TSTP Solution File: KRS157+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS157+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 17:45:00 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 91
% Syntax : Number of formulae : 172 ( 38 unt; 21 typ; 0 def)
% Number of atoms : 741 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1029 ( 451 ~; 191 |; 190 &)
% ( 197 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 22 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 111 ( 99 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
tff(cC28_type,type,
cC28: $i > $o ).
tff(iV3102_type,type,
iV3102: $i ).
tff(cC14_type,type,
cC14: $i > $o ).
tff(cC30_type,type,
cC30: $i > $o ).
tff(cC26xcomp_type,type,
cC26xcomp: $i > $o ).
tff(cC16xcomp_type,type,
cC16xcomp: $i > $o ).
tff(cC2xcomp_type,type,
cC2xcomp: $i > $o ).
tff(cC12xcomp_type,type,
cC12xcomp: $i > $o ).
tff(cC216_type,type,
cC216: $i > $o ).
tff(cC46_type,type,
cC46: $i > $o ).
tff(cTEST_type,type,
cTEST: $i > $o ).
tff(cC44_type,type,
cC44: $i > $o ).
tff(cC42xcomp_type,type,
cC42xcomp: $i > $o ).
tff(cC32xcomp_type,type,
cC32xcomp: $i > $o ).
tff(cC64_type,type,
cC64: $i > $o ).
tff(cTOP_type,type,
cTOP: $i > $o ).
tff(cC62xcomp_type,type,
cC62xcomp: $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(
( ( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) )
<=> ( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) )
<=> ! [X: $i] :
( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) )
<=> ( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) )
<=> ! [X: $i] :
( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) )
<=> ! [X: $i] :
( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] :
( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_131) ).
tff(7,plain,
! [X: $i] :
( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cC28(X)
<=> ( cC16xcomp(X)
& cC26xcomp(X) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] :
( cC28(X)
<=> ~ ( ~ cC16xcomp(X)
| ~ cC26xcomp(X) ) )
| ( cC28(iV3102)
<=> ~ ( ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( cC28(iV3102)
<=> ~ ( ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( cC16xcomp(iV3102)
<=> cC16xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
cC16xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_210) ).
tff(15,plain,
cC16xcomp(iV3102),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( cC26xcomp(iV3102)
<=> cC26xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
cC26xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_206) ).
tff(18,plain,
cC26xcomp(iV3102),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ( ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) )
| ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(20,plain,
~ ( ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ),
inference(unit_resolution,[status(thm)],[19,18,15]) ).
tff(21,plain,
( ~ ( cC28(iV3102)
<=> ~ ( ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ) )
| cC28(iV3102)
| ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(22,plain,
( ~ ( cC28(iV3102)
<=> ~ ( ~ cC16xcomp(iV3102)
| ~ cC26xcomp(iV3102) ) )
| cC28(iV3102) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
cC28(iV3102),
inference(unit_resolution,[status(thm)],[22,12]) ).
tff(24,plain,
^ [X: $i] :
refl(
( ( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) )
<=> ( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] :
( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) )
<=> ! [X: $i] :
( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [X: $i] :
rewrite(
( ( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) )
<=> ( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [X: $i] :
( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) )
<=> ! [X: $i] :
( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [X: $i] :
( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) )
<=> ! [X: $i] :
( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [X: $i] :
( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
tff(30,plain,
! [X: $i] :
( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] :
( cC14(X)
<=> ( cC2xcomp(X)
& cC12xcomp(X) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i] :
( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [X: $i] :
( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ~ ! [X: $i] :
( cC14(X)
<=> ~ ( ~ cC12xcomp(X)
| ~ cC2xcomp(X) ) )
| ( cC14(iV3102)
<=> ~ ( ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( cC14(iV3102)
<=> ~ ( ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
( cC12xcomp(iV3102)
<=> cC12xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
cC12xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_215) ).
tff(38,plain,
cC12xcomp(iV3102),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( cC2xcomp(iV3102)
<=> cC2xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
cC2xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_203) ).
tff(41,plain,
cC2xcomp(iV3102),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ( ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) )
| ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
~ ( ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ),
inference(unit_resolution,[status(thm)],[42,41,38]) ).
tff(44,plain,
( ~ ( cC14(iV3102)
<=> ~ ( ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ) )
| cC14(iV3102)
| ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
( ~ ( cC14(iV3102)
<=> ~ ( ~ cC12xcomp(iV3102)
| ~ cC2xcomp(iV3102) ) )
| cC14(iV3102) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
cC14(iV3102),
inference(unit_resolution,[status(thm)],[45,35]) ).
tff(47,plain,
( ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) )
| ~ cC14(iV3102)
| ~ cC28(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ),
inference(unit_resolution,[status(thm)],[47,46,23]) ).
tff(49,plain,
^ [X: $i] :
refl(
( ( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) )
<=> ( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
rewrite(
( ( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) )
<=> ( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [X: $i] :
( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_201) ).
tff(55,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC216(X)
& cC46(X) ) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ~ ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC216(X)
| ~ cC46(X) ) )
| ( cTEST(iV3102)
<=> ~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( cTEST(iV3102)
<=> ~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( cTEST(iV3102)
<=> cTEST(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
cTEST(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_202) ).
tff(63,plain,
cTEST(iV3102),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ ( cTEST(iV3102)
<=> ~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ) )
| ~ cTEST(iV3102)
| ~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
( ~ ( cTEST(iV3102)
<=> ~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ) )
| ~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
~ ( ~ cC216(iV3102)
| ~ cC46(iV3102) ),
inference(unit_resolution,[status(thm)],[65,60]) ).
tff(67,plain,
( ~ cC216(iV3102)
| ~ cC46(iV3102)
| cC216(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
cC216(iV3102),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
^ [X: $i] :
refl(
( ( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) )
<=> ( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X: $i] :
( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) )
<=> ! [X: $i] :
( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
^ [X: $i] :
rewrite(
( ( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) )
<=> ( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X: $i] :
( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) )
<=> ! [X: $i] :
( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i] :
( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) )
<=> ! [X: $i] :
( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [X: $i] :
( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_147) ).
tff(75,plain,
! [X: $i] :
( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] :
( cC44(X)
<=> ( cC42xcomp(X)
& cC32xcomp(X) ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i] :
( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [X: $i] :
( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ~ ! [X: $i] :
( cC44(X)
<=> ~ ( ~ cC32xcomp(X)
| ~ cC42xcomp(X) ) )
| ( cC44(iV3102)
<=> ~ ( ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( cC44(iV3102)
<=> ~ ( ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( cC42xcomp(iV3102)
<=> cC42xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
cC42xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_211) ).
tff(83,plain,
cC42xcomp(iV3102),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( cC32xcomp(iV3102)
<=> cC32xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
cC32xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_207) ).
tff(86,plain,
cC32xcomp(iV3102),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ( ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) )
| ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
~ ( ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ),
inference(unit_resolution,[status(thm)],[87,86,83]) ).
tff(89,plain,
( ~ ( cC44(iV3102)
<=> ~ ( ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ) )
| cC44(iV3102)
| ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
( ~ ( cC44(iV3102)
<=> ~ ( ~ cC32xcomp(iV3102)
| ~ cC42xcomp(iV3102) ) )
| cC44(iV3102) ),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
cC44(iV3102),
inference(unit_resolution,[status(thm)],[90,80]) ).
tff(92,plain,
^ [X: $i] :
refl(
( ( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) )
<=> ( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) )
<=> ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
^ [X: $i] :
rewrite(
( ( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) )
<=> ( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X: $i] :
( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i] :
( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
! [X: $i] :
( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_166) ).
tff(98,plain,
! [X: $i] :
( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i] :
( cC64(X)
<=> ( cC62xcomp(X)
& cTOP(X) ) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62xcomp(X)
| ~ cTOP(X) ) )
| ( cC64(iV3102)
<=> ~ ( ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( cC64(iV3102)
<=> ~ ( ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
( cC62xcomp(iV3102)
<=> cC62xcomp(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
cC62xcomp(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_212) ).
tff(106,plain,
cC62xcomp(iV3102),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( cTOP(iV3102)
<=> cTOP(iV3102) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
cTOP(iV3102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_205) ).
tff(109,plain,
cTOP(iV3102),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( ~ ( ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) )
| ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(111,plain,
~ ( ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ),
inference(unit_resolution,[status(thm)],[110,109,106]) ).
tff(112,plain,
( ~ ( cC64(iV3102)
<=> ~ ( ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ) )
| cC64(iV3102)
| ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(113,plain,
( ~ ( cC64(iV3102)
<=> ~ ( ~ cC62xcomp(iV3102)
| ~ cTOP(iV3102) ) )
| cC64(iV3102) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
cC64(iV3102),
inference(unit_resolution,[status(thm)],[113,103]) ).
tff(115,plain,
( ~ cC216(iV3102)
| ~ cC46(iV3102)
| cC46(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(116,plain,
cC46(iV3102),
inference(unit_resolution,[status(thm)],[115,66]) ).
tff(117,plain,
( ~ ~ ( ~ cC14(iV3102)
| ~ cC44(iV3102)
| ~ cC216(iV3102)
| ~ cC64(iV3102)
| ~ cC46(iV3102)
| ~ cC28(iV3102)
| ~ cC30(iV3102) )
<=> ( ~ cC14(iV3102)
| ~ cC44(iV3102)
| ~ cC216(iV3102)
| ~ cC64(iV3102)
| ~ cC46(iV3102)
| ~ cC28(iV3102)
| ~ cC30(iV3102) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) )
<=> ~ ( ~ cC14(iV3102)
| ~ cC44(iV3102)
| ~ cC216(iV3102)
| ~ cC64(iV3102)
| ~ cC46(iV3102)
| ~ cC28(iV3102)
| ~ cC30(iV3102) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) )
<=> ~ ~ ( ~ cC14(iV3102)
| ~ cC44(iV3102)
| ~ cC216(iV3102)
| ~ cC64(iV3102)
| ~ cC46(iV3102)
| ~ cC28(iV3102)
| ~ cC30(iV3102) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) )
<=> ( ~ cC14(iV3102)
| ~ cC44(iV3102)
| ~ cC216(iV3102)
| ~ cC64(iV3102)
| ~ cC46(iV3102)
| ~ cC28(iV3102)
| ~ cC30(iV3102) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
( ~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) )
<=> ~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) )
<=> ~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) )
<=> ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,axiom,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
tff(127,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cowlThing(iV3102)
& cC30(iV3102) ),
inference(modus_ponens,[status(thm)],[127,124]) ).
tff(129,plain,
~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) ),
inference(modus_ponens,[status(thm)],[128,122]) ).
tff(130,plain,
~ ( cC14(iV3102)
& cC44(iV3102)
& cC216(iV3102)
& cC64(iV3102)
& cC46(iV3102)
& cC28(iV3102)
& cC30(iV3102) ),
inference(modus_ponens,[status(thm)],[129,121]) ).
tff(131,plain,
( ~ cC14(iV3102)
| ~ cC44(iV3102)
| ~ cC216(iV3102)
| ~ cC64(iV3102)
| ~ cC46(iV3102)
| ~ cC28(iV3102)
| ~ cC30(iV3102) ),
inference(modus_ponens,[status(thm)],[130,120]) ).
tff(132,plain,
~ cC30(iV3102),
inference(unit_resolution,[status(thm)],[131,116,46,114,91,23,68]) ).
tff(133,plain,
( ~ ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) )
| cC30(iV3102)
| ~ cC14(iV3102)
| ~ cC28(iV3102) ),
inference(tautology,[status(thm)],]) ).
tff(134,plain,
~ ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ),
inference(unit_resolution,[status(thm)],[133,132,48]) ).
tff(135,plain,
^ [X: $i] :
refl(
( ( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
<=> ( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
<=> ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
^ [X: $i] :
rewrite(
( ( cC30(X)
<=> ( cC28(X)
& cC14(X) ) )
<=> ( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [X: $i] :
( cC30(X)
<=> ( cC28(X)
& cC14(X) ) )
<=> ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [X: $i] :
( cC30(X)
<=> ( cC28(X)
& cC14(X) ) )
<=> ! [X: $i] :
( cC30(X)
<=> ( cC28(X)
& cC14(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,axiom,
! [X: $i] :
( cC30(X)
<=> ( cC28(X)
& cC14(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_132) ).
tff(141,plain,
! [X: $i] :
( cC30(X)
<=> ( cC28(X)
& cC14(X) ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [X: $i] :
( cC30(X)
<=> ( cC28(X)
& cC14(X) ) ),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
( ( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ) )
<=> ( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( cC30(iV3102)
<=> ~ ( ~ cC28(iV3102)
| ~ cC14(iV3102) ) )
<=> ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC28(iV3102)
| ~ cC14(iV3102) ) ) )
<=> ( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC28(iV3102)
| ~ cC14(iV3102) ) ) )
<=> ( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ) ) ),
inference(transitivity,[status(thm)],[147,145]) ).
tff(149,plain,
( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC28(iV3102)
| ~ cC14(iV3102) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
( ~ ! [X: $i] :
( cC30(X)
<=> ~ ( ~ cC28(X)
| ~ cC14(X) ) )
| ( cC30(iV3102)
<=> ~ ( ~ cC14(iV3102)
| ~ cC28(iV3102) ) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
$false,
inference(unit_resolution,[status(thm)],[150,144,134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS157+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 : Thu Sep 1 09:39:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% See solution above
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