%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG112+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 : 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 08:55:13 AM UTC 2026
% Result : Theorem 34.96s 35.27s
% Output : Proof 34.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 89 ( 41 unt; 0 def)
% Number of atoms : 209 ( 76 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 216 ( 96 ~; 78 |; 38 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 7 sgn 24 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__2228,hypothesis,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('theBenchmark.p',m__2228) ).
fof(m__2351,hypothesis,
! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& aElementOf0(W2,xI) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& aElementOf0(W1,xI) ) ),
file('theBenchmark.p',m__2351) ).
fof(m__,conjecture,
? [W0] :
( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) )
& W0 != sz00
& aElementOf0(W0,xI) ),
file('theBenchmark.p',m__) ).
fof(f_42_1,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
inference(fof_nnf,[status(thm)],[m__2174]) ).
fof(f_42_2,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
inference(definitional_conversion,[status(esa)],[f_42_1]) ).
cnf(f_42_4,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_44_1,plain,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_nnf,[status(thm)],[m__2228]) ).
fof(f_44_2,plain,
? [U_125] :
( U_125 != sz00
& aElementOf0(U_125,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( sK24 != sz00
& aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_125,sK24)],[f_44_2]) ).
fof(f_44_4,plain,
( sK24 != sz00
& aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
sK24 != sz00,
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
! [W0] :
( ? [W1] :
( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
| W2 = sz00
| ~ aElementOf0(W2,xI) )
& W1 != sz00
& aElementOf0(W1,xI) )
| W0 = sz00
| ~ aElementOf0(W0,xI) ),
inference(fof_nnf,[status(thm)],[m__2351]) ).
fof(f_45_2,plain,
! [U_128] :
( ? [U_127] :
( ! [U_126] :
( ~ iLess0(sbrdtbr0(U_126),sbrdtbr0(U_127))
| U_126 = sz00
| ~ aElementOf0(U_126,xI) )
& U_127 != sz00
& aElementOf0(U_127,xI) )
| U_128 = sz00
| ~ aElementOf0(U_128,xI) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_128] :
( U_128 = sz00
| ~ aElementOf0(U_128,xI) )
| ? [U_127] :
( ! [U_126] :
( ~ iLess0(sbrdtbr0(U_126),sbrdtbr0(U_127))
| U_126 = sz00
| ~ aElementOf0(U_126,xI) )
& U_127 != sz00
& aElementOf0(U_127,xI) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_128] :
( U_128 = sz00
| ~ aElementOf0(U_128,xI) )
| ( ! [U_126] :
( ~ iLess0(sbrdtbr0(U_126),sbrdtbr0(sK25))
| U_126 = sz00
| ~ aElementOf0(U_126,xI) )
& sK25 != sz00
& aElementOf0(sK25,xI) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_127,sK25)],[f_45_3]) ).
fof(f_45_5,plain,
( ! [U_126] :
( ~ iLess0(sbrdtbr0(U_126),sbrdtbr0(sK25))
| U_126 = sz00
| ~ aElementOf0(U_126,xI)
| ~ sP40(U_126) )
& ! [U_126] :
( sK25 != sz00
| ~ sP40(U_126) )
& ! [U_126] :
( aElementOf0(sK25,xI)
| ~ sP40(U_126) )
& ! [U_126,U_128] :
( U_128 = sz00
| ~ aElementOf0(U_128,xI)
| sP40(U_126) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_45_4]) ).
cnf(f_45_6,plain,
( U_128 = sz00
| ~ aElementOf0(U_128,xI)
| sP40(U_126) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_7,plain,
( aElementOf0(sK25,xI)
| ~ sP40(U_126) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_8,plain,
( sK25 != sz00
| ~ sP40(U_126) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_9,plain,
( ~ iLess0(sbrdtbr0(U_126),sbrdtbr0(sK25))
| U_126 = sz00
| ~ aElementOf0(U_126,xI)
| ~ sP40(U_126) ),
inference(clausify,[status(thm)],[f_45_5]) ).
fof(f_46_1,negated_conjecture,
~ ? [W0] :
( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) )
& W0 != sz00
& aElementOf0(W0,xI) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_46_2,negated_conjecture,
! [W0] :
( ? [W1] :
( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
& W1 != sz00
& aElementOf0(W1,xI) )
| W0 = sz00
| ~ aElementOf0(W0,xI) ),
inference(fof_nnf,[status(thm)],[f_46_1]) ).
fof(f_46_3,negated_conjecture,
! [U_130] :
( ? [U_129] :
( iLess0(sbrdtbr0(U_129),sbrdtbr0(U_130))
& U_129 != sz00
& aElementOf0(U_129,xI) )
| U_130 = sz00
| ~ aElementOf0(U_130,xI) ),
inference(variable_rename,[status(thm)],[f_46_2]) ).
fof(f_46_4,negated_conjecture,
! [U_130] :
( ( iLess0(sbrdtbr0(sK26(U_130)),sbrdtbr0(U_130))
& sK26(U_130) != sz00
& aElementOf0(sK26(U_130),xI) )
| U_130 = sz00
| ~ aElementOf0(U_130,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_129,sK26(U_130))],[f_46_3]) ).
fof(f_46_5,negated_conjecture,
( ! [U_130] :
( iLess0(sbrdtbr0(sK26(U_130)),sbrdtbr0(U_130))
| ~ sP41(U_130) )
& ! [U_130] :
( sK26(U_130) != sz00
| ~ sP41(U_130) )
& ! [U_130] :
( aElementOf0(sK26(U_130),xI)
| ~ sP41(U_130) )
& ! [U_130] :
( sP41(U_130)
| U_130 = sz00
| ~ aElementOf0(U_130,xI) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_46_4]) ).
cnf(f_46_6,negated_conjecture,
( sP41(U_130)
| U_130 = sz00
| ~ aElementOf0(U_130,xI) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_7,negated_conjecture,
( aElementOf0(sK26(U_130),xI)
| ~ sP41(U_130) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_8,negated_conjecture,
( sK26(U_130) != sz00
| ~ sP41(U_130) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_9,negated_conjecture,
( iLess0(sbrdtbr0(sK26(U_130)),sbrdtbr0(U_130))
| ~ sP41(U_130) ),
inference(clausify,[status(thm)],[f_46_5]) ).
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_37,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,
( sK25 = sz00
| sP41(sK25)
| ~ aElementOf0(sK25,xI) ),
inference(start,[status(thm),parent(0:0)],[f_46_6]) ).
cnf(t2,plain,
( ~ sP40(U_4318)
| aElementOf0(sK25,xI) ),
inference(extension,[status(thm),parent(t1:1)],[f_45_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aElementOf0(sK24,xI)
| sK24 = sz00
| sP40(U_4318) ),
inference(extension,[status(thm),parent(t2:2)],[f_45_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sK24 != sz00,
inference(extension,[status(thm),parent(t4:2)],[f_44_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI
| ~ aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sK24 != sK24
| aElementOf0(sK24,xI) ),
inference(extension,[status(thm),parent(t4:3)],[equality_37]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( sK24 != sK24
| sK24 = sK24 ),
inference(extension,[status(thm),parent(t8:2)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
sK24 = sK24,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(extension,[status(thm),parent(t8:3)],[f_44_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
( xI != sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
| sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI ),
inference(extension,[status(thm),parent(t8:4)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:4]) ).
cnf(t18,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(extension,[status(thm),parent(t16:2)],[f_42_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( iLess0(sbrdtbr0(sK26(sK25)),sbrdtbr0(sK25))
| ~ sP41(sK25) ),
inference(extension,[status(thm),parent(t1:2)],[f_46_9]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t1:2]) ).
cnf(t22,plain,
( ~ aElementOf0(sK26(sK25),xI)
| sK26(sK25) = sz00
| ~ sP40(sK26(sK25))
| ~ iLess0(sbrdtbr0(sK26(sK25)),sbrdtbr0(sK25)) ),
inference(extension,[status(thm),parent(t20:2)],[f_45_9]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( ~ aElementOf0(sK26(sK25),xI)
| sK26(sK25) = sz00
| sP40(sK26(sK25)) ),
inference(extension,[status(thm),parent(t22:2)],[f_45_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ sP41(sK25)
| sK26(sK25) != sz00 ),
inference(extension,[status(thm),parent(t24:2)],[f_46_8]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
$false,
inference(reduction,[status(thm),parent(t26:2)],[t26:2,t1:2]) ).
cnf(t29,plain,
( ~ sP41(sK25)
| aElementOf0(sK26(sK25),xI) ),
inference(extension,[status(thm),parent(t24:3)],[f_46_7]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t24:3]) ).
cnf(t31,plain,
$false,
inference(reduction,[status(thm),parent(t29:2)],[t29:2,t1:2]) ).
cnf(t32,plain,
( ~ sP41(sK25)
| sK26(sK25) != sz00 ),
inference(extension,[status(thm),parent(t22:3)],[f_46_8]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t22:3]) ).
cnf(t34,plain,
$false,
inference(reduction,[status(thm),parent(t32:2)],[t32:2,t1:2]) ).
cnf(t35,plain,
( ~ sP41(sK25)
| aElementOf0(sK26(sK25),xI) ),
inference(extension,[status(thm),parent(t22:4)],[f_46_7]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t22:4]) ).
cnf(t37,plain,
$false,
inference(reduction,[status(thm),parent(t35:2)],[t35:2,t1:2]) ).
cnf(t38,plain,
( ~ sP40(U_4338)
| sK25 != sz00 ),
inference(extension,[status(thm),parent(t1:3)],[f_45_8]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t1:3]) ).
cnf(t40,plain,
( ~ aElementOf0(sK24,xI)
| sK24 = sz00
| sP40(U_4338) ),
inference(extension,[status(thm),parent(t38:2)],[f_45_6]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
sK24 != sz00,
inference(extension,[status(thm),parent(t40:2)],[f_44_6]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI
| ~ aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sK24 != sK24
| aElementOf0(sK24,xI) ),
inference(extension,[status(thm),parent(t40:3)],[equality_37]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
( sK24 != sK24
| sK24 = sK24 ),
inference(extension,[status(thm),parent(t44:2)],[equality_2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
sK24 = sK24,
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,
aElementOf0(sK24,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(extension,[status(thm),parent(t44:3)],[f_44_5]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t44:3]) ).
cnf(t52,plain,
( xI != sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
| sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI ),
inference(extension,[status(thm),parent(t44:4)],[equality_2]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t44:4]) ).
cnf(t54,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(extension,[status(thm),parent(t52:2)],[f_42_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG112+1 : 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
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 20:55:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 34.96/35.27 % SZS status Theorem for theBenchmark
% 34.96/35.27 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------