TSTP Solution File: SCT007-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SCT007-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Tue Sep 20 03:41:19 EDT 2022
% Result : Unsatisfiable 0.20s 0.59s
% Output : Proof 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 55 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 89 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 86 ( 42 ~; 29 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 11 >; 11 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 81 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Order__Relation_Ostrict__linear__order__on_type,type,
c_Order__Relation_Ostrict__linear__order__on: ( $i * $i ) > $i ).
tff(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Order__Relation_Olinear__order__on_type,type,
c_Order__Relation_Olinear__order__on: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
<=> ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
tff(5,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
| ( c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) = hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
<=> hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
<=> hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
<=> hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(16,plain,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
^ [V_r: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
<=> ( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
<=> ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
<=> ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
^ [V_r: $i,T_a: $i,V_A: $i] :
rewrite(
( ( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)) )
<=> ( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [V_r: $i,T_a: $i,V_A: $i] :
( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)) )
<=> ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__diff__Id_0) ).
tff(23,plain,
! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
| ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) )
<=> ( ~ ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
| ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
| ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [V_r: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)))) )
| ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(unit_resolution,[status(thm)],[29,26,16]) ).
tff(31,plain,
hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(modus_ponens,[status(thm)],[30,13]) ).
tff(32,plain,
^ [V_x: $i] :
refl(
( ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x))
<=> ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x))
<=> ! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x))
<=> ! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(36,plain,
! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [V_x: $i] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x))
| ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_r,c_HOL_Ouminus__class_Ouminus(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT007-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 23:12:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.59 % SZS status Unsatisfiable
% 0.20/0.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------