%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET794+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:32:41 PM UTC 2025
% Result : Theorem 59.82s 7.90s
% Output : CNFRefutation 59.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 106 ( 4 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 108 ( 40 ~; 40 |; 14 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 1 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV6,plain,
! [R,E,M] :
( ( total_order(R,E)
& min(M,R,E) )
=> least(M,R,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV6) ).
fof(thIV6_negated,plain,
~ ! [R,E,M] :
( ( total_order(R,E)
& min(M,R,E) )
=> least(M,R,E) ),
inference(negate_conjecture,[status(cth)],[thIV6]) ).
cnf(59,plain,
min(sK19,sK17,sK18),
inference(cnf,[status(esa)],[thIV6_negated]) ).
cnf(l0,plain,
min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
fof(min,plain,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
file('Axioms/SET006+3.ax',min) ).
cnf(42,plain,
( ~ member(X0,X1)
| ~ apply(X2,X0,X3)
| ~ min(X3,X2,X1)
| X3 = X0 ),
inference(cnf,[status(esa)],[min]) ).
cnf(l1,plain,
( ~ member(sK12(sK17,sK18,sK19),sK18)
| ~ apply(sK17,sK12(sK17,sK18,sK19),sK19)
| ~ min(sK19,sK17,sK18)
| sK19 = sK12(sK17,sK18,sK19) ),
inference(instantiation,[status(thm)],[42]) ).
fof(total_order,plain,
! [R,E] :
( total_order(R,E)
<=> ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
file('Axioms/SET006+3.ax',total_order) ).
cnf(17,plain,
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ total_order(X3,X1)
| apply(X3,X0,X2)
| apply(X3,X2,X0) ),
inference(cnf,[status(esa)],[total_order]) ).
cnf(l23,plain,
( ~ member(sK19,sK18)
| ~ member(sK12(sK17,sK18,sK19),sK18)
| ~ total_order(sK17,sK18)
| apply(sK17,sK19,sK12(sK17,sK18,sK19))
| apply(sK17,sK12(sK17,sK18,sK19),sK19) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(58,plain,
total_order(sK17,sK18),
inference(cnf,[status(esa)],[thIV6_negated]) ).
cnf(l166,plain,
total_order(sK17,sK18),
inference(instantiation,[status(thm)],[58]) ).
fof(least,plain,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
file('Axioms/SET006+3.ax',least) ).
cnf(34,plain,
( ~ member(X0,X1)
| member(sK12(X2,X1,X0),X1)
| least(X0,X2,X1) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l34,plain,
( ~ member(sK19,sK18)
| member(sK12(sK17,sK18,sK19),sK18)
| least(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(l2,plain,
( ~ member(sK19,sK18)
| member(sK12(sK17,sK18,sK19),sK18)
| least(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(41,plain,
( ~ min(X0,X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[min]) ).
cnf(l10,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l152,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(60,plain,
~ least(sK19,sK17,sK18),
inference(cnf,[status(esa)],[thIV6_negated]) ).
cnf(l120,plain,
~ least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(35,plain,
( ~ member(X0,X1)
| ~ apply(X2,X0,sK12(X2,X1,X0))
| least(X0,X2,X1) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l225,plain,
( ~ member(sK19,sK18)
| ~ apply(sK17,sK19,sK12(sK17,sK18,sK19))
| least(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[35]) ).
cnf(l383,plain,
~ least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(l520,plain,
~ least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(l385,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
fof(order,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('Axioms/SET006+3.ax',order) ).
cnf(0,plain,
( ~ order(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf,[status(esa)],[order]) ).
cnf(l28,plain,
( ~ order(sK17,sK18)
| ~ member(sK19,sK18)
| apply(sK17,sK19,sK19) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l163,plain,
( ~ member(sK19,sK18)
| ~ apply(sK17,sK19,sK12(sK17,sK18,sK19))
| least(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[35]) ).
cnf(l95,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l78,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l164,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l252,plain,
~ least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(16,plain,
( ~ total_order(X0,X1)
| order(X0,X1) ),
inference(cnf,[status(esa)],[total_order]) ).
cnf(l31,plain,
( ~ total_order(sK17,sK18)
| order(sK17,sK18) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l141,plain,
total_order(sK17,sK18),
inference(instantiation,[status(thm)],[58]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l23,l166,l34,l2,l10,l152,l120,l225,l383,l520,l385,l28,l163,l95,l78,l164,l252,l31,l141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET794+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 22:43:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.20/0.43 % launching worker at depth: 11
% 6.79/1.22 % launching worker at depth: 12
% 59.82/7.90 % SZS status Theorem for theBenchmark
% 59.82/7.90 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------