TSTP Solution File: SCT121+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SCT121+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:17:31 EDT 2023
% Result : Theorem 533.91s 68.17s
% Output : CNFRefutation 533.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 27 unt; 0 def)
% Number of atoms : 196 ( 22 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 200 ( 79 ~; 79 |; 23 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-5 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-4 aty)
% Number of variables : 173 ( 21 sgn; 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_insert__code,axiom,
! [X4,X7,X17,X5] :
( hBOOL(hAPP(c_Set_Oinsert(X5,X17,X7),X4))
<=> ( X17 = X4
| hBOOL(hAPP(X7,X4)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_insert__code) ).
fof(fact_insert__absorb,axiom,
! [X7,X13,X5] :
( c_member(X5,X13,X7)
=> c_Set_Oinsert(X5,X13,X7) = X7 ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_insert__absorb) ).
fof(fact_irrefl__def,axiom,
! [X6,X5] :
( c_Relation_Oirrefl(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_irrefl__def) ).
fof(fact_mem__def,axiom,
! [X7,X4,X5] :
( c_member(X5,X4,X7)
<=> hBOOL(hAPP(X7,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_mem__def) ).
fof(conj_3,hypothesis,
( ! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)) )
=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',conj_3) ).
fof(conj_1,hypothesis,
! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',conj_1) ).
fof(conj_2,hypothesis,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',conj_2) ).
fof(fact_trancl__id,axiom,
! [X6,X5] :
( c_Relation_Otrans(X5,X6)
=> c_Transitive__Closure_Otrancl(X5,X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_trancl__id) ).
fof(fact_r__r__into__trancl,axiom,
! [X11,X19,X12,X13,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X12),X19)
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X12,X11),X19)
=> c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X11),c_Transitive__Closure_Otrancl(X5,X19)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_r__r__into__trancl) ).
fof(conj_0,hypothesis,
! [X78] :
( ! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X78,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X78,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X78,X3)) )
=> ! [X38,X39] :
( X38 != X39
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X38,X39),hAPP(X78,v_i))
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X38,X39),v_F(X78)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',conj_0) ).
fof(fact_top1I,axiom,
! [X4,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_top1I) ).
fof(fact_acyclic__def,axiom,
! [X6,X5] :
( c_Wellfounded_Oacyclic(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_acyclic__def) ).
fof(fact_total__on__def,axiom,
! [X6,X7,X5] :
( c_Relation_Ototal__on(X5,X7,X6)
<=> ! [X3] :
( c_member(X5,X3,X7)
=> ! [X8] :
( c_member(X5,X8,X7)
=> ( X3 != X8
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X8),X6)
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X3),X6) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_total__on__def) ).
fof(fact_in__rel__def,axiom,
! [X17,X4,X19,X18,X5] :
( c_FunDef_Oin__rel(X5,X18,X19,X4,X17)
<=> c_member(tc_prod(X5,X18),c_Product__Type_OPair(X5,X18,X4,X17),X19) ),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',fact_in__rel__def) ).
fof(conj_4,conjecture,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
file('/export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p',conj_4) ).
fof(c_0_15,plain,
! [X956,X957,X958,X959] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X959,X958,X957),X956))
| X958 = X956
| hBOOL(hAPP(X957,X956)) )
& ( X958 != X956
| hBOOL(hAPP(c_Set_Oinsert(X959,X958,X957),X956)) )
& ( ~ hBOOL(hAPP(X957,X956))
| hBOOL(hAPP(c_Set_Oinsert(X959,X958,X957),X956)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
cnf(c_0_16,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X945,X946,X947] :
( ~ c_member(X947,X946,X945)
| c_Set_Oinsert(X947,X946,X945) = X945 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_18,plain,
! [X6,X5] :
( c_Relation_Oirrefl(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(c_0_19,plain,
! [X152,X153,X154] :
( ( ~ c_member(X154,X153,X152)
| hBOOL(hAPP(X152,X153)) )
& ( ~ hBOOL(hAPP(X152,X153))
| c_member(X154,X153,X152) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_20,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,hypothesis,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk90_0)) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk90_0)) )
& ( c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk90_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])]) ).
fof(c_0_23,hypothesis,
! [X2037] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2037))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2037))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X2037)) ),
inference(variable_rename,[status(thm)],[conj_1]) ).
fof(c_0_24,plain,
! [X84,X85,X86,X87,X88] :
( ( ~ c_Relation_Oirrefl(X85,X84)
| ~ c_member(tc_prod(X85,X85),c_Product__Type_OPair(X85,X85,X86,X86),X84) )
& ( c_member(tc_prod(X88,X88),c_Product__Type_OPair(X88,X88,esk2_2(X87,X88),esk2_2(X87,X88)),X87)
| c_Relation_Oirrefl(X88,X87) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
cnf(c_0_25,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_member(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(split_conjunct,[status(thm)],[conj_2]) ).
fof(c_0_28,plain,
! [X701,X702] :
( ~ c_Relation_Otrans(X702,X701)
| c_Transitive__Closure_Otrancl(X702,X701) = X701 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).
cnf(c_0_29,hypothesis,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk90_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
fof(c_0_35,plain,
! [X705,X706,X707,X708,X709] :
( ~ c_member(tc_prod(X709,X709),c_Product__Type_OPair(X709,X709,X708,X707),X706)
| ~ c_member(tc_prod(X709,X709),c_Product__Type_OPair(X709,X709,X707,X705),X706)
| c_member(tc_prod(X709,X709),c_Product__Type_OPair(X709,X709,X708,X705),c_Transitive__Closure_Otrancl(X709,X706)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
cnf(c_0_36,hypothesis,
hBOOL(hAPP(v_F(v_P),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X2
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_39,plain,
~ c_Relation_Oirrefl(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X5),c_Transitive__Closure_Otrancl(X1,X4))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X4)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_42,hypothesis,
c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk90_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_44,hypothesis,
! [X2031,X2035,X2036] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X2031,esk87_1(X2031)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X2031,esk88_1(X2031)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X2031,esk89_1(X2031)))
| X2035 = X2036
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2035,X2036),hAPP(X2031,v_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2035,X2036),v_F(X2031)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])])]) ).
fof(c_0_45,plain,
! [X115,X116] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)),X115)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(c_0_46,plain,
! [X6,X5] :
( c_Wellfounded_Oacyclic(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
cnf(c_0_47,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_48,hypothesis,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_b),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_a),v_F(v_P)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_49,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_50,hypothesis,
( X2 = X3
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_F(X1))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk87_1(X1)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk88_1(X1)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X1,esk89_1(X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X1,v_i)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_51,plain,
! [X90,X91,X92,X93,X94,X95,X96,X97] :
( ( ~ c_Relation_Ototal__on(X92,X91,X90)
| ~ c_member(X92,X93,X91)
| ~ c_member(X92,X94,X91)
| X93 = X94
| c_member(tc_prod(X92,X92),c_Product__Type_OPair(X92,X92,X93,X94),X90)
| c_member(tc_prod(X92,X92),c_Product__Type_OPair(X92,X92,X94,X93),X90) )
& ( c_member(X97,esk3_3(X95,X96,X97),X96)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( c_member(X97,esk4_3(X95,X96,X97),X96)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( esk3_3(X95,X96,X97) != esk4_3(X95,X96,X97)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( ~ c_member(tc_prod(X97,X97),c_Product__Type_OPair(X97,X97,esk3_3(X95,X96,X97),esk4_3(X95,X96,X97)),X95)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( ~ c_member(tc_prod(X97,X97),c_Product__Type_OPair(X97,X97,esk4_3(X95,X96,X97),esk3_3(X95,X96,X97)),X95)
| c_Relation_Ototal__on(X97,X96,X95) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__def])])])])])]) ).
cnf(c_0_52,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X857,X858,X859,X860,X861] :
( ( ~ c_Wellfounded_Oacyclic(X858,X857)
| ~ c_member(tc_prod(X858,X858),c_Product__Type_OPair(X858,X858,X859,X859),c_Transitive__Closure_Otrancl(X858,X857)) )
& ( c_member(tc_prod(X861,X861),c_Product__Type_OPair(X861,X861,esk67_2(X860,X861),esk67_2(X860,X861)),c_Transitive__Closure_Otrancl(X861,X860))
| c_Wellfounded_Oacyclic(X861,X860) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])]) ).
fof(c_0_54,plain,
! [X155,X156,X157,X158,X159] :
( ( ~ c_FunDef_Oin__rel(X159,X158,X157,X156,X155)
| c_member(tc_prod(X159,X158),c_Product__Type_OPair(X159,X158,X156,X155),X157) )
& ( ~ c_member(tc_prod(X159,X158),c_Product__Type_OPair(X159,X158,X156,X155),X157)
| c_FunDef_Oin__rel(X159,X158,X157,X156,X155) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(c_0_55,hypothesis,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_56,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_32]),c_0_31]),c_0_30])]) ).
cnf(c_0_57,plain,
( X4 = X5
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X3)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_member(X1,X4,X2)
| ~ c_member(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
fof(c_0_59,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_4])]) ).
cnf(c_0_60,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk67_2(X2,X1),esk67_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
( c_FunDef_Oin__rel(X1,X2,X5,X3,X4)
| ~ c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,hypothesis,
( v_b = v_a
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_32]),c_0_58]),c_0_58])]) ).
cnf(c_0_64,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_67,hypothesis,
c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_b),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_68,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_69,hypothesis,
( ~ c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X1),v_F(v_P)) ),
inference(spm,[status(thm)],[c_0_65,c_0_42]) ).
cnf(c_0_70,hypothesis,
c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_42]),c_0_49])]) ).
cnf(c_0_71,plain,
( c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X4,X5),X3)
| ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_72,hypothesis,
c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_a),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,hypothesis,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X1),v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SCT121+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 2400
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Oct 2 11:22:05 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.48 Running first-order model finding
% 0.17/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.kWeSJSC4ED/E---3.1_7061.p
% 533.91/68.17 # Version: 3.1pre001
% 533.91/68.17 # Preprocessing class: FSLSSMSSSSSNFFN.
% 533.91/68.17 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 533.91/68.17 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 533.91/68.17 # Starting new_bool_3 with 300s (1) cores
% 533.91/68.17 # Starting new_bool_1 with 300s (1) cores
% 533.91/68.17 # Starting sh5l with 300s (1) cores
% 533.91/68.17 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 7138 completed with status 0
% 533.91/68.17 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 533.91/68.17 # Preprocessing class: FSLSSMSSSSSNFFN.
% 533.91/68.17 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 533.91/68.17 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 533.91/68.17 # No SInE strategy applied
% 533.91/68.17 # Search class: FGHSM-FSLM33-DFFFFFNN
% 533.91/68.17 # Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 533.91/68.17 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S0S with 271s (1) cores
% 533.91/68.17 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 533.91/68.17 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 533.91/68.17 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 533.91/68.17 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 533.91/68.17 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 7149 completed with status 0
% 533.91/68.17 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 533.91/68.17 # Preprocessing class: FSLSSMSSSSSNFFN.
% 533.91/68.17 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 533.91/68.17 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 533.91/68.17 # No SInE strategy applied
% 533.91/68.17 # Search class: FGHSM-FSLM33-DFFFFFNN
% 533.91/68.17 # Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 533.91/68.17 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S0S with 271s (1) cores
% 533.91/68.17 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 533.91/68.17 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 533.91/68.17 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 533.91/68.17 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 533.91/68.17 # Preprocessing time : 0.011 s
% 533.91/68.17 # Presaturation interreduction done
% 533.91/68.17
% 533.91/68.17 # Proof found!
% 533.91/68.17 # SZS status Theorem
% 533.91/68.17 # SZS output start CNFRefutation
% See solution above
% 533.91/68.17 # Parsed axioms : 527
% 533.91/68.17 # Removed by relevancy pruning/SinE : 0
% 533.91/68.17 # Initial clauses : 790
% 533.91/68.17 # Removed in clause preprocessing : 33
% 533.91/68.17 # Initial clauses in saturation : 757
% 533.91/68.17 # Processed clauses : 24961
% 533.91/68.17 # ...of these trivial : 3307
% 533.91/68.17 # ...subsumed : 13581
% 533.91/68.17 # ...remaining for further processing : 8073
% 533.91/68.17 # Other redundant clauses eliminated : 24537
% 533.91/68.17 # Clauses deleted for lack of memory : 243287
% 533.91/68.17 # Backward-subsumed : 606
% 533.91/68.17 # Backward-rewritten : 443
% 533.91/68.17 # Generated clauses : 3314652
% 533.91/68.17 # ...of the previous two non-redundant : 3126965
% 533.91/68.17 # ...aggressively subsumed : 0
% 533.91/68.17 # Contextual simplify-reflections : 14
% 533.91/68.17 # Paramodulations : 3289977
% 533.91/68.17 # Factorizations : 132
% 533.91/68.17 # NegExts : 0
% 533.91/68.17 # Equation resolutions : 24554
% 533.91/68.17 # Total rewrite steps : 318764
% 533.91/68.17 # Propositional unsat checks : 0
% 533.91/68.17 # Propositional check models : 0
% 533.91/68.17 # Propositional check unsatisfiable : 0
% 533.91/68.17 # Propositional clauses : 0
% 533.91/68.17 # Propositional clauses after purity: 0
% 533.91/68.17 # Propositional unsat core size : 0
% 533.91/68.17 # Propositional preprocessing time : 0.000
% 533.91/68.17 # Propositional encoding time : 0.000
% 533.91/68.17 # Propositional solver time : 0.000
% 533.91/68.17 # Success case prop preproc time : 0.000
% 533.91/68.17 # Success case prop encoding time : 0.000
% 533.91/68.17 # Success case prop solver time : 0.000
% 533.91/68.17 # Current number of processed clauses : 6345
% 533.91/68.17 # Positive orientable unit clauses : 3267
% 533.91/68.17 # Positive unorientable unit clauses: 12
% 533.91/68.17 # Negative unit clauses : 401
% 533.91/68.17 # Non-unit-clauses : 2665
% 533.91/68.17 # Current number of unprocessed clauses: 1965297
% 533.91/68.17 # ...number of literals in the above : 5889615
% 533.91/68.17 # Current number of archived formulas : 0
% 533.91/68.17 # Current number of archived clauses : 1663
% 533.91/68.17 # Clause-clause subsumption calls (NU) : 1394252
% 533.91/68.17 # Rec. Clause-clause subsumption calls : 922407
% 533.91/68.17 # Non-unit clause-clause subsumptions : 9052
% 533.91/68.17 # Unit Clause-clause subsumption calls : 123924
% 533.91/68.17 # Rewrite failures with RHS unbound : 313
% 533.91/68.17 # BW rewrite match attempts : 667809
% 533.91/68.17 # BW rewrite match successes : 521
% 533.91/68.17 # Condensation attempts : 0
% 533.91/68.17 # Condensation successes : 0
% 533.91/68.17 # Termbank termtop insertions : 60676070
% 533.91/68.17
% 533.91/68.17 # -------------------------------------------------
% 533.91/68.17 # User time : 64.912 s
% 533.91/68.17 # System time : 1.572 s
% 533.91/68.17 # Total time : 66.484 s
% 533.91/68.17 # Maximum resident set size: 5368 pages
% 533.91/68.17
% 533.91/68.17 # -------------------------------------------------
% 533.91/68.17 # User time : 323.670 s
% 533.91/68.17 # System time : 7.532 s
% 533.91/68.17 # Total time : 331.203 s
% 533.91/68.17 # Maximum resident set size: 2400 pages
% 533.91/68.17 % E---3.1 exiting
%------------------------------------------------------------------------------