%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:55:12 AM UTC 2026
% Result : Theorem 66.45s 66.94s
% Output : Proof 66.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 76 ( 38 unt; 0 def)
% Number of atoms : 202 ( 50 equ)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 217 ( 91 ~; 81 |; 43 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 4 sgn 32 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aElement0(sz00),
file('theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('theBenchmark.p',mSortsC_01) ).
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulUnit) ).
fof(mMulZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__,conjecture,
( ( aElementOf0(xb,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_2_1,plain,
aElement0(sz00),
inference(fof_nnf,[status(thm)],[mSortsC]) ).
fof(f_2_2,plain,
aElement0(sz00),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
aElement0(sz10),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
fof(f_3_2,plain,
aElement0(sz10),
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_13_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulUnit]) ).
fof(f_13_2,plain,
! [U_18] :
( ( U_18 = sdtasdt0(sz10,U_18)
& sdtasdt0(U_18,sz10) = U_18 )
| ~ aElement0(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_18] :
( U_18 = sdtasdt0(sz10,U_18)
| ~ sP2(U_18) )
& ! [U_18] :
( sdtasdt0(U_18,sz10) = U_18
| ~ sP2(U_18) )
& ! [U_18] :
( sP2(U_18)
| ~ aElement0(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP2(U_18)
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( sdtasdt0(U_18,sz10) = U_18
| ~ sP2(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_16_1,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulZero]) ).
fof(f_16_2,plain,
! [U_23] :
( ( sz00 = sdtasdt0(sz00,U_23)
& sdtasdt0(U_23,sz00) = sz00 )
| ~ aElement0(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_23] :
( sz00 = sdtasdt0(sz00,U_23)
| ~ sP5(U_23) )
& ! [U_23] :
( sdtasdt0(U_23,sz00) = sz00
| ~ sP5(U_23) )
& ! [U_23] :
( sP5(U_23)
| ~ aElement0(U_23) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_16_2]) ).
cnf(f_16_4,plain,
( sP5(U_23)
| ~ aElement0(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( sdtasdt0(U_23,sz00) = sz00
| ~ sP5(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_39_1,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(fof_nnf,[status(thm)],[m__2091]) ).
fof(f_39_2,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(definitional_conversion,[status(esa)],[f_39_1]) ).
cnf(f_39_3,plain,
aElement0(xa),
inference(clausify,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
aElement0(xb),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_43_1,negated_conjecture,
~ ( ( aElementOf0(xb,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_43_2,negated_conjecture,
( ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != xb
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != sz00
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != xa
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != sz00
| ~ aElement0(W0) ) ) ),
inference(fof_nnf,[status(thm)],[f_43_1]) ).
fof(f_43_3,negated_conjecture,
( ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [U_154] :
( sdtasdt0(xb,U_154) != xb
| ~ aElement0(U_154) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [U_153] :
( sdtasdt0(xb,U_153) != sz00
| ~ aElement0(U_153) ) )
| ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [U_152] :
( sdtasdt0(xa,U_152) != xa
| ~ aElement0(U_152) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [U_151] :
( sdtasdt0(xa,U_151) != sz00
| ~ aElement0(U_151) ) ) ),
inference(variable_rename,[status(thm)],[f_43_2]) ).
fof(f_43_4,negated_conjecture,
( ! [U_154] :
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ sP51(U_154) )
& ! [U_154] :
( sdtasdt0(xb,U_154) != xb
| ~ aElement0(U_154)
| ~ sP51(U_154) )
& ! [U_153] :
( ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ sP50(U_153) )
& ! [U_153] :
( sdtasdt0(xb,U_153) != sz00
| ~ aElement0(U_153)
| ~ sP50(U_153) )
& ! [U_152] :
( ~ aElementOf0(xa,slsdtgt0(xa))
| ~ sP49(U_152) )
& ! [U_152] :
( sdtasdt0(xa,U_152) != xa
| ~ aElement0(U_152)
| ~ sP49(U_152) )
& ! [U_151] :
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ sP48(U_151) )
& ! [U_151] :
( sdtasdt0(xa,U_151) != sz00
| ~ aElement0(U_151)
| ~ sP48(U_151) )
& ! [U_151,U_153,U_152,U_154] :
( sP51(U_154)
| sP50(U_153)
| sP49(U_152)
| sP48(U_151) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48,sP49,sP50,sP51])],[f_43_3]) ).
cnf(f_43_5,negated_conjecture,
( sP51(U_154)
| sP50(U_153)
| sP49(U_152)
| sP48(U_151) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,negated_conjecture,
( sdtasdt0(xa,U_151) != sz00
| ~ aElement0(U_151)
| ~ sP48(U_151) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_8,negated_conjecture,
( sdtasdt0(xa,U_152) != xa
| ~ aElement0(U_152)
| ~ sP49(U_152) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_10,negated_conjecture,
( sdtasdt0(xb,U_153) != sz00
| ~ aElement0(U_153)
| ~ sP50(U_153) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_12,negated_conjecture,
( sdtasdt0(xb,U_154) != xb
| ~ aElement0(U_154)
| ~ sP51(U_154) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(t1,plain,
( sP49(sz10)
| sP50(sz00)
| sP51(sz10)
| sP48(sz00) ),
inference(start,[status(thm),parent(0:0)],[f_43_5]) ).
cnf(t2,plain,
( ~ aElement0(sz00)
| sdtasdt0(xa,sz00) != sz00
| ~ sP48(sz00) ),
inference(extension,[status(thm),parent(t1:1)],[f_43_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sP5(xa)
| sdtasdt0(xa,sz00) = sz00 ),
inference(extension,[status(thm),parent(t2:2)],[f_16_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ aElement0(xa)
| sP5(xa) ),
inference(extension,[status(thm),parent(t4:2)],[f_16_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
aElement0(xa),
inference(extension,[status(thm),parent(t6:2)],[f_39_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
aElement0(sz00),
inference(extension,[status(thm),parent(t2:3)],[f_2_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ aElement0(sz10)
| sdtasdt0(xb,sz10) != xb
| ~ sP51(sz10) ),
inference(extension,[status(thm),parent(t1:2)],[f_43_12]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:2]) ).
cnf(t14,plain,
( ~ sP2(xb)
| sdtasdt0(xb,sz10) = xb ),
inference(extension,[status(thm),parent(t12:2)],[f_13_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ aElement0(xb)
| sP2(xb) ),
inference(extension,[status(thm),parent(t14:2)],[f_13_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
aElement0(xb),
inference(extension,[status(thm),parent(t16:2)],[f_39_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
aElement0(sz10),
inference(extension,[status(thm),parent(t12:3)],[f_3_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t12:3]) ).
cnf(t22,plain,
( ~ aElement0(sz00)
| sdtasdt0(xb,sz00) != sz00
| ~ sP50(sz00) ),
inference(extension,[status(thm),parent(t1:3)],[f_43_10]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t1:3]) ).
cnf(t24,plain,
( ~ sP5(xb)
| sdtasdt0(xb,sz00) = sz00 ),
inference(extension,[status(thm),parent(t22:2)],[f_16_5]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ aElement0(xb)
| sP5(xb) ),
inference(extension,[status(thm),parent(t24:2)],[f_16_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
aElement0(xb),
inference(extension,[status(thm),parent(t26:2)],[f_39_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
aElement0(sz00),
inference(extension,[status(thm),parent(t22:3)],[f_2_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t22:3]) ).
cnf(t32,plain,
( ~ aElement0(sz10)
| sdtasdt0(xa,sz10) != xa
| ~ sP49(sz10) ),
inference(extension,[status(thm),parent(t1:4)],[f_43_8]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t1:4]) ).
cnf(t34,plain,
( ~ sP2(xa)
| sdtasdt0(xa,sz10) = xa ),
inference(extension,[status(thm),parent(t32:2)],[f_13_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( ~ aElement0(xa)
| sP2(xa) ),
inference(extension,[status(thm),parent(t34:2)],[f_13_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
aElement0(xa),
inference(extension,[status(thm),parent(t36:2)],[f_39_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
aElement0(sz10),
inference(extension,[status(thm),parent(t32:3)],[f_3_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t32:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG108+4 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n001.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sat Sep 19 21:00:56 UTC 2026
% 0.09/0.56 % CPUTime :
% 66.45/66.94 % SZS status Theorem for theBenchmark
% 66.45/66.94 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------