TSTP Solution File: KRS003_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS003_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Sat Sep 17 17:44:20 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 63
% Syntax : Number of formulae : 133 ( 29 unt; 11 typ; 0 def)
% Number of atoms : 555 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 691 ( 299 ~; 251 |; 53 &)
% ( 64 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 12 ( 10 >; 2 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 182 ( 159 !; 0 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( real * real ) > $o ).
tff(u1r1_type,type,
u1r1: unreal > real ).
tff(exist_type,type,
exist: unreal ).
tff(u1r2_type,type,
u1r2: unreal > real ).
tff(s2least_type,type,
s2least: unreal > $o ).
tff(c_type,type,
c: unreal > $o ).
tff(e_type,type,
e: unreal > $o ).
tff(f_type,type,
f: unreal > $o ).
tff(s_type,type,
s: ( unreal * real ) > $o ).
tff(s1most_type,type,
s1most: unreal > $o ).
tff(d_type,type,
d: unreal > $o ).
tff(1,plain,
( e(exist)
<=> e(exist) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ ( ~ e(exist)
| ~ f(exist) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1__clause_2) ).
tff(3,plain,
e(exist),
inference(or_elim,[status(thm)],[2]) ).
tff(4,plain,
e(exist),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [X1: unreal] :
refl(
( ( c(X1)
| ~ e(X1) )
<=> ( c(X1)
| ~ e(X1) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X1: unreal] :
( c(X1)
| ~ e(X1) )
<=> ! [X1: unreal] :
( c(X1)
| ~ e(X1) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X1: unreal] :
( c(X1)
| ~ e(X1) )
<=> ! [X1: unreal] :
( c(X1)
| ~ e(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
^ [X1: unreal] :
rewrite(
( ( e(X1)
=> c(X1) )
<=> ( c(X1)
| ~ e(X1) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X1: unreal] :
( e(X1)
=> c(X1) )
<=> ! [X1: unreal] :
( c(X1)
| ~ e(X1) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [X1: unreal] :
( e(X1)
=> c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
tff(11,plain,
! [X1: unreal] :
( c(X1)
| ~ e(X1) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X1: unreal] :
( c(X1)
| ~ e(X1) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X1: unreal] :
( c(X1)
| ~ e(X1) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X1: unreal] :
( c(X1)
| ~ e(X1) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
( ( ~ ! [X1: unreal] :
( c(X1)
| ~ e(X1) )
| c(exist)
| ~ e(exist) )
<=> ( ~ ! [X1: unreal] :
( c(X1)
| ~ e(X1) )
| c(exist)
| ~ e(exist) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X1: unreal] :
( c(X1)
| ~ e(X1) )
| c(exist)
| ~ e(exist) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
( ~ ! [X1: unreal] :
( c(X1)
| ~ e(X1) )
| c(exist)
| ~ e(exist) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c(exist),
inference(unit_resolution,[status(thm)],[17,14,4]) ).
tff(19,plain,
^ [X1: unreal] :
refl(
( ( s2least(X1)
| ~ c(X1) )
<=> ( s2least(X1)
| ~ c(X1) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) )
<=> ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) )
<=> ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X1: unreal] :
rewrite(
( ( c(X1)
=> s2least(X1) )
<=> ( s2least(X1)
| ~ c(X1) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X1: unreal] :
( c(X1)
=> s2least(X1) )
<=> ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X1: unreal] :
( c(X1)
=> s2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(25,plain,
! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X1: unreal] :
( s2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) )
| s2least(exist)
| ~ c(exist) )
<=> ( ~ ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) )
| s2least(exist)
| ~ c(exist) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) )
| s2least(exist)
| ~ c(exist) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [X1: unreal] :
( s2least(X1)
| ~ c(X1) )
| s2least(exist)
| ~ c(exist) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
s2least(exist),
inference(unit_resolution,[status(thm)],[31,28,18]) ).
tff(33,plain,
^ [X1: unreal] :
refl(
( ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
^ [X1: unreal] :
trans(
monotonicity(
rewrite(
( ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) )
<=> ~ ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
( ~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) )
<=> ~ ~ ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
rewrite(
( ~ ~ ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
( ~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) )
<=> ( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X1: unreal] :
~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X1: unreal] :
~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: unreal] :
~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [X1: unreal] :
~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(39,plain,
! [X1: unreal] :
~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X1: unreal] :
~ ( s2least(X1)
& equalish(u1r2(X1),u1r1(X1)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ s2least(exist)
| ~ equalish(u1r2(exist),u1r1(exist)) )
<=> ( ~ ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ s2least(exist)
| ~ equalish(u1r2(exist),u1r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ s2least(exist)
| ~ equalish(u1r2(exist),u1r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X1: unreal] :
( ~ s2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ s2least(exist)
| ~ equalish(u1r2(exist),u1r1(exist)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ equalish(u1r2(exist),u1r1(exist)),
inference(unit_resolution,[status(thm)],[45,42,32]) ).
tff(47,plain,
^ [X1: unreal] :
refl(
( ( ~ s2least(X1)
| s(X1,u1r1(X1)) )
<=> ( ~ s2least(X1)
| s(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [X1: unreal] :
rewrite(
( ( s2least(X1)
=> s(X1,u1r1(X1)) )
<=> ( ~ s2least(X1)
| s(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X1: unreal] :
( s2least(X1)
=> s(X1,u1r1(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [X1: unreal] :
( s2least(X1)
=> s(X1,u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(53,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) )
| ~ s2least(exist)
| s(exist,u1r1(exist)) )
<=> ( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) )
| ~ s2least(exist)
| s(exist,u1r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) )
| ~ s2least(exist)
| s(exist,u1r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) )
| ~ s2least(exist)
| s(exist,u1r1(exist)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
s(exist,u1r1(exist)),
inference(unit_resolution,[status(thm)],[59,56,32]) ).
tff(61,plain,
^ [X1: unreal] :
refl(
( ( ~ s2least(X1)
| s(X1,u1r2(X1)) )
<=> ( ~ s2least(X1)
| s(X1,u1r2(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [X1: unreal] :
rewrite(
( ( s2least(X1)
=> s(X1,u1r2(X1)) )
<=> ( ~ s2least(X1)
| s(X1,u1r2(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X1: unreal] :
( s2least(X1)
=> s(X1,u1r2(X1)) )
<=> ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [X1: unreal] :
( s2least(X1)
=> s(X1,u1r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(67,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) )
| ~ s2least(exist)
| s(exist,u1r2(exist)) )
<=> ( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) )
| ~ s2least(exist)
| s(exist,u1r2(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) )
| ~ s2least(exist)
| s(exist,u1r2(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X1: unreal] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) )
| ~ s2least(exist)
| s(exist,u1r2(exist)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
s(exist,u1r2(exist)),
inference(unit_resolution,[status(thm)],[73,70,32]) ).
tff(75,plain,
( f(exist)
<=> f(exist) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
f(exist),
inference(or_elim,[status(thm)],[2]) ).
tff(77,plain,
f(exist),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
^ [X1: unreal] :
refl(
( ( d(X1)
| ~ f(X1) )
<=> ( d(X1)
| ~ f(X1) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X1: unreal] :
( d(X1)
| ~ f(X1) )
<=> ! [X1: unreal] :
( d(X1)
| ~ f(X1) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X1: unreal] :
( d(X1)
| ~ f(X1) )
<=> ! [X1: unreal] :
( d(X1)
| ~ f(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [X1: unreal] :
rewrite(
( ( f(X1)
=> d(X1) )
<=> ( d(X1)
| ~ f(X1) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X1: unreal] :
( f(X1)
=> d(X1) )
<=> ! [X1: unreal] :
( d(X1)
| ~ f(X1) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [X1: unreal] :
( f(X1)
=> d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
tff(84,plain,
! [X1: unreal] :
( d(X1)
| ~ f(X1) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X1: unreal] :
( d(X1)
| ~ f(X1) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [X1: unreal] :
( d(X1)
| ~ f(X1) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X1: unreal] :
( d(X1)
| ~ f(X1) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [X1: unreal] :
( d(X1)
| ~ f(X1) )
| d(exist)
| ~ f(exist) )
<=> ( ~ ! [X1: unreal] :
( d(X1)
| ~ f(X1) )
| d(exist)
| ~ f(exist) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [X1: unreal] :
( d(X1)
| ~ f(X1) )
| d(exist)
| ~ f(exist) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [X1: unreal] :
( d(X1)
| ~ f(X1) )
| d(exist)
| ~ f(exist) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
d(exist),
inference(unit_resolution,[status(thm)],[90,87,77]) ).
tff(92,plain,
^ [X1: unreal] :
refl(
( ( s1most(X1)
| ~ d(X1) )
<=> ( s1most(X1)
| ~ d(X1) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) )
<=> ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) )
<=> ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
^ [X1: unreal] :
rewrite(
( ( d(X1)
=> s1most(X1) )
<=> ( s1most(X1)
| ~ d(X1) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X1: unreal] :
( d(X1)
=> s1most(X1) )
<=> ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [X1: unreal] :
( d(X1)
=> s1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(98,plain,
! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X1: unreal] :
( s1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( ~ ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) )
| s1most(exist)
| ~ d(exist) )
<=> ( ~ ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) )
| s1most(exist)
| ~ d(exist) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) )
| s1most(exist)
| ~ d(exist) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [X1: unreal] :
( s1most(X1)
| ~ d(X1) )
| s1most(exist)
| ~ d(exist) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
s1most(exist),
inference(unit_resolution,[status(thm)],[104,101,91]) ).
tff(106,plain,
^ [X2: real,X3: real,X1: unreal] :
refl(
( ( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
^ [X2: real,X3: real,X1: unreal] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
<=> ~ ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
<=> ~ ~ ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
rewrite(
( ~ ~ ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
<=> ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
( ( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) )
<=> ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2)
| equalish(X3,X2) ) )),
rewrite(
( ( ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2)
| equalish(X3,X2) )
<=> ( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
( ( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) )
<=> ( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) )
<=> ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) )
<=> ! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
^ [X2: real,X3: real,X1: unreal] :
trans(
monotonicity(
rewrite(
( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
<=> ( s1most(X1)
& s(X1,X3)
& s(X1,X2) ) )),
( ( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
=> equalish(X3,X2) )
<=> ( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
=> equalish(X3,X2) ) )),
rewrite(
( ( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
=> equalish(X3,X2) )
<=> ( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ) )),
( ( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
=> equalish(X3,X2) )
<=> ( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [X2: real,X3: real,X1: unreal] :
( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
=> equalish(X3,X2) )
<=> ! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,axiom,
! [X2: real,X3: real,X1: unreal] :
( ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
=> equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
tff(114,plain,
! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [X2: real,X3: real,X1: unreal] :
( ~ ( s1most(X1)
& s(X1,X3)
& s(X1,X2) )
| equalish(X3,X2) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ),
inference(modus_ponens,[status(thm)],[117,107]) ).
tff(119,plain,
( ( ~ ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
| equalish(u1r2(exist),u1r1(exist))
| ~ s1most(exist)
| ~ s(exist,u1r2(exist))
| ~ s(exist,u1r1(exist)) )
<=> ( ~ ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
| equalish(u1r2(exist),u1r1(exist))
| ~ s1most(exist)
| ~ s(exist,u1r2(exist))
| ~ s(exist,u1r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ~ ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
| equalish(u1r2(exist),u1r1(exist))
| ~ s1most(exist)
| ~ s(exist,u1r2(exist))
| ~ s(exist,u1r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X2: real,X3: real,X1: unreal] :
( equalish(X3,X2)
| ~ s1most(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
| equalish(u1r2(exist),u1r1(exist))
| ~ s1most(exist)
| ~ s(exist,u1r2(exist))
| ~ s(exist,u1r1(exist)) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,118,105,74,60,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS003_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 09:15:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------