TSTP Solution File: KRS150+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS150+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 17:44:58 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 75
% Syntax : Number of formulae : 145 ( 27 unt; 18 typ; 0 def)
% Number of atoms : 695 ( 0 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 949 ( 391 ~; 185 |; 185 &)
% ( 188 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 104 ( 94 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(cC12_type,type,
cC12: $i > $o ).
tff(iV16562_type,type,
iV16562: $i ).
tff(cC2_type,type,
cC2: $i > $o ).
tff(cC10_type,type,
cC10: $i > $o ).
tff(cC6_type,type,
cC6: $i > $o ).
tff(iV16561_type,type,
iV16561: $i ).
tff(cC4_type,type,
cC4: $i > $o ).
tff(cC16_type,type,
cC16: $i > $o ).
tff(iV16560_type,type,
iV16560: $i ).
tff(cTOP_type,type,
cTOP: $i > $o ).
tff(cC18_type,type,
cC18: $i > $o ).
tff(cTEST_type,type,
cTEST: $i > $o ).
tff(cC14_type,type,
cC14: $i > $o ).
tff(cC8_type,type,
cC8: $i > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(xsd_integer_type,type,
xsd_integer: $i > $o ).
tff(xsd_string_type,type,
xsd_string: $i > $o ).
tff(cowlNothing_type,type,
cowlNothing: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( ( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
<=> ( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
<=> ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) )
<=> ( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) )
<=> ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) )
<=> ! [X: $i] :
( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] :
( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(7,plain,
! [X: $i] :
( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cC12(X)
<=> ( ~ cC2(X)
& ~ cC10(X) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ) )
<=> ( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( cC12(iV16562)
<=> ~ ( cC2(iV16562)
| cC10(iV16562) ) )
<=> ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC2(iV16562)
| cC10(iV16562) ) ) )
<=> ( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC2(iV16562)
| cC10(iV16562) ) ) )
<=> ( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC2(iV16562)
| cC10(iV16562) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X: $i] :
( cC12(X)
<=> ~ ( cC2(X)
| cC10(X) ) )
| ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) ),
inference(unit_resolution,[status(thm)],[16,10]) ).
tff(18,plain,
( ~ cC2(iV16562)
<=> ~ cC2(iV16562) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
~ cC2(iV16562),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
tff(20,plain,
~ cC2(iV16562),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ cC10(iV16562)
<=> ~ cC10(iV16562) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
~ cC10(iV16562),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
tff(23,plain,
~ cC10(iV16562),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ ( cC10(iV16562)
| cC2(iV16562) )
| cC10(iV16562)
| cC2(iV16562) ),
inference(tautology,[status(thm)],]) ).
tff(25,plain,
~ ( cC10(iV16562)
| cC2(iV16562) ),
inference(unit_resolution,[status(thm)],[24,23,20]) ).
tff(26,plain,
( ~ ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) )
| cC12(iV16562)
| cC10(iV16562)
| cC2(iV16562) ),
inference(tautology,[status(thm)],]) ).
tff(27,plain,
( ~ ( cC12(iV16562)
<=> ~ ( cC10(iV16562)
| cC2(iV16562) ) )
| cC12(iV16562) ),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
cC12(iV16562),
inference(unit_resolution,[status(thm)],[27,17]) ).
tff(29,plain,
^ [X: $i] :
refl(
( ( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) )
<=> ( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X: $i] :
( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) )
<=> ! [X: $i] :
( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [X: $i] :
rewrite(
( ( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) )
<=> ( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [X: $i] :
( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) )
<=> ! [X: $i] :
( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X: $i] :
( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) )
<=> ! [X: $i] :
( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [X: $i] :
( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
tff(35,plain,
! [X: $i] :
( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X: $i] :
( cC6(X)
<=> ( ~ cC2(X)
& ~ cC4(X) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [X: $i] :
( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X: $i] :
( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ~ ! [X: $i] :
( cC6(X)
<=> ~ ( cC2(X)
| cC4(X) ) )
| ( cC6(iV16561)
<=> ~ ( cC2(iV16561)
| cC4(iV16561) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( cC6(iV16561)
<=> ~ ( cC2(iV16561)
| cC4(iV16561) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ cC2(iV16561)
<=> ~ cC2(iV16561) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
~ cC2(iV16561),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
tff(43,plain,
~ cC2(iV16561),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ cC4(iV16561)
<=> ~ cC4(iV16561) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
~ cC4(iV16561),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
tff(46,plain,
~ cC4(iV16561),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( cC2(iV16561)
| cC4(iV16561) )
| cC2(iV16561)
| cC4(iV16561) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
~ ( cC2(iV16561)
| cC4(iV16561) ),
inference(unit_resolution,[status(thm)],[47,46,43]) ).
tff(49,plain,
( ~ ( cC6(iV16561)
<=> ~ ( cC2(iV16561)
| cC4(iV16561) ) )
| cC6(iV16561)
| cC2(iV16561)
| cC4(iV16561) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
( ~ ( cC6(iV16561)
<=> ~ ( cC2(iV16561)
| cC4(iV16561) ) )
| cC6(iV16561) ),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
cC6(iV16561),
inference(unit_resolution,[status(thm)],[50,40]) ).
tff(52,plain,
^ [X: $i] :
refl(
( ( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
<=> ( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
<=> ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [X: $i] :
rewrite(
( ( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) )
<=> ( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X: $i] :
( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) )
<=> ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i] :
( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) )
<=> ! [X: $i] :
( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [X: $i] :
( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(58,plain,
! [X: $i] :
( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] :
( cC18(X)
<=> ( cTOP(X)
& cC16(X) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ) )
<=> ( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( cC18(iV16560)
<=> ~ ( ~ cTOP(iV16560)
| ~ cC16(iV16560) ) )
<=> ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cTOP(iV16560)
| ~ cC16(iV16560) ) ) )
<=> ( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cTOP(iV16560)
| ~ cC16(iV16560) ) ) )
<=> ( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cTOP(iV16560)
| ~ cC16(iV16560) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X: $i] :
( cC18(X)
<=> ~ ( ~ cTOP(X)
| ~ cC16(X) ) )
| ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ),
inference(unit_resolution,[status(thm)],[67,61]) ).
tff(69,plain,
^ [X: $i] :
refl(
( ( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) )
<=> ( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
^ [X: $i] :
rewrite(
( ( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) )
<=> ( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [X: $i] :
( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
tff(75,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC18(X)
& cTOP(X) ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ~ ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC18(X)
| ~ cTOP(X) ) )
| ( cTEST(iV16560)
<=> ~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( cTEST(iV16560)
<=> ~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( cTEST(iV16560)
<=> cTEST(iV16560) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
cTEST(iV16560),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
tff(83,plain,
cTEST(iV16560),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ ( cTEST(iV16560)
<=> ~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ) )
| ~ cTEST(iV16560)
| ~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
( ~ ( cTEST(iV16560)
<=> ~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ) )
| ~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
~ ( ~ cC18(iV16560)
| ~ cTOP(iV16560) ),
inference(unit_resolution,[status(thm)],[85,80]) ).
tff(87,plain,
( ~ cC18(iV16560)
| ~ cTOP(iV16560)
| cC18(iV16560) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
cC18(iV16560),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ ( cC18(iV16560)
<=> ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) )
| ~ cC18(iV16560)
| ~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
~ ( ~ cC16(iV16560)
| ~ cTOP(iV16560) ),
inference(unit_resolution,[status(thm)],[89,88,68]) ).
tff(91,plain,
( ~ cC16(iV16560)
| ~ cTOP(iV16560)
| cC16(iV16560) ),
inference(tautology,[status(thm)],]) ).
tff(92,plain,
cC16(iV16560),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
^ [X: $i] :
refl(
( ( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) )
<=> ( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) )
<=> ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
^ [X: $i] :
rewrite(
( ( cC16(X)
<=> ( cC14(X)
& cC8(X) ) )
<=> ( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC8(X) ) )
<=> ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC8(X) ) )
<=> ! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC8(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC8(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(99,plain,
! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC8(X) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC8(X) ) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC8(X) ) )
| ( cC16(iV16560)
<=> ~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( cC16(iV16560)
<=> ~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ ( cC16(iV16560)
<=> ~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ) )
| ~ cC16(iV16560)
| ~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ) ),
inference(tautology,[status(thm)],]) ).
tff(106,plain,
( ~ ( cC16(iV16560)
<=> ~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ) )
| ~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ) ),
inference(unit_resolution,[status(thm)],[105,92]) ).
tff(107,plain,
~ ( ~ cC14(iV16560)
| ~ cC8(iV16560) ),
inference(unit_resolution,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ cC14(iV16560)
| ~ cC8(iV16560)
| cC14(iV16560) ),
inference(tautology,[status(thm)],]) ).
tff(109,plain,
cC14(iV16560),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
( ~ cC14(iV16560)
| ~ cC8(iV16560)
| cC8(iV16560) ),
inference(tautology,[status(thm)],]) ).
tff(111,plain,
cC8(iV16560),
inference(unit_resolution,[status(thm)],[110,107]) ).
tff(112,plain,
( ~ ~ ( ~ cC16(iV16560)
| ~ cC14(iV16560)
| ~ cC18(iV16560)
| ~ cC8(iV16560)
| ~ cC6(iV16561)
| ~ cC12(iV16562) )
<=> ( ~ cC16(iV16560)
| ~ cC14(iV16560)
| ~ cC18(iV16560)
| ~ cC8(iV16560)
| ~ cC6(iV16561)
| ~ cC12(iV16562) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) )
<=> ~ ( ~ cC16(iV16560)
| ~ cC14(iV16560)
| ~ cC18(iV16560)
| ~ cC8(iV16560)
| ~ cC6(iV16561)
| ~ cC12(iV16562) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) )
<=> ~ ~ ( ~ cC16(iV16560)
| ~ cC14(iV16560)
| ~ cC18(iV16560)
| ~ cC8(iV16560)
| ~ cC6(iV16561)
| ~ cC12(iV16562) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) )
<=> ( ~ cC16(iV16560)
| ~ cC14(iV16560)
| ~ cC18(iV16560)
| ~ cC8(iV16560)
| ~ cC6(iV16561)
| ~ cC12(iV16562) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) )
<=> ~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) )
<=> ~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) )
<=> ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
tff(122,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC18(iV16560)
& cC16(iV16560)
& cowlThing(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cowlThing(iV16561)
& cC6(iV16561)
& cowlThing(iV16562)
& cC12(iV16562) ),
inference(modus_ponens,[status(thm)],[122,119]) ).
tff(124,plain,
~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) ),
inference(modus_ponens,[status(thm)],[123,117]) ).
tff(125,plain,
~ ( cC18(iV16560)
& cC16(iV16560)
& cC14(iV16560)
& cC8(iV16560)
& cC6(iV16561)
& cC12(iV16562) ),
inference(modus_ponens,[status(thm)],[124,116]) ).
tff(126,plain,
( ~ cC16(iV16560)
| ~ cC14(iV16560)
| ~ cC18(iV16560)
| ~ cC8(iV16560)
| ~ cC6(iV16561)
| ~ cC12(iV16562) ),
inference(modus_ponens,[status(thm)],[125,115]) ).
tff(127,plain,
$false,
inference(unit_resolution,[status(thm)],[126,111,109,88,92,51,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS150+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Sep 1 09:59:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------