%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM613+1 : 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 : 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 08:52:50 AM UTC 2026
% Result : Theorem 30.87s 31.16s
% Output : Proof 30.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 19 unt; 0 def)
% Number of atoms : 64 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 23 ~; 19 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSuccEquSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('theBenchmark.p',mSuccEquSucc) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('theBenchmark.p',m__3533) ).
fof(m__5255,hypothesis,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
file('theBenchmark.p',m__5255) ).
fof(m__,conjecture,
sbrdtbr0(xP) = xk,
file('theBenchmark.p',m__) ).
fof(f_26_1,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mSuccEquSucc]) ).
fof(f_26_2,plain,
! [U_63,U_62] :
( U_63 = U_62
| szszuzczcdt0(U_63) != szszuzczcdt0(U_62)
| ~ aElementOf0(U_62,szNzAzT0)
| ~ aElementOf0(U_63,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_63,U_62] :
( U_63 = U_62
| szszuzczcdt0(U_63) != szszuzczcdt0(U_62)
| ~ aElementOf0(U_62,szNzAzT0)
| ~ aElementOf0(U_63,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( U_63 = U_62
| szszuzczcdt0(U_63) != szszuzczcdt0(U_62)
| ~ aElementOf0(U_62,szNzAzT0)
| ~ aElementOf0(U_63,szNzAzT0) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_80_1,plain,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m__3533]) ).
fof(f_80_2,plain,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
inference(definitional_conversion,[status(esa)],[f_80_1]) ).
cnf(f_80_3,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_109_1,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
inference(fof_nnf,[status(thm)],[m__5255]) ).
fof(f_109_2,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
inference(definitional_conversion,[status(esa)],[f_109_1]) ).
cnf(f_109_3,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(clausify,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(clausify,[status(thm)],[f_109_2]) ).
cnf(f_109_5,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negate,[status(cth)],[m__]) ).
fof(f_110_2,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(definitional_conversion,[status(esa)],[f_110_1]) ).
cnf(f_110_3,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(clausify,[status(thm)],[f_110_2]) ).
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(t1,plain,
sbrdtbr0(xP) != xk,
inference(start,[status(thm),parent(0:0)],[f_110_3]) ).
cnf(t2,plain,
( ~ aElementOf0(xk,szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| sbrdtbr0(xP) = xk ),
inference(extension,[status(thm),parent(t1:1)],[f_26_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(extension,[status(thm),parent(t2:2)],[f_109_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sbrdtbr0(xQ) != szszuzczcdt0(xk)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(xk) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(extension,[status(thm),parent(t6:2)],[f_109_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(extension,[status(thm),parent(t6:3)],[f_109_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
aElementOf0(xk,szNzAzT0),
inference(extension,[status(thm),parent(t2:4)],[f_80_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n011.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 18:58:39 UTC 2026
% 0.07/0.36 % CPUTime :
% 30.87/31.16 % SZS status Theorem for theBenchmark
% 30.87/31.16 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------