%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET804+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n027.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 03:32:42 PM UTC 2025
% Result : Theorem 195.27s 24.85s
% Output : CNFRefutation 195.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 64 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 21 |; 7 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 32 ( 2 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV16,plain,
! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( min(M1,R,E)
& min(M2,R,E)
& M1 != M2 )
=> ~ ? [M] : least(M,R,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).
fof(thIV16_negated,plain,
~ ! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( min(M1,R,E)
& min(M2,R,E)
& M1 != M2 )
=> ~ ? [M] : least(M,R,E) ) ),
inference(negate_conjecture,[status(cth)],[thIV16]) ).
cnf(60,plain,
min(sK20,sK17,sK18),
inference(cnf,[status(esa)],[thIV16_negated]) ).
cnf(l0,plain,
min(sK20,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
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(sK21,sK18)
| ~ apply(sK17,sK21,sK20)
| ~ min(sK20,sK17,sK18)
| sK20 = sK21 ),
inference(instantiation,[status(thm)],[42]) ).
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(33,plain,
( ~ member(X0,X1)
| ~ least(X2,X3,X1)
| apply(X3,X2,X0) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l2,plain,
( ~ member(sK20,sK18)
| ~ least(sK21,sK17,sK18)
| apply(sK17,sK21,sK20) ),
inference(instantiation,[status(thm)],[33]) ).
cnf(41,plain,
( ~ min(X0,X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[min]) ).
cnf(l3,plain,
( ~ min(sK20,sK17,sK18)
| member(sK20,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(32,plain,
( ~ least(X0,X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l980,plain,
( ~ least(sK21,sK17,sK18)
| member(sK21,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(62,plain,
least(sK21,sK17,sK18),
inference(cnf,[status(esa)],[thIV16_negated]) ).
cnf(l1100,plain,
least(sK21,sK17,sK18),
inference(instantiation,[status(thm)],[62]) ).
cnf(l24,plain,
least(sK21,sK17,sK18),
inference(instantiation,[status(thm)],[62]) ).
cnf(l1019,plain,
( ~ member(sK21,sK18)
| ~ apply(sK17,sK21,sK19)
| ~ min(sK19,sK17,sK18)
| sK19 = sK21 ),
inference(instantiation,[status(thm)],[42]) ).
cnf(59,plain,
min(sK19,sK17,sK18),
inference(cnf,[status(esa)],[thIV16_negated]) ).
cnf(l1025,plain,
min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
cnf(l871,plain,
( ~ member(sK19,sK18)
| ~ least(sK20,sK17,sK18)
| apply(sK17,sK20,sK19) ),
inference(instantiation,[status(thm)],[33]) ).
cnf(l1063,plain,
( ~ min(sK20,sK17,sK18)
| member(sK20,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(61,plain,
sK19 != sK20,
inference(cnf,[status(esa)],[thIV16_negated]) ).
cnf(l1312,plain,
sK19 != sK20,
inference(instantiation,[status(thm)],[61]) ).
cnf(l1024,plain,
( ~ min(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l1040,plain,
least(sK21,sK17,sK18),
inference(instantiation,[status(thm)],[62]) ).
cnf(l1074,plain,
min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l980,l1100,l24,l1019,l1025,l871,l1063,l1312,l1024,l1040,l1074]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET804+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Jul 21 22:44:04 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 3
% 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
% 0.20/0.36 % launching worker at depth: 10
% 0.20/0.48 % launching worker at depth: 11
% 10.70/1.71 % launching worker at depth: 12
% 195.27/24.85 % SZS status Theorem for theBenchmark
% 195.27/24.85 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------