inference(definitional_conversion,[status(esa)],[f_30_1]) ).
cnf(f_30_3,plain,
aElement0(xx),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
aElement0(xy),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
inference(fof_nnf,[status(thm)],[m__1294]) ).
fof(f_31_2,plain,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
inference(definitional_conversion,[status(esa)],[f_31_1]) ).
cnf(f_31_3,plain,
aElementOf0(xa,xI),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
aElementOf0(xb,xJ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(fof_nnf,[status(thm)],[m__1319]) ).
fof(f_32_2,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(definitional_conversion,[status(esa)],[f_32_1]) ).
cnf(f_32_3,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_nnf,[status(thm)],[m__1332]) ).
fof(f_33_2,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(definitional_conversion,[status(esa)],[f_33_1]) ).
cnf(f_33_3,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(fof_nnf,[status(thm)],[m__1409]) ).
fof(f_34_2,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(definitional_conversion,[status(esa)],[f_34_1]) ).
cnf(f_34_3,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,negated_conjecture,
~ ? [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
& aElement0(W0) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_35_2,negated_conjecture,
! [W0] :
( ( ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
| ( ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
! [U_88] :
( ( ~ sdteqdtlpzmzozddtrp0(U_88,xy,xJ)
& ~ aElementOf0(sdtpldt0(U_88,smndt0(xy)),xJ) )
| ( ~ sdteqdtlpzmzozddtrp0(U_88,xx,xI)
& ~ aElementOf0(sdtpldt0(U_88,smndt0(xx)),xI) )
| ~ aElement0(U_88) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
( ! [U_88] :
( ~ sdteqdtlpzmzozddtrp0(U_88,xy,xJ)
| ~ sP28(U_88) )
& ! [U_88] :
( ~ aElementOf0(sdtpldt0(U_88,smndt0(xy)),xJ)
| ~ sP28(U_88) )
& ! [U_88] :
( ~ sdteqdtlpzmzozddtrp0(U_88,xx,xI)
| ~ sP27(U_88) )
& ! [U_88] :
( ~ aElementOf0(sdtpldt0(U_88,smndt0(xx)),xI)
| ~ sP27(U_88) )
& ! [U_88] :
( sP28(U_88)
| sP27(U_88)
| ~ aElement0(U_88) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27,sP28])],[f_35_3]) ).
cnf(f_35_5,negated_conjecture,
( sP28(U_88)
| sP27(U_88)
| ~ aElement0(U_88) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,negated_conjecture,
( ~ aElementOf0(sdtpldt0(U_88,smndt0(xx)),xI)
| ~ sP27(U_88) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,negated_conjecture,
( ~ aElementOf0(sdtpldt0(U_88,smndt0(xy)),xJ)
| ~ sP28(U_88) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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,
( smndt0(Eq_x_0) = smndt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( aElementOf0(Eq_y_0,Eq_y_1)
| ~ aElementOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| ~ sP28(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) ),
inference(start,[status(thm),parent(0:0)],[f_35_8]) ).
cnf(t2,plain,
( ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| sP27(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| sP28(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) ),
inference(extension,[status(thm),parent(t1:1)],[f_35_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| ~ sP27(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) ),
inference(extension,[status(thm),parent(t2:2)],[f_35_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| xI != xI
| sdtpldt0(xw,smndt0(xx)) != sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx))
| aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ),
inference(extension,[status(thm),parent(t4:2)],[equality_26]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( xw != sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))
| smndt0(xx) != smndt0(xx)
| sdtpldt0(xw,smndt0(xx)) = sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
smndt0(xx) = smndt0(xx),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(extension,[status(thm),parent(t8:3)],[f_32_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
xI = xI,
inference(extension,[status(thm),parent(t6:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(extension,[status(thm),parent(t6:4)],[f_33_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:4]) ).
cnf(t18,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb))
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) ),
inference(extension,[status(thm),parent(t2:3)],[f_5_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
( ~ aElement0(xx)
| ~ aElement0(xb)
| aElement0(sdtasdt0(xx,xb)) ),
inference(extension,[status(thm),parent(t18:2)],[f_6_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ aSet0(xJ)
| ~ aElementOf0(xb,xJ)
| aElement0(xb) ),
inference(extension,[status(thm),parent(t20:2)],[f_20_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
aElementOf0(xb,xJ),
inference(extension,[status(thm),parent(t22:2)],[f_31_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
aSet0(xJ),
inference(extension,[status(thm),parent(t22:3)],[f_28_7]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
aElement0(xx),
inference(extension,[status(thm),parent(t20:3)],[f_30_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t20:3]) ).
cnf(t30,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| aElement0(sdtasdt0(xy,xa)) ),
inference(extension,[status(thm),parent(t18:3)],[f_6_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t18:3]) ).
cnf(t32,plain,
( ~ aSet0(xI)
| ~ aElementOf0(xa,xI)
| aElement0(xa) ),
inference(extension,[status(thm),parent(t30:2)],[f_20_4]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
aElementOf0(xa,xI),
inference(extension,[status(thm),parent(t32:2)],[f_31_3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
aSet0(xI),
inference(extension,[status(thm),parent(t32:3)],[f_28_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
aElement0(xy),
inference(extension,[status(thm),parent(t30:3)],[f_30_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t30:3]) ).
cnf(t40,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
| xJ != xJ
| sdtpldt0(xw,smndt0(xy)) != sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy))
| aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ),
inference(extension,[status(thm),parent(t1:2)],[equality_26]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t1:2]) ).
cnf(t42,plain,
( sdtpldt0(xw,smndt0(xy)) != sdtpldt0(xw,smndt0(xy))
| sdtpldt0(xw,smndt0(xy)) != sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy))
| sdtpldt0(xw,smndt0(xy)) = sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)) ),
inference(extension,[status(thm),parent(t40:2)],[equality_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( sdtpldt0(xw,smndt0(xy)) != sdtpldt0(xw,smndt0(xy))
| sdtpldt0(xw,smndt0(xy)) != sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy))
| sdtpldt0(xw,smndt0(xy)) = sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)) ),
inference(extension,[status(thm),parent(t42:2)],[equality_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( xw != sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))
| smndt0(xy) != smndt0(xy)
| sdtpldt0(xw,smndt0(xy)) = sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)) ),
inference(extension,[status(thm),parent(t44:2)],[equality_5]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
smndt0(xy) = smndt0(xy),
inference(extension,[status(thm),parent(t46:2)],[equality_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(extension,[status(thm),parent(t46:3)],[f_32_3]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t46:3]) ).
cnf(t52,plain,
( xw != xw
| smndt0(xy) != smndt0(xy)
| sdtpldt0(xw,smndt0(xy)) = sdtpldt0(xw,smndt0(xy)) ),
inference(extension,[status(thm),parent(t44:3)],[equality_5]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t44:3]) ).
cnf(t54,plain,
smndt0(xy) = smndt0(xy),
inference(extension,[status(thm),parent(t52:2)],[equality_1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
xw = xw,
inference(extension,[status(thm),parent(t52:3)],[equality_1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
( xw != xw
| smndt0(xy) != smndt0(xy)
| sdtpldt0(xw,smndt0(xy)) = sdtpldt0(xw,smndt0(xy)) ),
inference(extension,[status(thm),parent(t42:3)],[equality_5]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t42:3]) ).
cnf(t60,plain,
( xy != xy
| smndt0(xy) = smndt0(xy) ),
inference(extension,[status(thm),parent(t58:2)],[equality_4]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
xy = xy,
inference(extension,[status(thm),parent(t60:2)],[equality_1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
xw = xw,
inference(extension,[status(thm),parent(t58:3)],[equality_1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t58:3]) ).
cnf(t66,plain,
xJ = xJ,
inference(extension,[status(thm),parent(t40:3)],[equality_1]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t40:3]) ).
cnf(t68,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(extension,[status(thm),parent(t40:4)],[f_34_3]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t40:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 20:52:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 208.52/208.80 % SZS status Theorem for theBenchmark
% 208.52/208.80 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------