TSTP Solution File: NLP143-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NLP143-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Sun Sep 18 08:47:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 90
% Syntax : Number of formulae : 180 ( 32 unt; 18 typ; 0 def)
% Number of atoms : 544 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 697 ( 329 ~; 309 |; 0 &)
% ( 59 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 16 >; 17 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 364 ( 336 !; 0 ?; 364 :)
% Comments :
%------------------------------------------------------------------------------
tff(object_type,type,
object: ( $i * $i ) > $o ).
tff(skf5_type,type,
skf5: $i > $i ).
tff(skf8_type,type,
skf8: ( $i * $i ) > $i ).
tff(skc6_type,type,
skc6: $i ).
tff(skc7_type,type,
skc7: $i ).
tff(unisex_type,type,
unisex: ( $i * $i ) > $o ).
tff(male_type,type,
male: ( $i * $i ) > $o ).
tff(man_type,type,
man: ( $i * $i ) > $o ).
tff(be_type,type,
be: ( $i * $i * $i * $i ) > $o ).
tff(skf6_type,type,
skf6: $i > $i ).
tff(member_type,type,
member: ( $i * $i * $i ) > $o ).
tff(two_type,type,
two: ( $i * $i ) > $o ).
tff(fellow_type,type,
fellow: ( $i * $i ) > $o ).
tff(artifact_type,type,
artifact: ( $i * $i ) > $o ).
tff(instrumentality_type,type,
instrumentality: ( $i * $i ) > $o ).
tff(furniture_type,type,
furniture: ( $i * $i ) > $o ).
tff(seat_type,type,
seat: ( $i * $i ) > $o ).
tff(frontseat_type,type,
frontseat: ( $i * $i ) > $o ).
tff(1,plain,
( two(skc6,skc7)
<=> two(skc6,skc7) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
two(skc6,skc7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
tff(3,plain,
two(skc6,skc7),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ two(U,V)
| member(U,skf8(V,U),V) )
<=> ( ~ two(U,V)
| member(U,skf8(V,U),V) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) )
<=> ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) )
<=> ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
tff(8,plain,
! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) )
| ~ two(skc6,skc7)
| member(skc6,skf8(skc7,skc6),skc7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) )
| ~ two(skc6,skc7)
| member(skc6,skf8(skc7,skc6),skc7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) )
| ~ two(skc6,skc7)
| member(skc6,skf8(skc7,skc6),skc7) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V: $i,U: $i] :
( ~ two(U,V)
| member(U,skf8(V,U),V) )
| ~ two(skc6,skc7)
| member(skc6,skf8(skc7,skc6),skc7) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
member(skc6,skf8(skc7,skc6),skc7),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [U: $i] :
refl(
( ( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
<=> ( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
<=> ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
<=> ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
tff(19,plain,
! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| be(skc6,skf6(U),U,skf5(U)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ be(U,V,W,X)
| ( W = X ) )
<=> ( ~ be(U,V,W,X)
| ( W = X ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
tff(30,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) )
| ~ be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6)))
| ( skf8(skc7,skc6) = skf5(skf8(skc7,skc6)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) )
| ~ be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6)))
| ( skf8(skc7,skc6) = skf5(skf8(skc7,skc6)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) )
| ~ be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6)))
| ( skf8(skc7,skc6) = skf5(skf8(skc7,skc6)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ be(U,V,W,X)
| ( W = X ) )
| ~ be(skc6,skf6(skf8(skc7,skc6)),skf8(skc7,skc6),skf5(skf8(skc7,skc6)))
| ( skf8(skc7,skc6) = skf5(skf8(skc7,skc6)) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
skf8(skc7,skc6) = skf5(skf8(skc7,skc6)),
inference(unit_resolution,[status(thm)],[35,32,25]) ).
tff(37,plain,
skf5(skf8(skc7,skc6)) = skf8(skc7,skc6),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( man(skc6,skf5(skf8(skc7,skc6)))
<=> man(skc6,skf8(skc7,skc6)) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( man(skc6,skf8(skc7,skc6))
<=> man(skc6,skf5(skf8(skc7,skc6))) ),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [U: $i] :
refl(
( ( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
<=> ( ~ member(skc6,U,skc7)
| fellow(skc6,U) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
<=> ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
<=> ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
tff(44,plain,
! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| fellow(skc6,skf8(skc7,skc6)) )
<=> ( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| fellow(skc6,skf8(skc7,skc6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| fellow(skc6,skf8(skc7,skc6)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [U: $i] :
( ~ member(skc6,U,skc7)
| fellow(skc6,U) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| fellow(skc6,skf8(skc7,skc6)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
fellow(skc6,skf8(skc7,skc6)),
inference(unit_resolution,[status(thm)],[49,46,14]) ).
tff(51,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ fellow(U,V)
| man(U,V) )
<=> ( ~ fellow(U,V)
| man(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) )
<=> ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) )
<=> ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
tff(55,plain,
! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) )
| ~ fellow(skc6,skf8(skc7,skc6))
| man(skc6,skf8(skc7,skc6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) )
| ~ fellow(skc6,skf8(skc7,skc6))
| man(skc6,skf8(skc7,skc6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) )
| ~ fellow(skc6,skf8(skc7,skc6))
| man(skc6,skf8(skc7,skc6)) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [V: $i,U: $i] :
( ~ fellow(U,V)
| man(U,V) )
| ~ fellow(skc6,skf8(skc7,skc6))
| man(skc6,skf8(skc7,skc6)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
man(skc6,skf8(skc7,skc6)),
inference(unit_resolution,[status(thm)],[60,57,50]) ).
tff(62,plain,
man(skc6,skf5(skf8(skc7,skc6))),
inference(modus_ponens,[status(thm)],[61,39]) ).
tff(63,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ man(U,V)
| male(U,V) )
<=> ( ~ man(U,V)
| male(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) )
<=> ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) )
<=> ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
tff(67,plain,
! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) )
| ~ man(skc6,skf5(skf8(skc7,skc6)))
| male(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) )
| ~ man(skc6,skf5(skf8(skc7,skc6)))
| male(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) )
| ~ man(skc6,skf5(skf8(skc7,skc6)))
| male(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [V: $i,U: $i] :
( ~ man(U,V)
| male(U,V) )
| ~ man(skc6,skf5(skf8(skc7,skc6)))
| male(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ~ man(skc6,skf5(skf8(skc7,skc6)))
| male(skc6,skf5(skf8(skc7,skc6))) ),
inference(unit_resolution,[status(thm)],[72,69]) ).
tff(74,plain,
male(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[73,62]) ).
tff(75,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ male(U,V)
| ~ unisex(U,V) )
<=> ( ~ male(U,V)
| ~ unisex(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) )
<=> ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) )
<=> ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
tff(79,plain,
! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) )
| ~ male(skc6,skf5(skf8(skc7,skc6)))
| ~ unisex(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) )
| ~ male(skc6,skf5(skf8(skc7,skc6)))
| ~ unisex(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) )
| ~ male(skc6,skf5(skf8(skc7,skc6)))
| ~ unisex(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [V: $i,U: $i] :
( ~ male(U,V)
| ~ unisex(U,V) )
| ~ male(skc6,skf5(skf8(skc7,skc6)))
| ~ unisex(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ unisex(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[84,81,74]) ).
tff(86,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ object(U,V)
| unisex(U,V) )
<=> ( ~ object(U,V)
| unisex(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) )
<=> ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) )
<=> ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
tff(90,plain,
! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) )
| ~ object(skc6,skf5(skf8(skc7,skc6)))
| unisex(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) )
| ~ object(skc6,skf5(skf8(skc7,skc6)))
| unisex(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) )
| ~ object(skc6,skf5(skf8(skc7,skc6)))
| unisex(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [V: $i,U: $i] :
( ~ object(U,V)
| unisex(U,V) )
| ~ object(skc6,skf5(skf8(skc7,skc6)))
| unisex(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
~ object(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[95,92,85]) ).
tff(97,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
<=> ( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
<=> ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
<=> ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
tff(101,plain,
! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| frontseat(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| frontseat(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| frontseat(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [V: $i,U: $i] :
( ~ member(skc6,U,skc7)
| frontseat(skc6,skf5(V)) )
| ~ member(skc6,skf8(skc7,skc6),skc7)
| frontseat(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
frontseat(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[106,103,14]) ).
tff(108,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ frontseat(U,V)
| seat(U,V) )
<=> ( ~ frontseat(U,V)
| seat(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) )
<=> ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) )
<=> ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,axiom,
! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
tff(112,plain,
! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) )
| ~ frontseat(skc6,skf5(skf8(skc7,skc6)))
| seat(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) )
| ~ frontseat(skc6,skf5(skf8(skc7,skc6)))
| seat(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ~ ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) )
| ~ frontseat(skc6,skf5(skf8(skc7,skc6)))
| seat(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [V: $i,U: $i] :
( ~ frontseat(U,V)
| seat(U,V) )
| ~ frontseat(skc6,skf5(skf8(skc7,skc6)))
| seat(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
seat(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[117,114,107]) ).
tff(119,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ seat(U,V)
| furniture(U,V) )
<=> ( ~ seat(U,V)
| furniture(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) )
<=> ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) )
<=> ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,axiom,
! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
tff(123,plain,
! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) )
| ~ seat(skc6,skf5(skf8(skc7,skc6)))
| furniture(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) )
| ~ seat(skc6,skf5(skf8(skc7,skc6)))
| furniture(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ~ ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) )
| ~ seat(skc6,skf5(skf8(skc7,skc6)))
| furniture(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( ~ ! [V: $i,U: $i] :
( ~ seat(U,V)
| furniture(U,V) )
| ~ seat(skc6,skf5(skf8(skc7,skc6)))
| furniture(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
furniture(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[128,125,118]) ).
tff(130,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ furniture(U,V)
| instrumentality(U,V) )
<=> ( ~ furniture(U,V)
| instrumentality(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) )
<=> ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) )
<=> ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
tff(134,plain,
! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) )
| ~ furniture(skc6,skf5(skf8(skc7,skc6)))
| instrumentality(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) )
| ~ furniture(skc6,skf5(skf8(skc7,skc6)))
| instrumentality(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ~ ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) )
| ~ furniture(skc6,skf5(skf8(skc7,skc6)))
| instrumentality(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
( ~ ! [V: $i,U: $i] :
( ~ furniture(U,V)
| instrumentality(U,V) )
| ~ furniture(skc6,skf5(skf8(skc7,skc6)))
| instrumentality(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
instrumentality(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[139,136,129]) ).
tff(141,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ instrumentality(U,V)
| artifact(U,V) )
<=> ( ~ instrumentality(U,V)
| artifact(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) )
<=> ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) )
<=> ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,axiom,
! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
tff(145,plain,
! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) )
| ~ instrumentality(skc6,skf5(skf8(skc7,skc6)))
| artifact(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) )
| ~ instrumentality(skc6,skf5(skf8(skc7,skc6)))
| artifact(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ~ ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) )
| ~ instrumentality(skc6,skf5(skf8(skc7,skc6)))
| artifact(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
( ~ ! [V: $i,U: $i] :
( ~ instrumentality(U,V)
| artifact(U,V) )
| ~ instrumentality(skc6,skf5(skf8(skc7,skc6)))
| artifact(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
artifact(skc6,skf5(skf8(skc7,skc6))),
inference(unit_resolution,[status(thm)],[150,147,140]) ).
tff(152,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ artifact(U,V)
| object(U,V) )
<=> ( ~ artifact(U,V)
| object(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) )
<=> ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,plain,
( ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) )
<=> ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,axiom,
! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
tff(156,plain,
! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) ),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) )
| ~ artifact(skc6,skf5(skf8(skc7,skc6)))
| object(skc6,skf5(skf8(skc7,skc6))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) )
| ~ artifact(skc6,skf5(skf8(skc7,skc6)))
| object(skc6,skf5(skf8(skc7,skc6))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ~ ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) )
| ~ artifact(skc6,skf5(skf8(skc7,skc6)))
| object(skc6,skf5(skf8(skc7,skc6))) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
( ~ ! [V: $i,U: $i] :
( ~ artifact(U,V)
| object(U,V) )
| ~ artifact(skc6,skf5(skf8(skc7,skc6)))
| object(skc6,skf5(skf8(skc7,skc6))) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
$false,
inference(unit_resolution,[status(thm)],[161,158,151,96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NLP143-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 04:55:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------