%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : ITP006+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Jul 24 06:46:15 PM UTC 2025
% Result : Theorem 2.55s 0.66s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 41 ( 2 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 40 ( 13 ~; 6 |; 5 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-6 aty)
% Number of variables : 52 ( 7 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,plain,
! [A_27a,A_27b,V0i_2E0,V1P_2E0,V2Q_2E0] :
( ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
fof(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT_negated,plain,
~ ! [A_27a,A_27b,V0i_2E0,V1P_2E0,V2Q_2E0] :
( ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) ) ),
inference(negate_conjecture,[status(cth)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
cnf(163,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23),s(sK19,X0))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22),s(sK19,X0)))) ),
inference(cnf,[status(esa)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT_negated]) ).
cnf(l0,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23),s(sK19,app_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(sK20,sK12(sK20,sK19,X4_1,X5_1,sK21,sK23)))))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22),s(sK19,app_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(sK20,sK12(sK20,sK19,X4_1,X5_1,sK21,sK23))))))) ),
inference(instantiation,[status(thm)],[163]) ).
fof(thm_2EquantHeuristics_2EGUESS__REWRITES,plain,
! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
<=> ! [V2v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0))))
=> ? [V3fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0)))))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
<=> ! [V4v_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0))))
=> ? [V5fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0)))))) ) )
& ! [V6i_2E0,V7P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0))))
<=> ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0)))))) )
& ! [V9i_2E0,V10P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0))))
<=> ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0)))))) )
& ! [V12i_2E0,V13P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0))))
<=> ! [V14v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0))))
=> ? [V15fv_2E0] : s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0))) ) )
& ! [V16i_2E0,V17P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0))))
<=> ! [V18v_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0))))
=> ? [V19fv_2E0] : s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_2E0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
cnf(86,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,app_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(X2,sK12(X2,X0,X4,X5,X3,X1)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ),
inference(cnf,[status(esa)],[thm_2EquantHeuristics_2EGUESS__REWRITES]) ).
cnf(l1,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23),s(sK19,app_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(sK20,sK12(sK20,sK19,X4_1,X5_1,sK21,sK23)))))))
| p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23)))) ),
inference(instantiation,[status(thm)],[86]) ).
cnf(165,plain,
~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23)))),
inference(cnf,[status(esa)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT_negated]) ).
cnf(l9,plain,
~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK23)))),
inference(instantiation,[status(thm)],[165]) ).
cnf(85,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,app_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(X2,X4))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ),
inference(cnf,[status(esa)],[thm_2EquantHeuristics_2EGUESS__REWRITES]) ).
cnf(l3,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22),s(sK19,app_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(sK20,sK12(sK20,sK19,X4_1,X5_1,sK21,sK23)))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22)))) ),
inference(instantiation,[status(thm)],[85]) ).
cnf(164,plain,
p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22)))),
inference(cnf,[status(esa)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT_negated]) ).
cnf(l6,plain,
p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK20,sK19),sK21),s(tyop_2Emin_2Efun(sK19,tyop_2Emin_2Ebool),sK22)))),
inference(instantiation,[status(thm)],[164]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l9,l3,l6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ITP006+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.05/0.10 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.30 % Computer : n017.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Jul 20 19:33:04 EDT 2025
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % launching worker at depth: 1
% 0.15/0.31 % launching worker at depth: 7
% 0.15/0.31 % launching worker at depth: 2
% 0.15/0.31 % launching worker at depth: 4
% 0.15/0.31 % launching worker at depth: 5
% 0.15/0.31 % launching worker at depth: 8
% 0.15/0.31 % launching worker at depth: 6
% 0.15/0.31 % launching worker at depth: 3
% 0.15/0.36 % launching worker at depth: 9
% 2.55/0.66 % SZS status Theorem for theBenchmark
% 2.55/0.66 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------