%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM436+3 : 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 08:52:15 AM UTC 2026
% Result : Theorem 4.65s 4.97s
% Output : Proof 4.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 22 unt; 0 def)
% Number of atoms : 128 ( 32 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 140 ( 59 ~; 45 |; 35 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mIntMult) ).
fof(m__979,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('theBenchmark.p',m__979) ).
fof(m__1032,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('theBenchmark.p',m__1032) ).
fof(m__1071,hypothesis,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
file('theBenchmark.p',m__1071) ).
fof(m__,conjecture,
( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_6_1,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntMult]) ).
fof(f_6_2,plain,
! [U_5,U_4] :
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_23_1,plain,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[m__979]) ).
cnf(f_23_4,plain,
aInteger0(xp),
inference(clausify,[status(thm)],[f_23_1]) ).
cnf(f_23_6,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_25_1,plain,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
inference(fof_nnf,[status(thm)],[m__1032]) ).
cnf(f_25_2,plain,
aInteger0(xm),
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(fof_nnf,[status(thm)],[m__1071]) ).
cnf(f_26_2,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(clausify,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_1,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_27_2,negated_conjecture,
( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) )
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xp,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) ) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [U_46] :
( sdtasdt0(xq,U_46) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_46) ) )
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [U_45] :
( sdtasdt0(xp,U_45) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_45) ) ) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
( ! [U_46] :
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sP1(U_46) )
& ! [U_46] :
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ sP1(U_46) )
& ! [U_46] :
( sdtasdt0(xq,U_46) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_46)
| ~ sP1(U_46) )
& ! [U_45] :
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ sP0(U_45) )
& ! [U_45] :
( ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ~ sP0(U_45) )
& ! [U_45] :
( sdtasdt0(xp,U_45) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_45)
| ~ sP0(U_45) )
& ! [U_45,U_46] :
( sP1(U_46)
| sP0(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_27_3]) ).
cnf(f_27_5,negated_conjecture,
( sP1(U_46)
| sP0(U_45) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,negated_conjecture,
( sdtasdt0(xp,U_45) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_45)
| ~ sP0(U_45) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_9,negated_conjecture,
( sdtasdt0(xq,U_46) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_46)
| ~ sP1(U_46) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| sdtasdt0(xp,sdtasdt0(xq,xm)) != sdtpldt0(xa,smndt0(xb))
| ~ sP0(sdtasdt0(xq,xm)) ),
inference(start,[status(thm),parent(0:0)],[f_27_6]) ).
cnf(t2,plain,
( sP1(sdtasdt0(xp,xm))
| sP0(sdtasdt0(xq,xm)) ),
inference(extension,[status(thm),parent(t1:1)],[f_27_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| sdtasdt0(xq,sdtasdt0(xp,xm)) != sdtpldt0(xa,smndt0(xb))
| ~ sP1(sdtasdt0(xp,xm)) ),
inference(extension,[status(thm),parent(t2:2)],[f_27_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm))
| sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(extension,[status(thm),parent(t6:2)],[f_26_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xp)
| aInteger0(sdtasdt0(xp,xm)) ),
inference(extension,[status(thm),parent(t4:3)],[f_6_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t10:2)],[f_23_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
aInteger0(xm),
inference(extension,[status(thm),parent(t10:3)],[f_25_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(extension,[status(thm),parent(t1:2)],[f_26_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t1:2]) ).
cnf(t18,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| aInteger0(sdtasdt0(xq,xm)) ),
inference(extension,[status(thm),parent(t1:3)],[f_6_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t1:3]) ).
cnf(t20,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t18:2)],[f_23_6]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
aInteger0(xm),
inference(extension,[status(thm),parent(t18:3)],[f_25_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM436+3 : 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
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 18:25:27 UTC 2026
% 0.07/0.34 % CPUTime :
% 4.65/4.97 % SZS status Theorem for theBenchmark
% 4.65/4.97 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------