%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG105+2 : 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 : n006.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 30.27s 30.51s
% Output : Proof 30.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 29 unt; 0 def)
% Number of atoms : 177 ( 48 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 168 ( 58 ~; 50 |; 58 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn 26 !; 11 ?)
% 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(m__1933,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
file('theBenchmark.p',m__1933) ).
fof(m__1956,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('theBenchmark.p',m__1956) ).
fof(m__1979,hypothesis,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('theBenchmark.p',m__1979) ).
fof(m__2010,hypothesis,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('theBenchmark.p',m__2010) ).
fof(m__2043,hypothesis,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('theBenchmark.p',m__2043) ).
fof(m__,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtasdt0(xz,xx)
& aElement0(W0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& 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_3,U_2] :
( 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_39_1,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__1933]) ).
fof(f_39_2,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [U_125] :
( sdtasdt0(xc,U_125) = xy
& aElement0(U_125) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [U_124] :
( sdtasdt0(xc,U_124) = xx
& aElement0(U_124) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [U_125] :
( sdtasdt0(xc,U_125) = xy
& aElement0(U_125) )
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK24) = xx
& aElement0(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_124,sK24)],[f_39_2]) ).
fof(f_39_4,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,sK25) = xy
& aElement0(sK25)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK24) = xx
& aElement0(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_125,sK25)],[f_39_3]) ).
fof(f_39_5,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,sK25) = xy
& aElement0(sK25)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK24) = xx
& aElement0(sK24) ),
inference(definitional_conversion,[status(esa)],[f_39_4]) ).
cnf(f_39_12,plain,
aElement0(xz),
inference(clausify,[status(thm)],[f_39_5]) ).
fof(f_40_1,plain,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
inference(fof_nnf,[status(thm)],[m__1956]) ).
fof(f_40_2,plain,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
aElement0(xu),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
inference(fof_nnf,[status(thm)],[m__1979]) ).
fof(f_41_2,plain,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
inference(definitional_conversion,[status(esa)],[f_41_1]) ).
cnf(f_41_3,plain,
aElement0(xv),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(fof_nnf,[status(thm)],[m__2010]) ).
fof(f_42_2,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(definitional_conversion,[status(esa)],[f_42_1]) ).
cnf(f_42_3,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(fof_nnf,[status(thm)],[m__2043]) ).
fof(f_43_2,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(definitional_conversion,[status(esa)],[f_43_1]) ).
cnf(f_43_3,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtasdt0(xz,xx)
& aElement0(W0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& aElement0(W0) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_44_2,negated_conjecture,
( ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtasdt0(xz,xx)
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [W0] :
( sdtasdt0(xc,W0) != sdtpldt0(xx,xy)
| ~ aElement0(W0) ) ) ),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
( ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& ! [U_127] :
( sdtasdt0(xc,U_127) != sdtasdt0(xz,xx)
| ~ aElement0(U_127) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [U_126] :
( sdtasdt0(xc,U_126) != sdtpldt0(xx,xy)
| ~ aElement0(U_126) ) ) ),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
( ! [U_127] :
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ sP41(U_127) )
& ! [U_127] :
( sdtasdt0(xc,U_127) != sdtasdt0(xz,xx)
| ~ aElement0(U_127)
| ~ sP41(U_127) )
& ! [U_126] :
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ sP40(U_126) )
& ! [U_126] :
( sdtasdt0(xc,U_126) != sdtpldt0(xx,xy)
| ~ aElement0(U_126)
| ~ sP40(U_126) )
& ! [U_126,U_127] :
( sP41(U_127)
| sP40(U_126) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40,sP41])],[f_44_3]) ).
cnf(f_44_5,negated_conjecture,
( sP41(U_127)
| sP40(U_126) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,negated_conjecture,
( sdtasdt0(xc,U_126) != sdtpldt0(xx,xy)
| ~ aElement0(U_126)
| ~ sP40(U_126) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_8,negated_conjecture,
( sdtasdt0(xc,U_127) != sdtasdt0(xz,xx)
| ~ aElement0(U_127)
| ~ sP41(U_127) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( sP41(sdtasdt0(xu,xz))
| sP40(sdtpldt0(xu,xv)) ),
inference(start,[status(thm),parent(0:0)],[f_44_5]) ).
cnf(t2,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(xx,xy)
| ~ sP40(sdtpldt0(xu,xv)) ),
inference(extension,[status(thm),parent(t1:1)],[f_44_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv))
| sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(extension,[status(thm),parent(t4:2)],[f_42_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ aElement0(xv)
| ~ aElement0(xu)
| aElement0(sdtpldt0(xu,xv)) ),
inference(extension,[status(thm),parent(t2:3)],[f_5_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
aElement0(xu),
inference(extension,[status(thm),parent(t8:2)],[f_40_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
aElement0(xv),
inference(extension,[status(thm),parent(t8:3)],[f_41_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xz,xx)
| ~ sP41(sdtasdt0(xu,xz)) ),
inference(extension,[status(thm),parent(t1:2)],[f_44_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t1:2]) ).
cnf(t16,plain,
( sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz))
| sdtasdt0(xc,sdtasdt0(xu,xz)) = sdtasdt0(xz,xx) ),
inference(extension,[status(thm),parent(t14:2)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(extension,[status(thm),parent(t16:2)],[f_43_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ aElement0(xz)
| ~ aElement0(xu)
| aElement0(sdtasdt0(xu,xz)) ),
inference(extension,[status(thm),parent(t14:3)],[f_6_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
cnf(t22,plain,
aElement0(xu),
inference(extension,[status(thm),parent(t20:2)],[f_40_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
aElement0(xz),
inference(extension,[status(thm),parent(t20:3)],[f_39_12]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG105+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.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 20:54:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 30.27/30.51 % SZS status Theorem for theBenchmark
% 30.27/30.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------