%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV948-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 03:24:30 PM UTC 2026
% Result : Unsatisfiable 57.74s 17.44s
% Output : CNFRefutation 57.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 63 ( 13 unt; 0 def)
% Number of atoms : 140 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 158 ( 81 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-5 aty)
% Number of functors : 28 ( 28 usr; 14 con; 0-5 aty)
% Number of variables : 151 ( 0 sgn 151 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( c_Progress_OWTrt_H(X3,X4,X0,c_Expr_Oexp_OVar(X1,tc_List_Olist(tc_String_Ochar)),X2)
| hAPP(X0,X1) != c_Option_Ooption_OSome(X2,tc_Type_Oty) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I4_J_0) ).
fof(f86,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Progress_OWTrt_H(X1,X2,X3,c_Expr_Oexp_OLAss(X4,X5,tc_List_Olist(tc_String_Ochar)),X0)
| X0 = c_Type_Oty_OVoid ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__elim__cases_0) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Progress_OWTrt_H(X1,X2,X3,c_Expr_Oexp_OLAss(X4,X5,tc_List_Olist(tc_String_Ochar)),X0)
| c_Type_Oty_OVoid = X0 ),
inference(reorient_equations,[],[f86]) ).
fof(f115,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Progress_OWTrt_H(X0,X1,X2,c_Expr_Oexp_OVar(X3,tc_List_Olist(tc_String_Ochar)),X6)
| ~ c_Progress_OWTrt_H(X0,X1,X2,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X5),X6))
| c_Progress_OWTrt_H(X0,X1,X2,c_Expr_Oexp_OLAss(X3,X4,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I7_J_0) ).
fof(f358,axiom,
c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssRed_I3_J_0) ).
fof(f361,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_WellTypeRT_OWTrt(X2,X4,X0,c_Expr_Oexp_OLAss(X1,X3,tc_List_Olist(tc_String_Ochar)),X5)
| hAPP(X0,X1) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(X0,X2,X3,X4,X1),tc_Type_Oty) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_1) ).
fof(f386,axiom,
! [X0,X1] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,X0,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,X0,v_ea______,X1)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(X0,v_P,X1,v_aa______,v_e_Ha______)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssRed_Ohyps_I2_J_1) ).
fof(f389,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_WellTypeRT_OWTrt(X0,X3,X1,c_Expr_Oexp_OLAss(X4,X2,tc_List_Olist(tc_String_Ochar)),X5)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(X1,X0,X2,X3,X4)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(X1,X0,X2,X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_3) ).
fof(f394,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4)
| c_Progress_OWTrt_H(X0,X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).
fof(f395,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Progress_OWTrt_H(X0,X1,X2,X3,X4)
| c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).
fof(f407,axiom,
! [X0,X1] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,X0,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,X0,v_ea______,X1)
| c_WellTypeRT_OWTrt(v_P,v_aa______,X0,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(X0,v_P,X1,v_aa______,v_e_Ha______)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssRed_Ohyps_I2_J_0) ).
fof(f409,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OLAss(X4,X3,tc_List_Olist(tc_String_Ochar)),X5)
| c_WellTypeRT_OWTrt(X0,X1,X2,X3,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(X2,X0,X3,X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_2) ).
fof(f410,axiom,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).
fof(f411,axiom,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X4),X3))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).
fof(f434,axiom,
c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f439,negated_conjecture,
! [X0] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),X0)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X0),v_T____)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Progress_OWTrt_H(X3,X4,X0,c_Expr_Oexp_OVar(X1,tc_List_Olist(tc_String_Ochar)),X2)
| ( hAPP(X0,X1) != c_Option_Ooption_OSome(X2,tc_Type_Oty) ) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = c_Type_Oty_OVoid )
| ~ c_Progress_OWTrt_H(X0,X1,X2,c_Expr_Oexp_OLAss(X3,X4,tc_List_Olist(tc_String_Ochar)),X5) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Progress_OWTrt_H(X0,X3,X4,c_Expr_Oexp_OLAss(X5,X6,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_Progress_OWTrt_H(X0,X3,X4,X6,X1)
| ~ c_Progress_OWTrt_H(X0,X3,X4,c_Expr_Oexp_OVar(X5,tc_List_Olist(tc_String_Ochar)),X2)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X1),X2)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_713,plain,
c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),
inference(cnf_transformation,[],[f358]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(X2,X0,X4,X1,X3),tc_Type_Oty) = hAPP(X2,X3) )
| ~ c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OLAss(X3,X4,tc_List_Olist(tc_String_Ochar)),X5) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(X0,v_P,X1,v_aa______,v_e_Ha______)),X1))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,X0,v_ea______,X1)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,X0,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(X2,X0,X4,X1,X3)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(X2,X0,X4,X1,X3)))
| ~ c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OLAss(X3,X4,tc_List_Olist(tc_String_Ochar)),X5) ),
inference(cnf_transformation,[],[f389]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Progress_OWTrt_H(X0,X1,X2,X3,X4)
| ~ c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f394]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4)
| ~ c_Progress_OWTrt_H(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,X0,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(X0,v_P,X1,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,X0,v_ea______,X1)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,X0,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ),
inference(cnf_transformation,[],[f407]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_WellTypeRT_OWTrt(X0,X1,X2,X4,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(X2,X0,X4,X1,X3))
| ~ c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OLAss(X3,X4,tc_List_Olist(tc_String_Ochar)),X5) ),
inference(cnf_transformation,[],[f409]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X2)),
inference(cnf_transformation,[],[f410]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3)) ),
inference(cnf_transformation,[],[f411]) ).
tcf(c_771,plain,
c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(cnf_transformation,[],[f434]) ).
tcf(c_775,negated_conjecture,
! [X0: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),X0)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X0),v_T____)) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_2203,plain,
! [X0: $i,X1: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,X0,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(X0,v_P,X1,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,X0,v_ea______,X1)
| ( v_P != v_P )
| ( X0 != v_E____ )
| ( c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))) != c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))) ) ),
inference(resolution_lifted,[status(thm)],[c_713,c_750]) ).
tcf(c_2204,plain,
! [X0: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,X0,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,X0) ),
inference(unflattening,[status(thm)],[c_2203]) ).
tcf(c_2221,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(X0,v_P,X1,v_aa______,v_e_Ha______)),X1))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,X0,v_ea______,X1)
| ( v_P != v_P )
| ( X0 != v_E____ )
| ( c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))) != c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))) ) ),
inference(resolution_lifted,[status(thm)],[c_713,c_735]) ).
tcf(c_2222,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,X0,v_aa______,v_e_Ha______)),X0))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,X0) ),
inference(unflattening,[status(thm)],[c_2221]) ).
tcf(c_2476,plain,
! [X0: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,X0,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,X0) ),
inference(prop_impl_just,[status(thm)],[c_2204]) ).
tcf(c_2480,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,X0,v_aa______,v_e_Ha______)),X0))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,X0) ),
inference(prop_impl_just,[status(thm)],[c_2222]) ).
tcf(c_3256,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5651,plain,
~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(superposition,[status(thm)],[c_753,c_775]) ).
tcf(c_5764,plain,
( ( c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) = hAPP(v_E____,v_V______) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(instantiation,[status(thm)],[c_716]) ).
tcf(c_5770,plain,
( c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(instantiation,[status(thm)],[c_752]) ).
tcf(c_5778,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(instantiation,[status(thm)],[c_737]) ).
tcf(c_5839,plain,
c_Progress_OWTrt_H(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(superposition,[status(thm)],[c_771,c_741]) ).
tcf(c_5873,plain,
c_Type_Oty_OVoid = v_T____,
inference(superposition,[status(thm)],[c_5839,c_482]) ).
tcf(c_5884,plain,
~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid),
inference(superposition,[status(thm)],[c_5873,c_5651]) ).
tcf(c_6647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(X0,X1) = c_Option_Ooption_OSome(X3,tc_Type_Oty) )
| ( c_Option_Ooption_OSome(X3,tc_Type_Oty) != X2 )
| ( hAPP(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_3258]) ).
tcf(c_8579,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)) ),
inference(instantiation,[status(thm)],[c_2480]) ).
tcf(c_8582,plain,
( c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)) ),
inference(instantiation,[status(thm)],[c_2476]) ).
tcf(c_8901,plain,
! [X0: $i,X1: $i] :
( ( hAPP(X0,X1) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) )
| ( hAPP(X0,X1) != hAPP(v_E____,v_V______) )
| ( c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) != hAPP(v_E____,v_V______) ) ),
inference(instantiation,[status(thm)],[c_6647]) ).
tcf(c_14253,plain,
( c_Progress_OWTrt_H(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ),
inference(instantiation,[status(thm)],[c_741]) ).
tcf(c_15911,plain,
( ( hAPP(v_E____,v_V______) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) )
| ( hAPP(v_E____,v_V______) != hAPP(v_E____,v_V______) )
| ( c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) != hAPP(v_E____,v_V______) ) ),
inference(instantiation,[status(thm)],[c_8901]) ).
tcf(c_15912,plain,
hAPP(v_E____,v_V______) = hAPP(v_E____,v_V______),
inference(instantiation,[status(thm)],[c_3256]) ).
tcf(c_18037,plain,
! [X0: $i,X1: $i] :
( c_Progress_OWTrt_H(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(X1,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_Progress_OWTrt_H(v_P,v_aa______,v_E____,c_Expr_Oexp_OVar(X1,tc_List_Olist(tc_String_Ochar)),X0)
| ~ c_Progress_OWTrt_H(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),X0)) ),
inference(instantiation,[status(thm)],[c_508]) ).
tcf(c_18193,plain,
! [X0: $i,X1: $i] :
( c_Progress_OWTrt_H(X0,X1,v_E____,c_Expr_Oexp_OVar(v_V______,tc_List_Olist(tc_String_Ochar)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ),
inference(instantiation,[status(thm)],[c_414]) ).
tcf(c_19214,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),X1))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),X0)) ),
inference(instantiation,[status(thm)],[c_754]) ).
tcf(c_25683,plain,
! [X0: $i,X1: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,X0,X1)
| ~ c_Progress_OWTrt_H(v_P,v_aa______,v_E____,X0,X1) ),
inference(instantiation,[status(thm)],[c_742]) ).
tcf(c_46565,plain,
( c_Progress_OWTrt_H(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_Progress_OWTrt_H(v_P,v_aa______,v_E____,c_Expr_Oexp_OVar(v_V______,tc_List_Olist(tc_String_Ochar)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_Progress_OWTrt_H(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(instantiation,[status(thm)],[c_18037]) ).
tcf(c_46566,plain,
( c_Progress_OWTrt_H(v_P,v_aa______,v_E____,c_Expr_Oexp_OVar(v_V______,tc_List_Olist(tc_String_Ochar)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ),
inference(instantiation,[status(thm)],[c_18193]) ).
tcf(c_46840,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),X0))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),X0))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(instantiation,[status(thm)],[c_19214]) ).
tcf(c_49639,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XLAssRed__Xhyps__2__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(instantiation,[status(thm)],[c_46840]) ).
tcf(c_54390,plain,
( c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_Progress_OWTrt_H(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(instantiation,[status(thm)],[c_25683]) ).
tcf(c_54391,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_54390,c_49639,c_46566,c_46565,c_15912,c_15911,c_14253,c_8579,c_8582,c_5884,c_5778,c_5770,c_5764,c_771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV948-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 21:22:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 57.74/17.44 % SZS status Started for theBenchmark.p
% 57.74/17.44 % SZS status Unsatisfiable for theBenchmark.p
% 57.74/17.44
% 57.74/17.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.74/17.44
% 57.74/17.44 % ------ iProver source info
% 57.74/17.44
% 57.74/17.44 % git: date: 2026-07-19 20:42:38 +0200
% 57.74/17.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.74/17.44 % git: non_committed_changes: false
% 57.74/17.44
% 57.74/17.44 % ------ Parsing...% successful
% 57.74/17.44
% 57.74/17.44
% 57.74/17.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 57.74/17.44
% 57.74/17.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 26 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 57.74/17.44
% 57.74/17.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 57.74/17.44
% 57.74/17.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 57.74/17.44 % ------ Proving...
% 57.74/17.44 % ------ Problem Properties
% 57.74/17.44
% 57.74/17.44 %
% 57.74/17.44 % clauses 231
% 57.74/17.44 % conjectures 1
% 57.74/17.44 % EPR 10
% 57.74/17.44 % Horn 224
% 57.74/17.44 % unary 144
% 57.74/17.44 % binary 64
% 57.74/17.44 % lits 366
% 57.74/17.44 % lits eq 225
% 57.74/17.44 % fd_pure 0
% 57.74/17.44 % fd_pseudo 0
% 57.74/17.44 % fd_cond 4
% 57.74/17.44 % fd_pseudo_cond 41
% 57.74/17.44 % AC symbols 0
% 57.74/17.44
% 57.74/17.44 % ------ Input Options Time Limit: Unbounded
% 57.74/17.44
% 57.74/17.44
% 57.74/17.44 % ------
% 57.74/17.44 % Current options:
% 57.74/17.44 % ------
% 57.74/17.44
% 57.74/17.44
% 57.74/17.44 %
% 57.74/17.44
% 57.74/17.44 % ------ Proving...
% 57.74/17.44 %
% 57.74/17.44
% 57.74/17.44 % SZS status Unsatisfiable for theBenchmark.p
% 57.74/17.44
% 57.74/17.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.74/17.45
% 57.74/17.45
%------------------------------------------------------------------------------