TSTP Solution File: CSR038-10 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR038-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 14:27:21 EDT 2022
% Result : Unsatisfiable 17.63s 11.61s
% Output : Proof 17.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 60
% Syntax : Number of formulae : 126 ( 75 unt; 21 typ; 0 def)
% Number of atoms : 155 ( 144 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 13 ~; 9 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 27 ( 10 >; 17 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-4 aty)
% Number of variables : 167 ( 147 !; 0 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(tuple2_type,type,
tuple2: ( $i * $i ) > $i ).
tff(genlmt_type,type,
genlmt: ( $i * $i ) > $i ).
tff(c_tptpgeo_spindleheadmt_type,type,
c_tptpgeo_spindleheadmt: $i ).
tff(c_tptpgeo_member8_mt_type,type,
c_tptpgeo_member8_mt: $i ).
tff(tptpcol_16_7738_type,type,
tptpcol_16_7738: $i > $i ).
tff(f_relationexistsallfn_type,type,
f_relationexistsallfn: ( $i * $i * $i * $i ) > $i ).
tff(f_subcollectionofwithrelationtotypefn_type,type,
f_subcollectionofwithrelationtotypefn: ( $i * $i * $i ) > $i ).
tff(c_correctivelensprescription_type,type,
c_correctivelensprescription: $i ).
tff(c_products_type,type,
c_products: $i ).
tff(c_issuingaprescription_type,type,
c_issuingaprescription: $i ).
tff(c_tptpcol_16_7738_type,type,
c_tptpcol_16_7738: $i ).
tff(c_tptp_8_968_type,type,
c_tptp_8_968: $i ).
tff(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804_type,type,
c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804: $i ).
tff(tptp_8_968_type,type,
tptp_8_968: ( $i * $i ) > $i ).
tff(true_type,type,
true: $i ).
tff(ifeq4_type,type,
ifeq4: ( $i * $i * $i * $i ) > $i ).
tff(isa_type,type,
isa: ( $i * $i ) > $i ).
tff(relationexistsall_type,type,
relationexistsall: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b )
<=> ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b )
<=> ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(true,true),a,b) = b )
<=> ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(true,true),a,b) = b )
<=> ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(true,true),a,b) = b )
<=> ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(true,true),a,b) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(true,true),a,b) = b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query88_1) ).
tff(7,plain,
! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(true,true),a,b) = b ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] : ( ifeq2(tuple2(tptp_8_968(X,c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(X)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b )
| ( ifeq2(tuple2(tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)))),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
ifeq2(tuple2(tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)))),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = b,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
<=> ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
<=> ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [X: $i] :
rewrite(
( ( ifeq4(isa(X,c_tptpcol_16_7738),true,tptpcol_16_7738(X),true) = true )
<=> ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),true,tptpcol_16_7738(X),true) = true )
<=> ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),true,tptpcol_16_7738(X),true) = true )
<=> ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),true,tptpcol_16_7738(X),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),true,tptpcol_16_7738(X),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_673) ).
tff(19,plain,
! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),true,tptpcol_16_7738(X),true) = true ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ~ ! [X: $i] : ( ifeq4(isa(X,c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(X),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
| ( ifeq4(isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
ifeq4(isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq4(A,A,B,C) = B )
<=> ( ifeq4(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B )
| ( ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( ( isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true )
<=> ( isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true )
<=> ( isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_134) ).
tff(37,plain,
isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true,
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) = isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B )
| ( ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(unit_resolution,[status(thm)],[42,31]) ).
tff(44,plain,
( ( relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true )
<=> ( relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true )
<=> ( relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_245) ).
tff(47,plain,
relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = true,
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) = relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
ifeq4(relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] :
refl(
( ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
<=> ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
<=> ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] :
rewrite(
( ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),true,ifeq4(isa(TERM,INDEPCOL),true,isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),true),true) = true )
<=> ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),true,ifeq4(isa(TERM,INDEPCOL),true,isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),true),true) = true )
<=> ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),true,ifeq4(isa(TERM,INDEPCOL),true,isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),true),true) = true )
<=> ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),true,ifeq4(isa(TERM,INDEPCOL),true,isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),true),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),true,ifeq4(isa(TERM,INDEPCOL),true,isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_64) ).
tff(58,plain,
! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),true,ifeq4(isa(TERM,INDEPCOL),true,isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),true),true) = true ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ~ ! [DEPCOL: $i,PRED: $i,INDEPCOL: $i,TERM: $i] : ( ifeq4(relationexistsall(PRED,DEPCOL,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(TERM,INDEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(TERM,PRED,DEPCOL,INDEPCOL),DEPCOL),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
| ( ifeq4(relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
ifeq4(relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) = ifeq4(relationexistsall(c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) = isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),
inference(transitivity,[status(thm)],[64,51,43,41,33]) ).
tff(66,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(isa(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpcol_16_7738),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B )
| ( ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),
inference(unit_resolution,[status(thm)],[67,31]) ).
tff(69,plain,
tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))) = ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription))) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(transitivity,[status(thm)],[69,66,24]) ).
tff(71,plain,
^ [TERM: $i] :
refl(
( ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
<=> ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
<=> ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
^ [TERM: $i] :
rewrite(
( ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),true,tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),true) = true )
<=> ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),true,tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),true) = true )
<=> ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),true,tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),true) = true )
<=> ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),true,tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),true,tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_244) ).
tff(77,plain,
! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),true,tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),true) = true ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[77,74]) ).
tff(79,plain,
! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ~ ! [TERM: $i] : ( ifeq4(isa(TERM,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(TERM,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),TERM),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) )
| ( ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = ifeq4(isa(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(monotonicity,[status(thm)],[39]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq4(A,A,B,C) = B )
| ( ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),
inference(unit_resolution,[status(thm)],[84,31]) ).
tff(86,plain,
tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804) = ifeq4(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804) = genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),
inference(transitivity,[status(thm)],[86,83,82]) ).
tff(88,plain,
tuple2(tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)))) = tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),
inference(monotonicity,[status(thm)],[87,70]) ).
tff(89,plain,
tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)) = tuple2(tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
ifeq2(tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = ifeq2(tuple2(tptp_8_968(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)),c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804),tptpcol_16_7738(f_relationexistsallfn(c_tptpnsubcollectionofwithrelationtotypefnissuingaprescriptionproductscorrectivelensprescription_2804,c_tptp_8_968,c_tptpcol_16_7738,f_subcollectionofwithrelationtotypefn(c_issuingaprescription,c_products,c_correctivelensprescription)))),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
tff(95,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
ifeq2(tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b) = a,
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
a = ifeq2(tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),tuple2(genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt),genlmt(c_tptpgeo_member8_mt,c_tptpgeo_spindleheadmt)),a,b),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
a = b,
inference(transitivity,[status(thm)],[100,90,12]) ).
tff(102,plain,
( ( a != b )
<=> ( a != b ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(104,plain,
a != b,
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CSR038-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Tue Aug 30 17:31:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 17.63/11.61 % SZS status Unsatisfiable
% 17.63/11.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------