TSTP Solution File: KRS151+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS151+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 17:44:59 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 441
% Syntax : Number of formulae : 908 ( 175 unt; 80 typ; 0 def)
% Number of atoms : 4594 ( 0 equ)
% Maximal formula atoms : 108 ( 5 avg)
% Number of connectives : 6249 (2559 ~;1333 |;1125 &)
% (1232 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 76 ( 76 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of predicates : 79 ( 78 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 647 ( 571 !; 0 ?; 647 :)
% Comments :
%------------------------------------------------------------------------------
tff(cC72_type,type,
cC72: $i > $o ).
tff(iV21030_type,type,
iV21030: $i ).
tff(cC18_type,type,
cC18: $i > $o ).
tff(cC74_type,type,
cC74: $i > $o ).
tff(cC66_type,type,
cC66: $i > $o ).
tff(cC68_type,type,
cC68: $i > $o ).
tff(cC44_type,type,
cC44: $i > $o ).
tff(iV21029_type,type,
iV21029: $i ).
tff(cC12_type,type,
cC12: $i > $o ).
tff(cC46_type,type,
cC46: $i > $o ).
tff(cC50_type,type,
cC50: $i > $o ).
tff(cC52_type,type,
cC52: $i > $o ).
tff(cC24_type,type,
cC24: $i > $o ).
tff(iV21027_type,type,
iV21027: $i ).
tff(cC2_type,type,
cC2: $i > $o ).
tff(cC26_type,type,
cC26: $i > $o ).
tff(cC30_type,type,
cC30: $i > $o ).
tff(cC32_type,type,
cC32: $i > $o ).
tff(cC90_type,type,
cC90: $i > $o ).
tff(iV21026_type,type,
iV21026: $i ).
tff(cC86_type,type,
cC86: $i > $o ).
tff(cC88_type,type,
cC88: $i > $o ).
tff(cC84_type,type,
cC84: $i > $o ).
tff(cC82_type,type,
cC82: $i > $o ).
tff(cC64_type,type,
cC64: $i > $o ).
tff(cC80_type,type,
cC80: $i > $o ).
tff(cC62_type,type,
cC62: $i > $o ).
tff(cC60_type,type,
cC60: $i > $o ).
tff(cC58_type,type,
cC58: $i > $o ).
tff(cC42_type,type,
cC42: $i > $o ).
tff(cC40_type,type,
cC40: $i > $o ).
tff(cC38_type,type,
cC38: $i > $o ).
tff(cTOP_type,type,
cTOP: $i > $o ).
tff(cC36_type,type,
cC36: $i > $o ).
tff(cC34_type,type,
cC34: $i > $o ).
tff(cC28_type,type,
cC28: $i > $o ).
tff(cC56_type,type,
cC56: $i > $o ).
tff(cC54_type,type,
cC54: $i > $o ).
tff(cC48_type,type,
cC48: $i > $o ).
tff(cC78_type,type,
cC78: $i > $o ).
tff(cC76_type,type,
cC76: $i > $o ).
tff(cC70_type,type,
cC70: $i > $o ).
tff(cC14_type,type,
cC14: $i > $o ).
tff(cC10_type,type,
cC10: $i > $o ).
tff(cC16_type,type,
cC16: $i > $o ).
tff(cC20_type,type,
cC20: $i > $o ).
tff(cC22_type,type,
cC22: $i > $o ).
tff(cC156_type,type,
cC156: $i > $o ).
tff(cC158_type,type,
cC158: $i > $o ).
tff(cC180_type,type,
cC180: $i > $o ).
tff(cTEST_type,type,
cTEST: $i > $o ).
tff(cC108_type,type,
cC108: $i > $o ).
tff(cC98_type,type,
cC98: $i > $o ).
tff(cC106_type,type,
cC106: $i > $o ).
tff(cC138_type,type,
cC138: $i > $o ).
tff(cC154_type,type,
cC154: $i > $o ).
tff(cC116_type,type,
cC116: $i > $o ).
tff(cC132_type,type,
cC132: $i > $o ).
tff(cC134_type,type,
cC134: $i > $o ).
tff(cC136_type,type,
cC136: $i > $o ).
tff(cC110_type,type,
cC110: $i > $o ).
tff(cC114_type,type,
cC114: $i > $o ).
tff(cC112_type,type,
cC112: $i > $o ).
tff(cC152_type,type,
cC152: $i > $o ).
tff(cC150_type,type,
cC150: $i > $o ).
tff(cC144_type,type,
cC144: $i > $o ).
tff(cC130_type,type,
cC130: $i > $o ).
tff(cC128_type,type,
cC128: $i > $o ).
tff(cC122_type,type,
cC122: $i > $o ).
tff(cC168_type,type,
cC168: $i > $o ).
tff(cC166_type,type,
cC166: $i > $o ).
tff(cC162_type,type,
cC162: $i > $o ).
tff(cC174_type,type,
cC174: $i > $o ).
tff(cC172_type,type,
cC172: $i > $o ).
tff(cC4_type,type,
cC4: $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(
( ( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) )
<=> ( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) )
<=> ! [X: $i] :
( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) )
<=> ( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) )
<=> ! [X: $i] :
( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) )
<=> ! [X: $i] :
( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] :
( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_73) ).
tff(7,plain,
! [X: $i] :
( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cC74(X)
<=> ( ~ cC18(X)
& ~ cC72(X) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] :
( cC74(X)
<=> ~ ( cC18(X)
| cC72(X) ) )
| ( cC74(iV21030)
<=> ~ ( cC18(iV21030)
| cC72(iV21030) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( cC74(iV21030)
<=> ~ ( cC18(iV21030)
| cC72(iV21030) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ cC74(iV21030)
<=> ~ cC74(iV21030) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
~ cC74(iV21030),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_192) ).
tff(15,plain,
~ cC74(iV21030),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( cC74(iV21030)
<=> ~ ( cC18(iV21030)
| cC72(iV21030) ) )
| cC74(iV21030)
| cC18(iV21030)
| cC72(iV21030) ),
inference(tautology,[status(thm)],]) ).
tff(17,plain,
( ~ ( cC74(iV21030)
<=> ~ ( cC18(iV21030)
| cC72(iV21030) ) )
| cC18(iV21030)
| cC72(iV21030) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( cC18(iV21030)
| cC72(iV21030) ),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
( ~ cC18(iV21030)
<=> ~ cC18(iV21030) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
~ cC18(iV21030),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_202) ).
tff(21,plain,
~ cC18(iV21030),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ ( cC18(iV21030)
| cC72(iV21030) )
| cC18(iV21030)
| cC72(iV21030) ),
inference(tautology,[status(thm)],]) ).
tff(23,plain,
( ~ ( cC18(iV21030)
| cC72(iV21030) )
| cC72(iV21030) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
cC72(iV21030),
inference(unit_resolution,[status(thm)],[23,18]) ).
tff(25,plain,
^ [X: $i] :
refl(
( ( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) )
<=> ( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [X: $i] :
( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) )
<=> ! [X: $i] :
( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X: $i] :
rewrite(
( ( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) )
<=> ( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X: $i] :
( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) )
<=> ! [X: $i] :
( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X: $i] :
( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) )
<=> ! [X: $i] :
( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [X: $i] :
( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_70) ).
tff(31,plain,
! [X: $i] :
( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X: $i] :
( cC68(X)
<=> ( ~ cC66(X)
& ~ cC18(X) ) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X: $i] :
( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [X: $i] :
( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ~ ! [X: $i] :
( cC68(X)
<=> ~ ( cC18(X)
| cC66(X) ) )
| ( cC68(iV21030)
<=> ~ ( cC18(iV21030)
| cC66(iV21030) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( cC68(iV21030)
<=> ~ ( cC18(iV21030)
| cC66(iV21030) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ cC68(iV21030)
<=> ~ cC68(iV21030) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
~ cC68(iV21030),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_191) ).
tff(39,plain,
~ cC68(iV21030),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ( cC68(iV21030)
<=> ~ ( cC18(iV21030)
| cC66(iV21030) ) )
| cC68(iV21030)
| cC18(iV21030)
| cC66(iV21030) ),
inference(tautology,[status(thm)],]) ).
tff(41,plain,
( ~ ( cC68(iV21030)
<=> ~ ( cC18(iV21030)
| cC66(iV21030) ) )
| cC18(iV21030)
| cC66(iV21030) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( cC18(iV21030)
| cC66(iV21030) ),
inference(unit_resolution,[status(thm)],[41,36]) ).
tff(43,plain,
( ~ ( cC18(iV21030)
| cC66(iV21030) )
| cC18(iV21030)
| cC66(iV21030) ),
inference(tautology,[status(thm)],]) ).
tff(44,plain,
( ~ ( cC18(iV21030)
| cC66(iV21030) )
| cC66(iV21030) ),
inference(unit_resolution,[status(thm)],[43,21]) ).
tff(45,plain,
cC66(iV21030),
inference(unit_resolution,[status(thm)],[44,42]) ).
tff(46,plain,
^ [X: $i] :
refl(
( ( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) )
<=> ( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X: $i] :
( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) )
<=> ! [X: $i] :
( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
^ [X: $i] :
rewrite(
( ( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) )
<=> ( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i] :
( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) )
<=> ! [X: $i] :
( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] :
( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) )
<=> ! [X: $i] :
( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [X: $i] :
( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
tff(52,plain,
! [X: $i] :
( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] :
( cC46(X)
<=> ( ~ cC12(X)
& ~ cC44(X) ) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] :
( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [X: $i] :
( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ~ ! [X: $i] :
( cC46(X)
<=> ~ ( cC12(X)
| cC44(X) ) )
| ( cC46(iV21029)
<=> ~ ( cC12(iV21029)
| cC44(iV21029) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( cC46(iV21029)
<=> ~ ( cC12(iV21029)
| cC44(iV21029) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ cC46(iV21029)
<=> ~ cC46(iV21029) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
~ cC46(iV21029),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_157) ).
tff(60,plain,
~ cC46(iV21029),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ( cC46(iV21029)
<=> ~ ( cC12(iV21029)
| cC44(iV21029) ) )
| cC46(iV21029)
| cC12(iV21029)
| cC44(iV21029) ),
inference(tautology,[status(thm)],]) ).
tff(62,plain,
( ~ ( cC46(iV21029)
<=> ~ ( cC12(iV21029)
| cC44(iV21029) ) )
| cC12(iV21029)
| cC44(iV21029) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( cC12(iV21029)
| cC44(iV21029) ),
inference(unit_resolution,[status(thm)],[62,57]) ).
tff(64,plain,
( ~ cC12(iV21029)
<=> ~ cC12(iV21029) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
~ cC12(iV21029),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_163) ).
tff(66,plain,
~ cC12(iV21029),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ( cC12(iV21029)
| cC44(iV21029) )
| cC12(iV21029)
| cC44(iV21029) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
( ~ ( cC12(iV21029)
| cC44(iV21029) )
| cC44(iV21029) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
cC44(iV21029),
inference(unit_resolution,[status(thm)],[68,63]) ).
tff(70,plain,
^ [X: $i] :
refl(
( ( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) )
<=> ( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] :
( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) )
<=> ! [X: $i] :
( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [X: $i] :
rewrite(
( ( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) )
<=> ( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] :
( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) )
<=> ! [X: $i] :
( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i] :
( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) )
<=> ! [X: $i] :
( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [X: $i] :
( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).
tff(76,plain,
! [X: $i] :
( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [X: $i] :
( cC52(X)
<=> ( ~ cC12(X)
& ~ cC50(X) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X: $i] :
( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [X: $i] :
( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( ~ ! [X: $i] :
( cC52(X)
<=> ~ ( cC12(X)
| cC50(X) ) )
| ( cC52(iV21029)
<=> ~ ( cC12(iV21029)
| cC50(iV21029) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( cC52(iV21029)
<=> ~ ( cC12(iV21029)
| cC50(iV21029) ) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
( ~ cC52(iV21029)
<=> ~ cC52(iV21029) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
~ cC52(iV21029),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_168) ).
tff(84,plain,
~ cC52(iV21029),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ( cC52(iV21029)
<=> ~ ( cC12(iV21029)
| cC50(iV21029) ) )
| cC52(iV21029)
| cC12(iV21029)
| cC50(iV21029) ),
inference(tautology,[status(thm)],]) ).
tff(86,plain,
( ~ ( cC52(iV21029)
<=> ~ ( cC12(iV21029)
| cC50(iV21029) ) )
| cC12(iV21029)
| cC50(iV21029) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( cC12(iV21029)
| cC50(iV21029) ),
inference(unit_resolution,[status(thm)],[86,81]) ).
tff(88,plain,
( ~ ( cC12(iV21029)
| cC50(iV21029) )
| cC12(iV21029)
| cC50(iV21029) ),
inference(tautology,[status(thm)],]) ).
tff(89,plain,
( ~ ( cC12(iV21029)
| cC50(iV21029) )
| cC50(iV21029) ),
inference(unit_resolution,[status(thm)],[88,66]) ).
tff(90,plain,
cC50(iV21029),
inference(unit_resolution,[status(thm)],[89,87]) ).
tff(91,plain,
^ [X: $i] :
refl(
( ( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
<=> ( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
<=> ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
^ [X: $i] :
rewrite(
( ( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) )
<=> ( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [X: $i] :
( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) )
<=> ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X: $i] :
( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) )
<=> ! [X: $i] :
( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
! [X: $i] :
( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
tff(97,plain,
! [X: $i] :
( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [X: $i] :
( cC26(X)
<=> ( ~ cC24(X)
& ~ cC2(X) ) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ) )
<=> ( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( cC26(iV21027)
<=> ~ ( cC24(iV21027)
| cC2(iV21027) ) )
<=> ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC24(iV21027)
| cC2(iV21027) ) ) )
<=> ( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC24(iV21027)
| cC2(iV21027) ) ) )
<=> ( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,plain,
( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC24(iV21027)
| cC2(iV21027) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [X: $i] :
( cC26(X)
<=> ~ ( cC24(X)
| cC2(X) ) )
| ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) ),
inference(unit_resolution,[status(thm)],[106,100]) ).
tff(108,plain,
( ~ cC26(iV21027)
<=> ~ cC26(iV21027) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
~ cC26(iV21027),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_126) ).
tff(110,plain,
~ cC26(iV21027),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ~ ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) )
| cC26(iV21027)
| cC2(iV21027)
| cC24(iV21027) ),
inference(tautology,[status(thm)],]) ).
tff(112,plain,
( ~ ( cC26(iV21027)
<=> ~ ( cC2(iV21027)
| cC24(iV21027) ) )
| cC2(iV21027)
| cC24(iV21027) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
( cC2(iV21027)
| cC24(iV21027) ),
inference(unit_resolution,[status(thm)],[112,107]) ).
tff(114,plain,
( ~ cC2(iV21027)
<=> ~ cC2(iV21027) ),
inference(rewrite,[status(thm)],]) ).
tff(115,axiom,
~ cC2(iV21027),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_150) ).
tff(116,plain,
~ cC2(iV21027),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( ~ ( cC2(iV21027)
| cC24(iV21027) )
| cC2(iV21027)
| cC24(iV21027) ),
inference(tautology,[status(thm)],]) ).
tff(118,plain,
( ~ ( cC2(iV21027)
| cC24(iV21027) )
| cC24(iV21027) ),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
cC24(iV21027),
inference(unit_resolution,[status(thm)],[118,113]) ).
tff(120,plain,
^ [X: $i] :
refl(
( ( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) )
<=> ( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [X: $i] :
( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) )
<=> ! [X: $i] :
( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [X: $i] :
rewrite(
( ( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) )
<=> ( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [X: $i] :
( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) )
<=> ! [X: $i] :
( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [X: $i] :
( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) )
<=> ! [X: $i] :
( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
! [X: $i] :
( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
tff(126,plain,
! [X: $i] :
( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [X: $i] :
( cC32(X)
<=> ( ~ cC2(X)
& ~ cC30(X) ) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [X: $i] :
( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [X: $i] :
( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) ),
inference(modus_ponens,[status(thm)],[128,121]) ).
tff(130,plain,
( ~ ! [X: $i] :
( cC32(X)
<=> ~ ( cC2(X)
| cC30(X) ) )
| ( cC32(iV21027)
<=> ~ ( cC2(iV21027)
| cC30(iV21027) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( cC32(iV21027)
<=> ~ ( cC2(iV21027)
| cC30(iV21027) ) ),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ cC32(iV21027)
<=> ~ cC32(iV21027) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
~ cC32(iV21027),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_136) ).
tff(134,plain,
~ cC32(iV21027),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ ( cC32(iV21027)
<=> ~ ( cC2(iV21027)
| cC30(iV21027) ) )
| cC32(iV21027)
| cC2(iV21027)
| cC30(iV21027) ),
inference(tautology,[status(thm)],]) ).
tff(136,plain,
( ~ ( cC32(iV21027)
<=> ~ ( cC2(iV21027)
| cC30(iV21027) ) )
| cC2(iV21027)
| cC30(iV21027) ),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
( cC2(iV21027)
| cC30(iV21027) ),
inference(unit_resolution,[status(thm)],[136,131]) ).
tff(138,plain,
( ~ ( cC2(iV21027)
| cC30(iV21027) )
| cC2(iV21027)
| cC30(iV21027) ),
inference(tautology,[status(thm)],]) ).
tff(139,plain,
( ~ ( cC2(iV21027)
| cC30(iV21027) )
| cC30(iV21027) ),
inference(unit_resolution,[status(thm)],[138,116]) ).
tff(140,plain,
cC30(iV21027),
inference(unit_resolution,[status(thm)],[139,137]) ).
tff(141,plain,
^ [X: $i] :
refl(
( ( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) )
<=> ( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [X: $i] :
( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) )
<=> ! [X: $i] :
( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
^ [X: $i] :
rewrite(
( ( cC90(X)
<=> ( cC88(X)
& cC86(X) ) )
<=> ( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [X: $i] :
( cC90(X)
<=> ( cC88(X)
& cC86(X) ) )
<=> ! [X: $i] :
( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [X: $i] :
( cC90(X)
<=> ( cC88(X)
& cC86(X) ) )
<=> ! [X: $i] :
( cC90(X)
<=> ( cC88(X)
& cC86(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,axiom,
! [X: $i] :
( cC90(X)
<=> ( cC88(X)
& cC86(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_82) ).
tff(147,plain,
! [X: $i] :
( cC90(X)
<=> ( cC88(X)
& cC86(X) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [X: $i] :
( cC90(X)
<=> ( cC88(X)
& cC86(X) ) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [X: $i] :
( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [X: $i] :
( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ~ ! [X: $i] :
( cC90(X)
<=> ~ ( ~ cC88(X)
| ~ cC86(X) ) )
| ( cC90(iV21026)
<=> ~ ( ~ cC88(iV21026)
| ~ cC86(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
( cC90(iV21026)
<=> ~ ( ~ cC88(iV21026)
| ~ cC86(iV21026) ) ),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
^ [X: $i] :
refl(
( ( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) )
<=> ( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(154,plain,
( ! [X: $i] :
( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) )
<=> ! [X: $i] :
( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
^ [X: $i] :
rewrite(
( ( cC86(X)
<=> ( cC82(X)
& cC84(X) ) )
<=> ( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [X: $i] :
( cC86(X)
<=> ( cC82(X)
& cC84(X) ) )
<=> ! [X: $i] :
( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [X: $i] :
( cC86(X)
<=> ( cC82(X)
& cC84(X) ) )
<=> ! [X: $i] :
( cC86(X)
<=> ( cC82(X)
& cC84(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,axiom,
! [X: $i] :
( cC86(X)
<=> ( cC82(X)
& cC84(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_80) ).
tff(159,plain,
! [X: $i] :
( cC86(X)
<=> ( cC82(X)
& cC84(X) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [X: $i] :
( cC86(X)
<=> ( cC82(X)
& cC84(X) ) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [X: $i] :
( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [X: $i] :
( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) ),
inference(modus_ponens,[status(thm)],[161,154]) ).
tff(163,plain,
( ~ ! [X: $i] :
( cC86(X)
<=> ~ ( ~ cC82(X)
| ~ cC84(X) ) )
| ( cC86(iV21026)
<=> ~ ( ~ cC82(iV21026)
| ~ cC84(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( cC86(iV21026)
<=> ~ ( ~ cC82(iV21026)
| ~ cC84(iV21026) ) ),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,plain,
^ [X: $i] :
refl(
( ( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) )
<=> ( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(166,plain,
( ! [X: $i] :
( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) )
<=> ! [X: $i] :
( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,plain,
^ [X: $i] :
rewrite(
( ( cC82(X)
<=> ( cC80(X)
& cC64(X) ) )
<=> ( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(168,plain,
( ! [X: $i] :
( cC82(X)
<=> ( cC80(X)
& cC64(X) ) )
<=> ! [X: $i] :
( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) ) ),
inference(quant_intro,[status(thm)],[167]) ).
tff(169,plain,
( ! [X: $i] :
( cC82(X)
<=> ( cC80(X)
& cC64(X) ) )
<=> ! [X: $i] :
( cC82(X)
<=> ( cC80(X)
& cC64(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,axiom,
! [X: $i] :
( cC82(X)
<=> ( cC80(X)
& cC64(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_78) ).
tff(171,plain,
! [X: $i] :
( cC82(X)
<=> ( cC80(X)
& cC64(X) ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
! [X: $i] :
( cC82(X)
<=> ( cC80(X)
& cC64(X) ) ),
inference(skolemize,[status(sab)],[171]) ).
tff(173,plain,
! [X: $i] :
( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
! [X: $i] :
( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) ),
inference(modus_ponens,[status(thm)],[173,166]) ).
tff(175,plain,
( ~ ! [X: $i] :
( cC82(X)
<=> ~ ( ~ cC80(X)
| ~ cC64(X) ) )
| ( cC82(iV21026)
<=> ~ ( ~ cC80(iV21026)
| ~ cC64(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
( cC82(iV21026)
<=> ~ ( ~ cC80(iV21026)
| ~ cC64(iV21026) ) ),
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
^ [X: $i] :
refl(
( ( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
<=> ( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(178,plain,
( ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
<=> ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,plain,
^ [X: $i] :
rewrite(
( ( cC64(X)
<=> ( cC62(X)
& cC60(X) ) )
<=> ( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(180,plain,
( ! [X: $i] :
( cC64(X)
<=> ( cC62(X)
& cC60(X) ) )
<=> ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
( ! [X: $i] :
( cC64(X)
<=> ( cC62(X)
& cC60(X) ) )
<=> ! [X: $i] :
( cC64(X)
<=> ( cC62(X)
& cC60(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,axiom,
! [X: $i] :
( cC64(X)
<=> ( cC62(X)
& cC60(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_68) ).
tff(183,plain,
! [X: $i] :
( cC64(X)
<=> ( cC62(X)
& cC60(X) ) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
! [X: $i] :
( cC64(X)
<=> ( cC62(X)
& cC60(X) ) ),
inference(skolemize,[status(sab)],[183]) ).
tff(185,plain,
! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) ),
inference(modus_ponens,[status(thm)],[184,180]) ).
tff(186,plain,
! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) ),
inference(modus_ponens,[status(thm)],[185,178]) ).
tff(187,plain,
( ( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ( cC64(iV21026)
<=> ~ ( ~ cC62(iV21026)
| ~ cC60(iV21026) ) )
<=> ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC62(iV21026)
| ~ cC60(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC62(iV21026)
| ~ cC60(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC62(iV21026)
| ~ cC60(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
( ~ ! [X: $i] :
( cC64(X)
<=> ~ ( ~ cC62(X)
| ~ cC60(X) ) )
| ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) ),
inference(unit_resolution,[status(thm)],[192,186]) ).
tff(194,plain,
^ [X: $i] :
refl(
( ( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
<=> ( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(195,plain,
( ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
<=> ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
^ [X: $i] :
rewrite(
( ( cC60(X)
<=> ( cC58(X)
& cC42(X) ) )
<=> ( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(197,plain,
( ! [X: $i] :
( cC60(X)
<=> ( cC58(X)
& cC42(X) ) )
<=> ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ! [X: $i] :
( cC60(X)
<=> ( cC58(X)
& cC42(X) ) )
<=> ! [X: $i] :
( cC60(X)
<=> ( cC58(X)
& cC42(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(199,axiom,
! [X: $i] :
( cC60(X)
<=> ( cC58(X)
& cC42(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_66) ).
tff(200,plain,
! [X: $i] :
( cC60(X)
<=> ( cC58(X)
& cC42(X) ) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [X: $i] :
( cC60(X)
<=> ( cC58(X)
& cC42(X) ) ),
inference(skolemize,[status(sab)],[200]) ).
tff(202,plain,
! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) ),
inference(modus_ponens,[status(thm)],[201,197]) ).
tff(203,plain,
! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) ),
inference(modus_ponens,[status(thm)],[202,195]) ).
tff(204,plain,
( ( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(205,plain,
( ( cC60(iV21026)
<=> ~ ( ~ cC58(iV21026)
| ~ cC42(iV21026) ) )
<=> ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC58(iV21026)
| ~ cC42(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC58(iV21026)
| ~ cC42(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[206,204]) ).
tff(208,plain,
( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC58(iV21026)
| ~ cC42(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
( ~ ! [X: $i] :
( cC60(X)
<=> ~ ( ~ cC58(X)
| ~ cC42(X) ) )
| ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) ),
inference(unit_resolution,[status(thm)],[209,203]) ).
tff(211,plain,
^ [X: $i] :
refl(
( ( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
<=> ( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(212,plain,
( ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
<=> ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,plain,
^ [X: $i] :
rewrite(
( ( cC42(X)
<=> ( cC40(X)
& cC38(X) ) )
<=> ( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(214,plain,
( ! [X: $i] :
( cC42(X)
<=> ( cC40(X)
& cC38(X) ) )
<=> ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,plain,
( ! [X: $i] :
( cC42(X)
<=> ( cC40(X)
& cC38(X) ) )
<=> ! [X: $i] :
( cC42(X)
<=> ( cC40(X)
& cC38(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(216,axiom,
! [X: $i] :
( cC42(X)
<=> ( cC40(X)
& cC38(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_57) ).
tff(217,plain,
! [X: $i] :
( cC42(X)
<=> ( cC40(X)
& cC38(X) ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [X: $i] :
( cC42(X)
<=> ( cC40(X)
& cC38(X) ) ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) ),
inference(modus_ponens,[status(thm)],[218,214]) ).
tff(220,plain,
! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) ),
inference(modus_ponens,[status(thm)],[219,212]) ).
tff(221,plain,
( ( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,plain,
( ( cC42(iV21026)
<=> ~ ( ~ cC40(iV21026)
| ~ cC38(iV21026) ) )
<=> ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
( ( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC40(iV21026)
| ~ cC38(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( ( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC40(iV21026)
| ~ cC38(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[223,221]) ).
tff(225,plain,
( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC40(iV21026)
| ~ cC38(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(226,plain,
( ~ ! [X: $i] :
( cC42(X)
<=> ~ ( ~ cC40(X)
| ~ cC38(X) ) )
| ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) ),
inference(unit_resolution,[status(thm)],[226,220]) ).
tff(228,plain,
^ [X: $i] :
refl(
( ( cC40(X)
<=> cTOP(X) )
<=> ( cC40(X)
<=> cTOP(X) ) )),
inference(bind,[status(th)],]) ).
tff(229,plain,
( ! [X: $i] :
( cC40(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC40(X)
<=> cTOP(X) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
( ! [X: $i] :
( cC40(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC40(X)
<=> cTOP(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(231,axiom,
! [X: $i] :
( cC40(X)
<=> cTOP(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
tff(232,plain,
! [X: $i] :
( cC40(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
! [X: $i] :
( cC40(X)
<=> cTOP(X) ),
inference(skolemize,[status(sab)],[232]) ).
tff(234,plain,
! [X: $i] :
( cC40(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[233,229]) ).
tff(235,plain,
( ~ ! [X: $i] :
( cC40(X)
<=> cTOP(X) )
| ( cC40(iV21026)
<=> cTOP(iV21026) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
( cC40(iV21026)
<=> cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[235,234]) ).
tff(237,plain,
( cTOP(iV21026)
<=> cTOP(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(238,axiom,
cTOP(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_88) ).
tff(239,plain,
cTOP(iV21026),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
( ~ ( cC40(iV21026)
<=> cTOP(iV21026) )
| cC40(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(241,plain,
( ~ ( cC40(iV21026)
<=> cTOP(iV21026) )
| cC40(iV21026) ),
inference(unit_resolution,[status(thm)],[240,239]) ).
tff(242,plain,
cC40(iV21026),
inference(unit_resolution,[status(thm)],[241,236]) ).
tff(243,plain,
^ [X: $i] :
refl(
( ( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) )
<=> ( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(244,plain,
( ! [X: $i] :
( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) )
<=> ! [X: $i] :
( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,plain,
^ [X: $i] :
rewrite(
( ( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) )
<=> ( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(246,plain,
( ! [X: $i] :
( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[245]) ).
tff(247,plain,
( ! [X: $i] :
( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(248,axiom,
! [X: $i] :
( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_54) ).
tff(249,plain,
! [X: $i] :
( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
! [X: $i] :
( cC38(X)
<=> ( cC36(X)
& cTOP(X) ) ),
inference(skolemize,[status(sab)],[249]) ).
tff(251,plain,
! [X: $i] :
( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[250,246]) ).
tff(252,plain,
! [X: $i] :
( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[251,244]) ).
tff(253,plain,
( ~ ! [X: $i] :
( cC38(X)
<=> ~ ( ~ cC36(X)
| ~ cTOP(X) ) )
| ( cC38(iV21026)
<=> ~ ( ~ cC36(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
( cC38(iV21026)
<=> ~ ( ~ cC36(iV21026)
| ~ cTOP(iV21026) ) ),
inference(unit_resolution,[status(thm)],[253,252]) ).
tff(255,plain,
^ [X: $i] :
refl(
( ( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) )
<=> ( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(256,plain,
( ! [X: $i] :
( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) )
<=> ! [X: $i] :
( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) ) ),
inference(quant_intro,[status(thm)],[255]) ).
tff(257,plain,
^ [X: $i] :
rewrite(
( ( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) )
<=> ( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(258,plain,
( ! [X: $i] :
( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) )
<=> ! [X: $i] :
( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,plain,
( ! [X: $i] :
( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) )
<=> ! [X: $i] :
( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(260,axiom,
! [X: $i] :
( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
tff(261,plain,
! [X: $i] :
( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) ),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
! [X: $i] :
( cC36(X)
<=> ( ~ cC28(X)
& ~ cC34(X) ) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [X: $i] :
( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) ),
inference(modus_ponens,[status(thm)],[262,258]) ).
tff(264,plain,
! [X: $i] :
( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) ),
inference(modus_ponens,[status(thm)],[263,256]) ).
tff(265,plain,
( ~ ! [X: $i] :
( cC36(X)
<=> ~ ( cC28(X)
| cC34(X) ) )
| ( cC36(iV21026)
<=> ~ ( cC28(iV21026)
| cC34(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
( cC36(iV21026)
<=> ~ ( cC28(iV21026)
| cC34(iV21026) ) ),
inference(unit_resolution,[status(thm)],[265,264]) ).
tff(267,plain,
( ~ cC28(iV21026)
<=> ~ cC28(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(268,axiom,
~ cC28(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_96) ).
tff(269,plain,
~ cC28(iV21026),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
( ~ cC34(iV21026)
<=> ~ cC34(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(271,axiom,
~ cC34(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_95) ).
tff(272,plain,
~ cC34(iV21026),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
( ~ ( cC28(iV21026)
| cC34(iV21026) )
| cC28(iV21026)
| cC34(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(274,plain,
~ ( cC28(iV21026)
| cC34(iV21026) ),
inference(unit_resolution,[status(thm)],[273,272,269]) ).
tff(275,plain,
( ~ ( cC36(iV21026)
<=> ~ ( cC28(iV21026)
| cC34(iV21026) ) )
| cC36(iV21026)
| cC28(iV21026)
| cC34(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(276,plain,
( ~ ( cC36(iV21026)
<=> ~ ( cC28(iV21026)
| cC34(iV21026) ) )
| cC36(iV21026) ),
inference(unit_resolution,[status(thm)],[275,274]) ).
tff(277,plain,
cC36(iV21026),
inference(unit_resolution,[status(thm)],[276,266]) ).
tff(278,plain,
( ~ ( ~ cC36(iV21026)
| ~ cTOP(iV21026) )
| ~ cC36(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(279,plain,
( ~ ( ~ cC36(iV21026)
| ~ cTOP(iV21026) )
| ~ cC36(iV21026) ),
inference(unit_resolution,[status(thm)],[278,239]) ).
tff(280,plain,
~ ( ~ cC36(iV21026)
| ~ cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[279,277]) ).
tff(281,plain,
( ~ ( cC38(iV21026)
<=> ~ ( ~ cC36(iV21026)
| ~ cTOP(iV21026) ) )
| cC38(iV21026)
| ~ cC36(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(282,plain,
cC38(iV21026),
inference(unit_resolution,[status(thm)],[281,280,254]) ).
tff(283,plain,
( ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) )
| ~ cC38(iV21026)
| ~ cC40(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(284,plain,
~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ),
inference(unit_resolution,[status(thm)],[283,282,242]) ).
tff(285,plain,
( ~ ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) )
| cC42(iV21026)
| ~ cC38(iV21026)
| ~ cC40(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(286,plain,
( ~ ( cC42(iV21026)
<=> ~ ( ~ cC38(iV21026)
| ~ cC40(iV21026) ) )
| cC42(iV21026) ),
inference(unit_resolution,[status(thm)],[285,284]) ).
tff(287,plain,
cC42(iV21026),
inference(unit_resolution,[status(thm)],[286,227]) ).
tff(288,plain,
^ [X: $i] :
refl(
( ( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) )
<=> ( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(289,plain,
( ! [X: $i] :
( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) )
<=> ! [X: $i] :
( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[288]) ).
tff(290,plain,
^ [X: $i] :
rewrite(
( ( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) )
<=> ( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(291,plain,
( ! [X: $i] :
( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[290]) ).
tff(292,plain,
( ! [X: $i] :
( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(293,axiom,
! [X: $i] :
( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
tff(294,plain,
! [X: $i] :
( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[293,292]) ).
tff(295,plain,
! [X: $i] :
( cC58(X)
<=> ( cC56(X)
& cTOP(X) ) ),
inference(skolemize,[status(sab)],[294]) ).
tff(296,plain,
! [X: $i] :
( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[295,291]) ).
tff(297,plain,
! [X: $i] :
( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[296,289]) ).
tff(298,plain,
( ~ ! [X: $i] :
( cC58(X)
<=> ~ ( ~ cC56(X)
| ~ cTOP(X) ) )
| ( cC58(iV21026)
<=> ~ ( ~ cC56(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(299,plain,
( cC58(iV21026)
<=> ~ ( ~ cC56(iV21026)
| ~ cTOP(iV21026) ) ),
inference(unit_resolution,[status(thm)],[298,297]) ).
tff(300,plain,
^ [X: $i] :
refl(
( ( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) )
<=> ( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(301,plain,
( ! [X: $i] :
( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) )
<=> ! [X: $i] :
( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) ) ),
inference(quant_intro,[status(thm)],[300]) ).
tff(302,plain,
^ [X: $i] :
rewrite(
( ( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) )
<=> ( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(303,plain,
( ! [X: $i] :
( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) )
<=> ! [X: $i] :
( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) ) ),
inference(quant_intro,[status(thm)],[302]) ).
tff(304,plain,
( ! [X: $i] :
( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) )
<=> ! [X: $i] :
( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(305,axiom,
! [X: $i] :
( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_64) ).
tff(306,plain,
! [X: $i] :
( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) ),
inference(modus_ponens,[status(thm)],[305,304]) ).
tff(307,plain,
! [X: $i] :
( cC56(X)
<=> ( ~ cC48(X)
& ~ cC54(X) ) ),
inference(skolemize,[status(sab)],[306]) ).
tff(308,plain,
! [X: $i] :
( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) ),
inference(modus_ponens,[status(thm)],[307,303]) ).
tff(309,plain,
! [X: $i] :
( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) ),
inference(modus_ponens,[status(thm)],[308,301]) ).
tff(310,plain,
( ~ ! [X: $i] :
( cC56(X)
<=> ~ ( cC48(X)
| cC54(X) ) )
| ( cC56(iV21026)
<=> ~ ( cC48(iV21026)
| cC54(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(311,plain,
( cC56(iV21026)
<=> ~ ( cC48(iV21026)
| cC54(iV21026) ) ),
inference(unit_resolution,[status(thm)],[310,309]) ).
tff(312,plain,
( ~ cC48(iV21026)
<=> ~ cC48(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(313,axiom,
~ cC48(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_112) ).
tff(314,plain,
~ cC48(iV21026),
inference(modus_ponens,[status(thm)],[313,312]) ).
tff(315,plain,
( ~ cC54(iV21026)
<=> ~ cC54(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(316,axiom,
~ cC54(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_109) ).
tff(317,plain,
~ cC54(iV21026),
inference(modus_ponens,[status(thm)],[316,315]) ).
tff(318,plain,
( ~ ( cC48(iV21026)
| cC54(iV21026) )
| cC48(iV21026)
| cC54(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(319,plain,
~ ( cC48(iV21026)
| cC54(iV21026) ),
inference(unit_resolution,[status(thm)],[318,317,314]) ).
tff(320,plain,
( ~ ( cC56(iV21026)
<=> ~ ( cC48(iV21026)
| cC54(iV21026) ) )
| cC56(iV21026)
| cC48(iV21026)
| cC54(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(321,plain,
( ~ ( cC56(iV21026)
<=> ~ ( cC48(iV21026)
| cC54(iV21026) ) )
| cC56(iV21026) ),
inference(unit_resolution,[status(thm)],[320,319]) ).
tff(322,plain,
cC56(iV21026),
inference(unit_resolution,[status(thm)],[321,311]) ).
tff(323,plain,
( ~ ( ~ cC56(iV21026)
| ~ cTOP(iV21026) )
| ~ cC56(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(324,plain,
( ~ ( ~ cC56(iV21026)
| ~ cTOP(iV21026) )
| ~ cC56(iV21026) ),
inference(unit_resolution,[status(thm)],[323,239]) ).
tff(325,plain,
~ ( ~ cC56(iV21026)
| ~ cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[324,322]) ).
tff(326,plain,
( ~ ( cC58(iV21026)
<=> ~ ( ~ cC56(iV21026)
| ~ cTOP(iV21026) ) )
| cC58(iV21026)
| ~ cC56(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(327,plain,
cC58(iV21026),
inference(unit_resolution,[status(thm)],[326,325,299]) ).
tff(328,plain,
( ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) )
| ~ cC42(iV21026)
| ~ cC58(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(329,plain,
( ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) )
| ~ cC42(iV21026) ),
inference(unit_resolution,[status(thm)],[328,327]) ).
tff(330,plain,
~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ),
inference(unit_resolution,[status(thm)],[329,287]) ).
tff(331,plain,
( ~ ( cC60(iV21026)
<=> ~ ( ~ cC42(iV21026)
| ~ cC58(iV21026) ) )
| cC60(iV21026)
| ~ cC42(iV21026)
| ~ cC58(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(332,plain,
cC60(iV21026),
inference(unit_resolution,[status(thm)],[331,330,210]) ).
tff(333,plain,
^ [X: $i] :
refl(
( ( cC62(X)
<=> cTOP(X) )
<=> ( cC62(X)
<=> cTOP(X) ) )),
inference(bind,[status(th)],]) ).
tff(334,plain,
( ! [X: $i] :
( cC62(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC62(X)
<=> cTOP(X) ) ),
inference(quant_intro,[status(thm)],[333]) ).
tff(335,plain,
( ! [X: $i] :
( cC62(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC62(X)
<=> cTOP(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(336,axiom,
! [X: $i] :
( cC62(X)
<=> cTOP(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_67) ).
tff(337,plain,
! [X: $i] :
( cC62(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[336,335]) ).
tff(338,plain,
! [X: $i] :
( cC62(X)
<=> cTOP(X) ),
inference(skolemize,[status(sab)],[337]) ).
tff(339,plain,
! [X: $i] :
( cC62(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[338,334]) ).
tff(340,plain,
( ~ ! [X: $i] :
( cC62(X)
<=> cTOP(X) )
| ( cC62(iV21026)
<=> cTOP(iV21026) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(341,plain,
( cC62(iV21026)
<=> cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[340,339]) ).
tff(342,plain,
( ~ ( cC62(iV21026)
<=> cTOP(iV21026) )
| cC62(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(343,plain,
( ~ ( cC62(iV21026)
<=> cTOP(iV21026) )
| cC62(iV21026) ),
inference(unit_resolution,[status(thm)],[342,239]) ).
tff(344,plain,
cC62(iV21026),
inference(unit_resolution,[status(thm)],[343,341]) ).
tff(345,plain,
( ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) )
| ~ cC60(iV21026)
| ~ cC62(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(346,plain,
( ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) )
| ~ cC60(iV21026) ),
inference(unit_resolution,[status(thm)],[345,344]) ).
tff(347,plain,
~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ),
inference(unit_resolution,[status(thm)],[346,332]) ).
tff(348,plain,
( ~ ( cC64(iV21026)
<=> ~ ( ~ cC60(iV21026)
| ~ cC62(iV21026) ) )
| cC64(iV21026)
| ~ cC60(iV21026)
| ~ cC62(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(349,plain,
cC64(iV21026),
inference(unit_resolution,[status(thm)],[348,347,193]) ).
tff(350,plain,
^ [X: $i] :
refl(
( ( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
<=> ( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(351,plain,
( ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
<=> ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) ) ),
inference(quant_intro,[status(thm)],[350]) ).
tff(352,plain,
^ [X: $i] :
rewrite(
( ( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) )
<=> ( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(353,plain,
( ! [X: $i] :
( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) )
<=> ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) ) ),
inference(quant_intro,[status(thm)],[352]) ).
tff(354,plain,
( ! [X: $i] :
( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) )
<=> ! [X: $i] :
( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(355,axiom,
! [X: $i] :
( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_77) ).
tff(356,plain,
! [X: $i] :
( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) ),
inference(modus_ponens,[status(thm)],[355,354]) ).
tff(357,plain,
! [X: $i] :
( cC80(X)
<=> ( cTOP(X)
& cC78(X) ) ),
inference(skolemize,[status(sab)],[356]) ).
tff(358,plain,
! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) ),
inference(modus_ponens,[status(thm)],[357,353]) ).
tff(359,plain,
! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) ),
inference(modus_ponens,[status(thm)],[358,351]) ).
tff(360,plain,
( ( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(361,plain,
( ( cC80(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC78(iV21026) ) )
<=> ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(362,plain,
( ( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC78(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
( ( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC78(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[362,360]) ).
tff(364,plain,
( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC78(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(365,plain,
( ~ ! [X: $i] :
( cC80(X)
<=> ~ ( ~ cTOP(X)
| ~ cC78(X) ) )
| ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[364,363]) ).
tff(366,plain,
( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) ),
inference(unit_resolution,[status(thm)],[365,359]) ).
tff(367,plain,
^ [X: $i] :
refl(
( ( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) )
<=> ( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(368,plain,
( ! [X: $i] :
( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) )
<=> ! [X: $i] :
( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) ) ),
inference(quant_intro,[status(thm)],[367]) ).
tff(369,plain,
^ [X: $i] :
rewrite(
( ( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) )
<=> ( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(370,plain,
( ! [X: $i] :
( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) )
<=> ! [X: $i] :
( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) ) ),
inference(quant_intro,[status(thm)],[369]) ).
tff(371,plain,
( ! [X: $i] :
( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) )
<=> ! [X: $i] :
( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(372,axiom,
! [X: $i] :
( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_75) ).
tff(373,plain,
! [X: $i] :
( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) ),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
! [X: $i] :
( cC78(X)
<=> ( ~ cC70(X)
& ~ cC76(X) ) ),
inference(skolemize,[status(sab)],[373]) ).
tff(375,plain,
! [X: $i] :
( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) ),
inference(modus_ponens,[status(thm)],[374,370]) ).
tff(376,plain,
! [X: $i] :
( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) ),
inference(modus_ponens,[status(thm)],[375,368]) ).
tff(377,plain,
( ~ ! [X: $i] :
( cC78(X)
<=> ~ ( cC70(X)
| cC76(X) ) )
| ( cC78(iV21026)
<=> ~ ( cC70(iV21026)
| cC76(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(378,plain,
( cC78(iV21026)
<=> ~ ( cC70(iV21026)
| cC76(iV21026) ) ),
inference(unit_resolution,[status(thm)],[377,376]) ).
tff(379,plain,
( ~ cC76(iV21026)
<=> ~ cC76(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(380,axiom,
~ cC76(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_113) ).
tff(381,plain,
~ cC76(iV21026),
inference(modus_ponens,[status(thm)],[380,379]) ).
tff(382,plain,
( ~ cC70(iV21026)
<=> ~ cC70(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(383,axiom,
~ cC70(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_98) ).
tff(384,plain,
~ cC70(iV21026),
inference(modus_ponens,[status(thm)],[383,382]) ).
tff(385,plain,
( ~ ( cC70(iV21026)
| cC76(iV21026) )
| cC70(iV21026)
| cC76(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(386,plain,
~ ( cC70(iV21026)
| cC76(iV21026) ),
inference(unit_resolution,[status(thm)],[385,384,381]) ).
tff(387,plain,
( ~ ( cC78(iV21026)
<=> ~ ( cC70(iV21026)
| cC76(iV21026) ) )
| cC78(iV21026)
| cC70(iV21026)
| cC76(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(388,plain,
( ~ ( cC78(iV21026)
<=> ~ ( cC70(iV21026)
| cC76(iV21026) ) )
| cC78(iV21026) ),
inference(unit_resolution,[status(thm)],[387,386]) ).
tff(389,plain,
cC78(iV21026),
inference(unit_resolution,[status(thm)],[388,378]) ).
tff(390,plain,
( ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) )
| ~ cC78(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(391,plain,
( ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) )
| ~ cC78(iV21026) ),
inference(unit_resolution,[status(thm)],[390,239]) ).
tff(392,plain,
~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[391,389]) ).
tff(393,plain,
( ~ ( cC80(iV21026)
<=> ~ ( ~ cC78(iV21026)
| ~ cTOP(iV21026) ) )
| cC80(iV21026)
| ~ cC78(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(394,plain,
cC80(iV21026),
inference(unit_resolution,[status(thm)],[393,392,366]) ).
tff(395,plain,
( ~ ( ~ cC80(iV21026)
| ~ cC64(iV21026) )
| ~ cC80(iV21026)
| ~ cC64(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(396,plain,
( ~ ( ~ cC80(iV21026)
| ~ cC64(iV21026) )
| ~ cC64(iV21026) ),
inference(unit_resolution,[status(thm)],[395,394]) ).
tff(397,plain,
~ ( ~ cC80(iV21026)
| ~ cC64(iV21026) ),
inference(unit_resolution,[status(thm)],[396,349]) ).
tff(398,plain,
( ~ ( cC82(iV21026)
<=> ~ ( ~ cC80(iV21026)
| ~ cC64(iV21026) ) )
| cC82(iV21026)
| ~ cC80(iV21026)
| ~ cC64(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(399,plain,
cC82(iV21026),
inference(unit_resolution,[status(thm)],[398,397,176]) ).
tff(400,plain,
^ [X: $i] :
refl(
( ( cC84(X)
<=> cTOP(X) )
<=> ( cC84(X)
<=> cTOP(X) ) )),
inference(bind,[status(th)],]) ).
tff(401,plain,
( ! [X: $i] :
( cC84(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC84(X)
<=> cTOP(X) ) ),
inference(quant_intro,[status(thm)],[400]) ).
tff(402,plain,
( ! [X: $i] :
( cC84(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC84(X)
<=> cTOP(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(403,axiom,
! [X: $i] :
( cC84(X)
<=> cTOP(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_79) ).
tff(404,plain,
! [X: $i] :
( cC84(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[403,402]) ).
tff(405,plain,
! [X: $i] :
( cC84(X)
<=> cTOP(X) ),
inference(skolemize,[status(sab)],[404]) ).
tff(406,plain,
! [X: $i] :
( cC84(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[405,401]) ).
tff(407,plain,
( ~ ! [X: $i] :
( cC84(X)
<=> cTOP(X) )
| ( cC84(iV21026)
<=> cTOP(iV21026) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
( cC84(iV21026)
<=> cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[407,406]) ).
tff(409,plain,
( ~ ( cC84(iV21026)
<=> cTOP(iV21026) )
| cC84(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(410,plain,
( ~ ( cC84(iV21026)
<=> cTOP(iV21026) )
| cC84(iV21026) ),
inference(unit_resolution,[status(thm)],[409,239]) ).
tff(411,plain,
cC84(iV21026),
inference(unit_resolution,[status(thm)],[410,408]) ).
tff(412,plain,
( ~ ( ~ cC82(iV21026)
| ~ cC84(iV21026) )
| ~ cC82(iV21026)
| ~ cC84(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(413,plain,
( ~ ( ~ cC82(iV21026)
| ~ cC84(iV21026) )
| ~ cC82(iV21026) ),
inference(unit_resolution,[status(thm)],[412,411]) ).
tff(414,plain,
~ ( ~ cC82(iV21026)
| ~ cC84(iV21026) ),
inference(unit_resolution,[status(thm)],[413,399]) ).
tff(415,plain,
( ~ ( cC86(iV21026)
<=> ~ ( ~ cC82(iV21026)
| ~ cC84(iV21026) ) )
| cC86(iV21026)
| ~ cC82(iV21026)
| ~ cC84(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(416,plain,
cC86(iV21026),
inference(unit_resolution,[status(thm)],[415,414,164]) ).
tff(417,plain,
^ [X: $i] :
refl(
( ( cC88(X)
<=> cTOP(X) )
<=> ( cC88(X)
<=> cTOP(X) ) )),
inference(bind,[status(th)],]) ).
tff(418,plain,
( ! [X: $i] :
( cC88(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC88(X)
<=> cTOP(X) ) ),
inference(quant_intro,[status(thm)],[417]) ).
tff(419,plain,
( ! [X: $i] :
( cC88(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC88(X)
<=> cTOP(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(420,axiom,
! [X: $i] :
( cC88(X)
<=> cTOP(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_81) ).
tff(421,plain,
! [X: $i] :
( cC88(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[420,419]) ).
tff(422,plain,
! [X: $i] :
( cC88(X)
<=> cTOP(X) ),
inference(skolemize,[status(sab)],[421]) ).
tff(423,plain,
! [X: $i] :
( cC88(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[422,418]) ).
tff(424,plain,
( ~ ! [X: $i] :
( cC88(X)
<=> cTOP(X) )
| ( cC88(iV21026)
<=> cTOP(iV21026) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(425,plain,
( cC88(iV21026)
<=> cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[424,423]) ).
tff(426,plain,
( ~ ( cC88(iV21026)
<=> cTOP(iV21026) )
| cC88(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(427,plain,
( ~ ( cC88(iV21026)
<=> cTOP(iV21026) )
| cC88(iV21026) ),
inference(unit_resolution,[status(thm)],[426,239]) ).
tff(428,plain,
cC88(iV21026),
inference(unit_resolution,[status(thm)],[427,425]) ).
tff(429,plain,
( ~ ( ~ cC88(iV21026)
| ~ cC86(iV21026) )
| ~ cC88(iV21026)
| ~ cC86(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(430,plain,
( ~ ( ~ cC88(iV21026)
| ~ cC86(iV21026) )
| ~ cC86(iV21026) ),
inference(unit_resolution,[status(thm)],[429,428]) ).
tff(431,plain,
~ ( ~ cC88(iV21026)
| ~ cC86(iV21026) ),
inference(unit_resolution,[status(thm)],[430,416]) ).
tff(432,plain,
( ~ ( cC90(iV21026)
<=> ~ ( ~ cC88(iV21026)
| ~ cC86(iV21026) ) )
| cC90(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(433,plain,
cC90(iV21026),
inference(unit_resolution,[status(thm)],[432,431,152]) ).
tff(434,plain,
^ [X: $i] :
refl(
( ( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
<=> ( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(435,plain,
( ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
<=> ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) ) ),
inference(quant_intro,[status(thm)],[434]) ).
tff(436,plain,
^ [X: $i] :
rewrite(
( ( cC16(X)
<=> ( cC14(X)
& cC10(X) ) )
<=> ( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(437,plain,
( ! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC10(X) ) )
<=> ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) ) ),
inference(quant_intro,[status(thm)],[436]) ).
tff(438,plain,
( ! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC10(X) ) )
<=> ! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC10(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(439,axiom,
! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC10(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
tff(440,plain,
! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC10(X) ) ),
inference(modus_ponens,[status(thm)],[439,438]) ).
tff(441,plain,
! [X: $i] :
( cC16(X)
<=> ( cC14(X)
& cC10(X) ) ),
inference(skolemize,[status(sab)],[440]) ).
tff(442,plain,
! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) ),
inference(modus_ponens,[status(thm)],[441,437]) ).
tff(443,plain,
! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) ),
inference(modus_ponens,[status(thm)],[442,435]) ).
tff(444,plain,
( ( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(445,plain,
( ( cC16(iV21026)
<=> ~ ( ~ cC14(iV21026)
| ~ cC10(iV21026) ) )
<=> ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(446,plain,
( ( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC14(iV21026)
| ~ cC10(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
( ( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC14(iV21026)
| ~ cC10(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[446,444]) ).
tff(448,plain,
( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC14(iV21026)
| ~ cC10(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(449,plain,
( ~ ! [X: $i] :
( cC16(X)
<=> ~ ( ~ cC14(X)
| ~ cC10(X) ) )
| ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[448,447]) ).
tff(450,plain,
( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ),
inference(unit_resolution,[status(thm)],[449,443]) ).
tff(451,plain,
^ [X: $i] :
refl(
( ( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) )
<=> ( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(452,plain,
( ! [X: $i] :
( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) )
<=> ! [X: $i] :
( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) ) ),
inference(quant_intro,[status(thm)],[451]) ).
tff(453,plain,
^ [X: $i] :
rewrite(
( ( cC22(X)
<=> ( cC16(X)
& cC20(X) ) )
<=> ( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(454,plain,
( ! [X: $i] :
( cC22(X)
<=> ( cC16(X)
& cC20(X) ) )
<=> ! [X: $i] :
( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) ) ),
inference(quant_intro,[status(thm)],[453]) ).
tff(455,plain,
( ! [X: $i] :
( cC22(X)
<=> ( cC16(X)
& cC20(X) ) )
<=> ! [X: $i] :
( cC22(X)
<=> ( cC16(X)
& cC20(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(456,axiom,
! [X: $i] :
( cC22(X)
<=> ( cC16(X)
& cC20(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
tff(457,plain,
! [X: $i] :
( cC22(X)
<=> ( cC16(X)
& cC20(X) ) ),
inference(modus_ponens,[status(thm)],[456,455]) ).
tff(458,plain,
! [X: $i] :
( cC22(X)
<=> ( cC16(X)
& cC20(X) ) ),
inference(skolemize,[status(sab)],[457]) ).
tff(459,plain,
! [X: $i] :
( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) ),
inference(modus_ponens,[status(thm)],[458,454]) ).
tff(460,plain,
! [X: $i] :
( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) ),
inference(modus_ponens,[status(thm)],[459,452]) ).
tff(461,plain,
( ~ ! [X: $i] :
( cC22(X)
<=> ~ ( ~ cC16(X)
| ~ cC20(X) ) )
| ( cC22(iV21026)
<=> ~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(462,plain,
( cC22(iV21026)
<=> ~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ) ),
inference(unit_resolution,[status(thm)],[461,460]) ).
tff(463,plain,
^ [X: $i] :
refl(
( ( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
<=> ( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(464,plain,
( ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
<=> ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) ) ),
inference(quant_intro,[status(thm)],[463]) ).
tff(465,plain,
^ [X: $i] :
rewrite(
( ( cC158(X)
<=> ( cC22(X)
& cC156(X) ) )
<=> ( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(466,plain,
( ! [X: $i] :
( cC158(X)
<=> ( cC22(X)
& cC156(X) ) )
<=> ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) ) ),
inference(quant_intro,[status(thm)],[465]) ).
tff(467,plain,
( ! [X: $i] :
( cC158(X)
<=> ( cC22(X)
& cC156(X) ) )
<=> ! [X: $i] :
( cC158(X)
<=> ( cC22(X)
& cC156(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(468,axiom,
! [X: $i] :
( cC158(X)
<=> ( cC22(X)
& cC156(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
tff(469,plain,
! [X: $i] :
( cC158(X)
<=> ( cC22(X)
& cC156(X) ) ),
inference(modus_ponens,[status(thm)],[468,467]) ).
tff(470,plain,
! [X: $i] :
( cC158(X)
<=> ( cC22(X)
& cC156(X) ) ),
inference(skolemize,[status(sab)],[469]) ).
tff(471,plain,
! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) ),
inference(modus_ponens,[status(thm)],[470,466]) ).
tff(472,plain,
! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) ),
inference(modus_ponens,[status(thm)],[471,464]) ).
tff(473,plain,
( ( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(474,plain,
( ( cC158(iV21026)
<=> ~ ( ~ cC22(iV21026)
| ~ cC156(iV21026) ) )
<=> ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(475,plain,
( ( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC22(iV21026)
| ~ cC156(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[474]) ).
tff(476,plain,
( ( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC22(iV21026)
| ~ cC156(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[475,473]) ).
tff(477,plain,
( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC22(iV21026)
| ~ cC156(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(478,plain,
( ~ ! [X: $i] :
( cC158(X)
<=> ~ ( ~ cC22(X)
| ~ cC156(X) ) )
| ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[477,476]) ).
tff(479,plain,
( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ),
inference(unit_resolution,[status(thm)],[478,472]) ).
tff(480,plain,
^ [X: $i] :
refl(
( ( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) )
<=> ( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(481,plain,
( ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) ) ),
inference(quant_intro,[status(thm)],[480]) ).
tff(482,plain,
^ [X: $i] :
rewrite(
( ( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) )
<=> ( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(483,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) ) ),
inference(quant_intro,[status(thm)],[482]) ).
tff(484,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(485,axiom,
! [X: $i] :
( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_86) ).
tff(486,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) ),
inference(modus_ponens,[status(thm)],[485,484]) ).
tff(487,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC158(X)
& cC180(X) ) ),
inference(skolemize,[status(sab)],[486]) ).
tff(488,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) ),
inference(modus_ponens,[status(thm)],[487,483]) ).
tff(489,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) ),
inference(modus_ponens,[status(thm)],[488,481]) ).
tff(490,plain,
( ~ ! [X: $i] :
( cTEST(X)
<=> ~ ( ~ cC158(X)
| ~ cC180(X) ) )
| ( cTEST(iV21026)
<=> ~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(491,plain,
( cTEST(iV21026)
<=> ~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ) ),
inference(unit_resolution,[status(thm)],[490,489]) ).
tff(492,plain,
( cTEST(iV21026)
<=> cTEST(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(493,axiom,
cTEST(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_89) ).
tff(494,plain,
cTEST(iV21026),
inference(modus_ponens,[status(thm)],[493,492]) ).
tff(495,plain,
( ~ ( cTEST(iV21026)
<=> ~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ) )
| ~ cTEST(iV21026)
| ~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(496,plain,
( ~ ( cTEST(iV21026)
<=> ~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ) )
| ~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ) ),
inference(unit_resolution,[status(thm)],[495,494]) ).
tff(497,plain,
~ ( ~ cC158(iV21026)
| ~ cC180(iV21026) ),
inference(unit_resolution,[status(thm)],[496,491]) ).
tff(498,plain,
( ~ cC158(iV21026)
| ~ cC180(iV21026)
| cC158(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(499,plain,
cC158(iV21026),
inference(unit_resolution,[status(thm)],[498,497]) ).
tff(500,plain,
( ~ ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) )
| ~ cC158(iV21026)
| ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(501,plain,
( ~ ( cC158(iV21026)
<=> ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) )
| ~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ) ),
inference(unit_resolution,[status(thm)],[500,499]) ).
tff(502,plain,
~ ( ~ cC156(iV21026)
| ~ cC22(iV21026) ),
inference(unit_resolution,[status(thm)],[501,479]) ).
tff(503,plain,
( ~ cC156(iV21026)
| ~ cC22(iV21026)
| cC22(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(504,plain,
cC22(iV21026),
inference(unit_resolution,[status(thm)],[503,502]) ).
tff(505,plain,
( ~ ( cC22(iV21026)
<=> ~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ) )
| ~ cC22(iV21026)
| ~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(506,plain,
( ~ ( cC22(iV21026)
<=> ~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ) )
| ~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ) ),
inference(unit_resolution,[status(thm)],[505,504]) ).
tff(507,plain,
~ ( ~ cC16(iV21026)
| ~ cC20(iV21026) ),
inference(unit_resolution,[status(thm)],[506,462]) ).
tff(508,plain,
( ~ cC16(iV21026)
| ~ cC20(iV21026)
| cC16(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(509,plain,
cC16(iV21026),
inference(unit_resolution,[status(thm)],[508,507]) ).
tff(510,plain,
( ~ ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) )
| ~ cC16(iV21026)
| ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(511,plain,
( ~ ( cC16(iV21026)
<=> ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) )
| ~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ) ),
inference(unit_resolution,[status(thm)],[510,509]) ).
tff(512,plain,
~ ( ~ cC10(iV21026)
| ~ cC14(iV21026) ),
inference(unit_resolution,[status(thm)],[511,450]) ).
tff(513,plain,
( ~ cC10(iV21026)
| ~ cC14(iV21026)
| cC14(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(514,plain,
cC14(iV21026),
inference(unit_resolution,[status(thm)],[513,512]) ).
tff(515,plain,
^ [X: $i] :
refl(
( ( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) )
<=> ( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(516,plain,
( ! [X: $i] :
( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) )
<=> ! [X: $i] :
( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) ) ),
inference(quant_intro,[status(thm)],[515]) ).
tff(517,plain,
^ [X: $i] :
rewrite(
( ( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) )
<=> ( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(518,plain,
( ! [X: $i] :
( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) )
<=> ! [X: $i] :
( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) ) ),
inference(quant_intro,[status(thm)],[517]) ).
tff(519,plain,
( ! [X: $i] :
( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) )
<=> ! [X: $i] :
( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(520,axiom,
! [X: $i] :
( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(521,plain,
! [X: $i] :
( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) ),
inference(modus_ponens,[status(thm)],[520,519]) ).
tff(522,plain,
! [X: $i] :
( cC108(X)
<=> ( ~ cC106(X)
& ~ cC98(X) ) ),
inference(skolemize,[status(sab)],[521]) ).
tff(523,plain,
! [X: $i] :
( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) ),
inference(modus_ponens,[status(thm)],[522,518]) ).
tff(524,plain,
! [X: $i] :
( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) ),
inference(modus_ponens,[status(thm)],[523,516]) ).
tff(525,plain,
( ~ ! [X: $i] :
( cC108(X)
<=> ~ ( cC106(X)
| cC98(X) ) )
| ( cC108(iV21026)
<=> ~ ( cC106(iV21026)
| cC98(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(526,plain,
( cC108(iV21026)
<=> ~ ( cC106(iV21026)
| cC98(iV21026) ) ),
inference(unit_resolution,[status(thm)],[525,524]) ).
tff(527,plain,
( ~ cC106(iV21026)
<=> ~ cC106(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(528,axiom,
~ cC106(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_110) ).
tff(529,plain,
~ cC106(iV21026),
inference(modus_ponens,[status(thm)],[528,527]) ).
tff(530,plain,
( ~ cC98(iV21026)
<=> ~ cC98(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(531,axiom,
~ cC98(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_91) ).
tff(532,plain,
~ cC98(iV21026),
inference(modus_ponens,[status(thm)],[531,530]) ).
tff(533,plain,
( ~ ( cC106(iV21026)
| cC98(iV21026) )
| cC106(iV21026)
| cC98(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(534,plain,
~ ( cC106(iV21026)
| cC98(iV21026) ),
inference(unit_resolution,[status(thm)],[533,532,529]) ).
tff(535,plain,
( ~ ( cC108(iV21026)
<=> ~ ( cC106(iV21026)
| cC98(iV21026) ) )
| cC108(iV21026)
| cC106(iV21026)
| cC98(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(536,plain,
( ~ ( cC108(iV21026)
<=> ~ ( cC106(iV21026)
| cC98(iV21026) ) )
| cC108(iV21026) ),
inference(unit_resolution,[status(thm)],[535,534]) ).
tff(537,plain,
cC108(iV21026),
inference(unit_resolution,[status(thm)],[536,526]) ).
tff(538,plain,
( ~ cC10(iV21026)
| ~ cC14(iV21026)
| cC10(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(539,plain,
cC10(iV21026),
inference(unit_resolution,[status(thm)],[538,512]) ).
tff(540,plain,
^ [X: $i] :
refl(
( ( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) )
<=> ( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(541,plain,
( ! [X: $i] :
( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) )
<=> ! [X: $i] :
( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) ) ),
inference(quant_intro,[status(thm)],[540]) ).
tff(542,plain,
^ [X: $i] :
rewrite(
( ( cC156(X)
<=> ( cC154(X)
& cC138(X) ) )
<=> ( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(543,plain,
( ! [X: $i] :
( cC156(X)
<=> ( cC154(X)
& cC138(X) ) )
<=> ! [X: $i] :
( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) ) ),
inference(quant_intro,[status(thm)],[542]) ).
tff(544,plain,
( ! [X: $i] :
( cC156(X)
<=> ( cC154(X)
& cC138(X) ) )
<=> ! [X: $i] :
( cC156(X)
<=> ( cC154(X)
& cC138(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(545,axiom,
! [X: $i] :
( cC156(X)
<=> ( cC154(X)
& cC138(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
tff(546,plain,
! [X: $i] :
( cC156(X)
<=> ( cC154(X)
& cC138(X) ) ),
inference(modus_ponens,[status(thm)],[545,544]) ).
tff(547,plain,
! [X: $i] :
( cC156(X)
<=> ( cC154(X)
& cC138(X) ) ),
inference(skolemize,[status(sab)],[546]) ).
tff(548,plain,
! [X: $i] :
( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) ),
inference(modus_ponens,[status(thm)],[547,543]) ).
tff(549,plain,
! [X: $i] :
( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) ),
inference(modus_ponens,[status(thm)],[548,541]) ).
tff(550,plain,
( ~ ! [X: $i] :
( cC156(X)
<=> ~ ( ~ cC154(X)
| ~ cC138(X) ) )
| ( cC156(iV21026)
<=> ~ ( ~ cC154(iV21026)
| ~ cC138(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(551,plain,
( cC156(iV21026)
<=> ~ ( ~ cC154(iV21026)
| ~ cC138(iV21026) ) ),
inference(unit_resolution,[status(thm)],[550,549]) ).
tff(552,plain,
( ~ cC156(iV21026)
| ~ cC22(iV21026)
| cC156(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(553,plain,
cC156(iV21026),
inference(unit_resolution,[status(thm)],[552,502]) ).
tff(554,plain,
( ~ ( cC156(iV21026)
<=> ~ ( ~ cC154(iV21026)
| ~ cC138(iV21026) ) )
| ~ cC156(iV21026)
| ~ ( ~ cC154(iV21026)
| ~ cC138(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(555,plain,
~ ( ~ cC154(iV21026)
| ~ cC138(iV21026) ),
inference(unit_resolution,[status(thm)],[554,553,551]) ).
tff(556,plain,
( ~ cC154(iV21026)
| ~ cC138(iV21026)
| cC138(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(557,plain,
cC138(iV21026),
inference(unit_resolution,[status(thm)],[556,555]) ).
tff(558,plain,
^ [X: $i] :
refl(
( ( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) )
<=> ( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(559,plain,
( ! [X: $i] :
( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) )
<=> ! [X: $i] :
( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) ) ),
inference(quant_intro,[status(thm)],[558]) ).
tff(560,plain,
^ [X: $i] :
rewrite(
( ( cC134(X)
<=> ( cC132(X)
& cC116(X) ) )
<=> ( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(561,plain,
( ! [X: $i] :
( cC134(X)
<=> ( cC132(X)
& cC116(X) ) )
<=> ! [X: $i] :
( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) ) ),
inference(quant_intro,[status(thm)],[560]) ).
tff(562,plain,
( ! [X: $i] :
( cC134(X)
<=> ( cC132(X)
& cC116(X) ) )
<=> ! [X: $i] :
( cC134(X)
<=> ( cC132(X)
& cC116(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(563,axiom,
! [X: $i] :
( cC134(X)
<=> ( cC132(X)
& cC116(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
tff(564,plain,
! [X: $i] :
( cC134(X)
<=> ( cC132(X)
& cC116(X) ) ),
inference(modus_ponens,[status(thm)],[563,562]) ).
tff(565,plain,
! [X: $i] :
( cC134(X)
<=> ( cC132(X)
& cC116(X) ) ),
inference(skolemize,[status(sab)],[564]) ).
tff(566,plain,
! [X: $i] :
( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) ),
inference(modus_ponens,[status(thm)],[565,561]) ).
tff(567,plain,
! [X: $i] :
( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) ),
inference(modus_ponens,[status(thm)],[566,559]) ).
tff(568,plain,
( ~ ! [X: $i] :
( cC134(X)
<=> ~ ( ~ cC132(X)
| ~ cC116(X) ) )
| ( cC134(iV21026)
<=> ~ ( ~ cC132(iV21026)
| ~ cC116(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(569,plain,
( cC134(iV21026)
<=> ~ ( ~ cC132(iV21026)
| ~ cC116(iV21026) ) ),
inference(unit_resolution,[status(thm)],[568,567]) ).
tff(570,plain,
^ [X: $i] :
refl(
( ( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
<=> ( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(571,plain,
( ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
<=> ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) ) ),
inference(quant_intro,[status(thm)],[570]) ).
tff(572,plain,
^ [X: $i] :
rewrite(
( ( cC138(X)
<=> ( cC136(X)
& cC134(X) ) )
<=> ( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(573,plain,
( ! [X: $i] :
( cC138(X)
<=> ( cC136(X)
& cC134(X) ) )
<=> ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) ) ),
inference(quant_intro,[status(thm)],[572]) ).
tff(574,plain,
( ! [X: $i] :
( cC138(X)
<=> ( cC136(X)
& cC134(X) ) )
<=> ! [X: $i] :
( cC138(X)
<=> ( cC136(X)
& cC134(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(575,axiom,
! [X: $i] :
( cC138(X)
<=> ( cC136(X)
& cC134(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
tff(576,plain,
! [X: $i] :
( cC138(X)
<=> ( cC136(X)
& cC134(X) ) ),
inference(modus_ponens,[status(thm)],[575,574]) ).
tff(577,plain,
! [X: $i] :
( cC138(X)
<=> ( cC136(X)
& cC134(X) ) ),
inference(skolemize,[status(sab)],[576]) ).
tff(578,plain,
! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) ),
inference(modus_ponens,[status(thm)],[577,573]) ).
tff(579,plain,
! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) ),
inference(modus_ponens,[status(thm)],[578,571]) ).
tff(580,plain,
( ( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(581,plain,
( ( cC138(iV21026)
<=> ~ ( ~ cC136(iV21026)
| ~ cC134(iV21026) ) )
<=> ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(582,plain,
( ( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC136(iV21026)
| ~ cC134(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[581]) ).
tff(583,plain,
( ( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC136(iV21026)
| ~ cC134(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[582,580]) ).
tff(584,plain,
( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC136(iV21026)
| ~ cC134(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(585,plain,
( ~ ! [X: $i] :
( cC138(X)
<=> ~ ( ~ cC136(X)
| ~ cC134(X) ) )
| ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[584,583]) ).
tff(586,plain,
( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ),
inference(unit_resolution,[status(thm)],[585,579]) ).
tff(587,plain,
( ~ ( cC138(iV21026)
<=> ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) )
| ~ cC138(iV21026)
| ~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(588,plain,
~ ( ~ cC134(iV21026)
| ~ cC136(iV21026) ),
inference(unit_resolution,[status(thm)],[587,557,586]) ).
tff(589,plain,
( ~ cC134(iV21026)
| ~ cC136(iV21026)
| cC134(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(590,plain,
cC134(iV21026),
inference(unit_resolution,[status(thm)],[589,588]) ).
tff(591,plain,
( ~ ( cC134(iV21026)
<=> ~ ( ~ cC132(iV21026)
| ~ cC116(iV21026) ) )
| ~ cC134(iV21026)
| ~ ( ~ cC132(iV21026)
| ~ cC116(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(592,plain,
~ ( ~ cC132(iV21026)
| ~ cC116(iV21026) ),
inference(unit_resolution,[status(thm)],[591,590,569]) ).
tff(593,plain,
( ~ cC132(iV21026)
| ~ cC116(iV21026)
| cC116(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(594,plain,
cC116(iV21026),
inference(unit_resolution,[status(thm)],[593,592]) ).
tff(595,plain,
^ [X: $i] :
refl(
( ( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) )
<=> ( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(596,plain,
( ! [X: $i] :
( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) )
<=> ! [X: $i] :
( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[595]) ).
tff(597,plain,
^ [X: $i] :
rewrite(
( ( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) )
<=> ( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(598,plain,
( ! [X: $i] :
( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) ) ),
inference(quant_intro,[status(thm)],[597]) ).
tff(599,plain,
( ! [X: $i] :
( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) )
<=> ! [X: $i] :
( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(600,axiom,
! [X: $i] :
( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
tff(601,plain,
! [X: $i] :
( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[600,599]) ).
tff(602,plain,
! [X: $i] :
( cC110(X)
<=> ( cC108(X)
& cTOP(X) ) ),
inference(skolemize,[status(sab)],[601]) ).
tff(603,plain,
! [X: $i] :
( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[602,598]) ).
tff(604,plain,
! [X: $i] :
( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) ),
inference(modus_ponens,[status(thm)],[603,596]) ).
tff(605,plain,
( ~ ! [X: $i] :
( cC110(X)
<=> ~ ( ~ cC108(X)
| ~ cTOP(X) ) )
| ( cC110(iV21026)
<=> ~ ( ~ cC108(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(606,plain,
( cC110(iV21026)
<=> ~ ( ~ cC108(iV21026)
| ~ cTOP(iV21026) ) ),
inference(unit_resolution,[status(thm)],[605,604]) ).
tff(607,plain,
( ~ ( ~ cC108(iV21026)
| ~ cTOP(iV21026) )
| ~ cC108(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(608,plain,
( ~ ( ~ cC108(iV21026)
| ~ cTOP(iV21026) )
| ~ cC108(iV21026) ),
inference(unit_resolution,[status(thm)],[607,239]) ).
tff(609,plain,
~ ( ~ cC108(iV21026)
| ~ cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[608,537]) ).
tff(610,plain,
( ~ ( cC110(iV21026)
<=> ~ ( ~ cC108(iV21026)
| ~ cTOP(iV21026) ) )
| cC110(iV21026)
| ~ cC108(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(611,plain,
cC110(iV21026),
inference(unit_resolution,[status(thm)],[610,609,606]) ).
tff(612,plain,
^ [X: $i] :
refl(
( ( cC114(X)
<=> cTOP(X) )
<=> ( cC114(X)
<=> cTOP(X) ) )),
inference(bind,[status(th)],]) ).
tff(613,plain,
( ! [X: $i] :
( cC114(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC114(X)
<=> cTOP(X) ) ),
inference(quant_intro,[status(thm)],[612]) ).
tff(614,plain,
( ! [X: $i] :
( cC114(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC114(X)
<=> cTOP(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(615,axiom,
! [X: $i] :
( cC114(X)
<=> cTOP(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(616,plain,
! [X: $i] :
( cC114(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[615,614]) ).
tff(617,plain,
! [X: $i] :
( cC114(X)
<=> cTOP(X) ),
inference(skolemize,[status(sab)],[616]) ).
tff(618,plain,
! [X: $i] :
( cC114(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[617,613]) ).
tff(619,plain,
( ~ ! [X: $i] :
( cC114(X)
<=> cTOP(X) )
| ( cC114(iV21026)
<=> cTOP(iV21026) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(620,plain,
( cC114(iV21026)
<=> cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[619,618]) ).
tff(621,plain,
( ~ ( cC114(iV21026)
<=> cTOP(iV21026) )
| cC114(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(622,plain,
( ~ ( cC114(iV21026)
<=> cTOP(iV21026) )
| cC114(iV21026) ),
inference(unit_resolution,[status(thm)],[621,239]) ).
tff(623,plain,
cC114(iV21026),
inference(unit_resolution,[status(thm)],[622,620]) ).
tff(624,plain,
( ~ cC158(iV21026)
| ~ cC180(iV21026)
| cC180(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(625,plain,
cC180(iV21026),
inference(unit_resolution,[status(thm)],[624,497]) ).
tff(626,plain,
^ [X: $i] :
refl(
( ( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
<=> ( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(627,plain,
( ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
<=> ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) ) ),
inference(quant_intro,[status(thm)],[626]) ).
tff(628,plain,
^ [X: $i] :
rewrite(
( ( cC116(X)
<=> ( cC114(X)
& cC112(X) ) )
<=> ( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(629,plain,
( ! [X: $i] :
( cC116(X)
<=> ( cC114(X)
& cC112(X) ) )
<=> ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) ) ),
inference(quant_intro,[status(thm)],[628]) ).
tff(630,plain,
( ! [X: $i] :
( cC116(X)
<=> ( cC114(X)
& cC112(X) ) )
<=> ! [X: $i] :
( cC116(X)
<=> ( cC114(X)
& cC112(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(631,axiom,
! [X: $i] :
( cC116(X)
<=> ( cC114(X)
& cC112(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
tff(632,plain,
! [X: $i] :
( cC116(X)
<=> ( cC114(X)
& cC112(X) ) ),
inference(modus_ponens,[status(thm)],[631,630]) ).
tff(633,plain,
! [X: $i] :
( cC116(X)
<=> ( cC114(X)
& cC112(X) ) ),
inference(skolemize,[status(sab)],[632]) ).
tff(634,plain,
! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) ),
inference(modus_ponens,[status(thm)],[633,629]) ).
tff(635,plain,
! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) ),
inference(modus_ponens,[status(thm)],[634,627]) ).
tff(636,plain,
( ( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(637,plain,
( ( cC116(iV21026)
<=> ~ ( ~ cC114(iV21026)
| ~ cC112(iV21026) ) )
<=> ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(638,plain,
( ( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC114(iV21026)
| ~ cC112(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[637]) ).
tff(639,plain,
( ( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC114(iV21026)
| ~ cC112(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[638,636]) ).
tff(640,plain,
( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC114(iV21026)
| ~ cC112(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(641,plain,
( ~ ! [X: $i] :
( cC116(X)
<=> ~ ( ~ cC114(X)
| ~ cC112(X) ) )
| ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[640,639]) ).
tff(642,plain,
( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ),
inference(unit_resolution,[status(thm)],[641,635]) ).
tff(643,plain,
( ~ ( cC116(iV21026)
<=> ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) )
| ~ cC116(iV21026)
| ~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(644,plain,
~ ( ~ cC112(iV21026)
| ~ cC114(iV21026) ),
inference(unit_resolution,[status(thm)],[643,594,642]) ).
tff(645,plain,
( ~ cC112(iV21026)
| ~ cC114(iV21026)
| cC112(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(646,plain,
cC112(iV21026),
inference(unit_resolution,[status(thm)],[645,644]) ).
tff(647,plain,
^ [X: $i] :
refl(
( ( cC136(X)
<=> cTOP(X) )
<=> ( cC136(X)
<=> cTOP(X) ) )),
inference(bind,[status(th)],]) ).
tff(648,plain,
( ! [X: $i] :
( cC136(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC136(X)
<=> cTOP(X) ) ),
inference(quant_intro,[status(thm)],[647]) ).
tff(649,plain,
( ! [X: $i] :
( cC136(X)
<=> cTOP(X) )
<=> ! [X: $i] :
( cC136(X)
<=> cTOP(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(650,axiom,
! [X: $i] :
( cC136(X)
<=> cTOP(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
tff(651,plain,
! [X: $i] :
( cC136(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[650,649]) ).
tff(652,plain,
! [X: $i] :
( cC136(X)
<=> cTOP(X) ),
inference(skolemize,[status(sab)],[651]) ).
tff(653,plain,
! [X: $i] :
( cC136(X)
<=> cTOP(X) ),
inference(modus_ponens,[status(thm)],[652,648]) ).
tff(654,plain,
( ~ ! [X: $i] :
( cC136(X)
<=> cTOP(X) )
| ( cC136(iV21026)
<=> cTOP(iV21026) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(655,plain,
( cC136(iV21026)
<=> cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[654,653]) ).
tff(656,plain,
( ~ ( cC136(iV21026)
<=> cTOP(iV21026) )
| cC136(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(657,plain,
( ~ ( cC136(iV21026)
<=> cTOP(iV21026) )
| cC136(iV21026) ),
inference(unit_resolution,[status(thm)],[656,239]) ).
tff(658,plain,
cC136(iV21026),
inference(unit_resolution,[status(thm)],[657,655]) ).
tff(659,plain,
( ~ cC16(iV21026)
| ~ cC20(iV21026)
| cC20(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(660,plain,
cC20(iV21026),
inference(unit_resolution,[status(thm)],[659,507]) ).
tff(661,plain,
^ [X: $i] :
refl(
( ( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
<=> ( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(662,plain,
( ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
<=> ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) ) ),
inference(quant_intro,[status(thm)],[661]) ).
tff(663,plain,
^ [X: $i] :
rewrite(
( ( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) )
<=> ( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(664,plain,
( ! [X: $i] :
( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) )
<=> ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) ) ),
inference(quant_intro,[status(thm)],[663]) ).
tff(665,plain,
( ! [X: $i] :
( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) )
<=> ! [X: $i] :
( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(666,axiom,
! [X: $i] :
( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
tff(667,plain,
! [X: $i] :
( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) ),
inference(modus_ponens,[status(thm)],[666,665]) ).
tff(668,plain,
! [X: $i] :
( cC154(X)
<=> ( cTOP(X)
& cC152(X) ) ),
inference(skolemize,[status(sab)],[667]) ).
tff(669,plain,
! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) ),
inference(modus_ponens,[status(thm)],[668,664]) ).
tff(670,plain,
! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) ),
inference(modus_ponens,[status(thm)],[669,662]) ).
tff(671,plain,
( ( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(672,plain,
( ( cC154(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC152(iV21026) ) )
<=> ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(673,plain,
( ( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC152(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[672]) ).
tff(674,plain,
( ( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC152(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[673,671]) ).
tff(675,plain,
( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC152(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(676,plain,
( ~ ! [X: $i] :
( cC154(X)
<=> ~ ( ~ cTOP(X)
| ~ cC152(X) ) )
| ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[675,674]) ).
tff(677,plain,
( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) ),
inference(unit_resolution,[status(thm)],[676,670]) ).
tff(678,plain,
^ [X: $i] :
refl(
( ( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) )
<=> ( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(679,plain,
( ! [X: $i] :
( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) )
<=> ! [X: $i] :
( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) ) ),
inference(quant_intro,[status(thm)],[678]) ).
tff(680,plain,
^ [X: $i] :
rewrite(
( ( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) )
<=> ( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(681,plain,
( ! [X: $i] :
( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) )
<=> ! [X: $i] :
( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) ) ),
inference(quant_intro,[status(thm)],[680]) ).
tff(682,plain,
( ! [X: $i] :
( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) )
<=> ! [X: $i] :
( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(683,axiom,
! [X: $i] :
( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
tff(684,plain,
! [X: $i] :
( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) ),
inference(modus_ponens,[status(thm)],[683,682]) ).
tff(685,plain,
! [X: $i] :
( cC152(X)
<=> ( ~ cC150(X)
& ~ cC144(X) ) ),
inference(skolemize,[status(sab)],[684]) ).
tff(686,plain,
! [X: $i] :
( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) ),
inference(modus_ponens,[status(thm)],[685,681]) ).
tff(687,plain,
! [X: $i] :
( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) ),
inference(modus_ponens,[status(thm)],[686,679]) ).
tff(688,plain,
( ~ ! [X: $i] :
( cC152(X)
<=> ~ ( cC144(X)
| cC150(X) ) )
| ( cC152(iV21026)
<=> ~ ( cC144(iV21026)
| cC150(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(689,plain,
( cC152(iV21026)
<=> ~ ( cC144(iV21026)
| cC150(iV21026) ) ),
inference(unit_resolution,[status(thm)],[688,687]) ).
tff(690,plain,
( ~ cC144(iV21026)
<=> ~ cC144(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(691,axiom,
~ cC144(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_111) ).
tff(692,plain,
~ cC144(iV21026),
inference(modus_ponens,[status(thm)],[691,690]) ).
tff(693,plain,
( ~ cC150(iV21026)
<=> ~ cC150(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(694,axiom,
~ cC150(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_108) ).
tff(695,plain,
~ cC150(iV21026),
inference(modus_ponens,[status(thm)],[694,693]) ).
tff(696,plain,
( ~ ( cC144(iV21026)
| cC150(iV21026) )
| cC144(iV21026)
| cC150(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(697,plain,
~ ( cC144(iV21026)
| cC150(iV21026) ),
inference(unit_resolution,[status(thm)],[696,695,692]) ).
tff(698,plain,
( ~ ( cC152(iV21026)
<=> ~ ( cC144(iV21026)
| cC150(iV21026) ) )
| cC152(iV21026)
| cC144(iV21026)
| cC150(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(699,plain,
( ~ ( cC152(iV21026)
<=> ~ ( cC144(iV21026)
| cC150(iV21026) ) )
| cC152(iV21026) ),
inference(unit_resolution,[status(thm)],[698,697]) ).
tff(700,plain,
cC152(iV21026),
inference(unit_resolution,[status(thm)],[699,689]) ).
tff(701,plain,
( ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) )
| ~ cC152(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(702,plain,
( ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) )
| ~ cC152(iV21026) ),
inference(unit_resolution,[status(thm)],[701,239]) ).
tff(703,plain,
~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[702,700]) ).
tff(704,plain,
( ~ ( cC154(iV21026)
<=> ~ ( ~ cC152(iV21026)
| ~ cTOP(iV21026) ) )
| cC154(iV21026)
| ~ cC152(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(705,plain,
cC154(iV21026),
inference(unit_resolution,[status(thm)],[704,703,677]) ).
tff(706,plain,
^ [X: $i] :
refl(
( ( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) )
<=> ( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(707,plain,
( ! [X: $i] :
( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) )
<=> ! [X: $i] :
( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) ) ),
inference(quant_intro,[status(thm)],[706]) ).
tff(708,plain,
^ [X: $i] :
rewrite(
( ( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) )
<=> ( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(709,plain,
( ! [X: $i] :
( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) )
<=> ! [X: $i] :
( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) ) ),
inference(quant_intro,[status(thm)],[708]) ).
tff(710,plain,
( ! [X: $i] :
( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) )
<=> ! [X: $i] :
( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(711,axiom,
! [X: $i] :
( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
tff(712,plain,
! [X: $i] :
( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) ),
inference(modus_ponens,[status(thm)],[711,710]) ).
tff(713,plain,
! [X: $i] :
( cC130(X)
<=> ( ~ cC122(X)
& ~ cC128(X) ) ),
inference(skolemize,[status(sab)],[712]) ).
tff(714,plain,
! [X: $i] :
( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) ),
inference(modus_ponens,[status(thm)],[713,709]) ).
tff(715,plain,
! [X: $i] :
( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) ),
inference(modus_ponens,[status(thm)],[714,707]) ).
tff(716,plain,
( ~ ! [X: $i] :
( cC130(X)
<=> ~ ( cC122(X)
| cC128(X) ) )
| ( cC130(iV21026)
<=> ~ ( cC122(iV21026)
| cC128(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(717,plain,
( cC130(iV21026)
<=> ~ ( cC122(iV21026)
| cC128(iV21026) ) ),
inference(unit_resolution,[status(thm)],[716,715]) ).
tff(718,plain,
( ~ cC128(iV21026)
<=> ~ cC128(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(719,axiom,
~ cC128(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_115) ).
tff(720,plain,
~ cC128(iV21026),
inference(modus_ponens,[status(thm)],[719,718]) ).
tff(721,plain,
( ~ cC122(iV21026)
<=> ~ cC122(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(722,axiom,
~ cC122(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_92) ).
tff(723,plain,
~ cC122(iV21026),
inference(modus_ponens,[status(thm)],[722,721]) ).
tff(724,plain,
( ~ ( cC122(iV21026)
| cC128(iV21026) )
| cC122(iV21026)
| cC128(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(725,plain,
~ ( cC122(iV21026)
| cC128(iV21026) ),
inference(unit_resolution,[status(thm)],[724,723,720]) ).
tff(726,plain,
( ~ ( cC130(iV21026)
<=> ~ ( cC122(iV21026)
| cC128(iV21026) ) )
| cC130(iV21026)
| cC122(iV21026)
| cC128(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(727,plain,
( ~ ( cC130(iV21026)
<=> ~ ( cC122(iV21026)
| cC128(iV21026) ) )
| cC130(iV21026) ),
inference(unit_resolution,[status(thm)],[726,725]) ).
tff(728,plain,
cC130(iV21026),
inference(unit_resolution,[status(thm)],[727,717]) ).
tff(729,plain,
^ [X: $i] :
refl(
( ( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
<=> ( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(730,plain,
( ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
<=> ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) ) ),
inference(quant_intro,[status(thm)],[729]) ).
tff(731,plain,
^ [X: $i] :
rewrite(
( ( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) )
<=> ( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(732,plain,
( ! [X: $i] :
( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) )
<=> ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) ) ),
inference(quant_intro,[status(thm)],[731]) ).
tff(733,plain,
( ! [X: $i] :
( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) )
<=> ! [X: $i] :
( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(734,axiom,
! [X: $i] :
( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
tff(735,plain,
! [X: $i] :
( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) ),
inference(modus_ponens,[status(thm)],[734,733]) ).
tff(736,plain,
! [X: $i] :
( cC132(X)
<=> ( cTOP(X)
& cC130(X) ) ),
inference(skolemize,[status(sab)],[735]) ).
tff(737,plain,
! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) ),
inference(modus_ponens,[status(thm)],[736,732]) ).
tff(738,plain,
! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) ),
inference(modus_ponens,[status(thm)],[737,730]) ).
tff(739,plain,
( ( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(740,plain,
( ( cC132(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC130(iV21026) ) )
<=> ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(741,plain,
( ( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC130(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(monotonicity,[status(thm)],[740]) ).
tff(742,plain,
( ( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC130(iV21026) ) ) )
<=> ( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ) ) ),
inference(transitivity,[status(thm)],[741,739]) ).
tff(743,plain,
( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cTOP(iV21026)
| ~ cC130(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(744,plain,
( ~ ! [X: $i] :
( cC132(X)
<=> ~ ( ~ cTOP(X)
| ~ cC130(X) ) )
| ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ) ),
inference(modus_ponens,[status(thm)],[743,742]) ).
tff(745,plain,
( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) ),
inference(unit_resolution,[status(thm)],[744,738]) ).
tff(746,plain,
( ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) )
| ~ cC130(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(747,plain,
( ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) )
| ~ cC130(iV21026) ),
inference(unit_resolution,[status(thm)],[746,239]) ).
tff(748,plain,
~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ),
inference(unit_resolution,[status(thm)],[747,728]) ).
tff(749,plain,
( ~ ( cC132(iV21026)
<=> ~ ( ~ cC130(iV21026)
| ~ cTOP(iV21026) ) )
| cC132(iV21026)
| ~ cC130(iV21026)
| ~ cTOP(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(750,plain,
cC132(iV21026),
inference(unit_resolution,[status(thm)],[749,748,745]) ).
tff(751,plain,
^ [X: $i] :
refl(
( ( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) )
<=> ( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(752,plain,
( ! [X: $i] :
( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) )
<=> ! [X: $i] :
( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) ) ),
inference(quant_intro,[status(thm)],[751]) ).
tff(753,plain,
^ [X: $i] :
rewrite(
( ( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) )
<=> ( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(754,plain,
( ! [X: $i] :
( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) )
<=> ! [X: $i] :
( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) ) ),
inference(quant_intro,[status(thm)],[753]) ).
tff(755,plain,
( ! [X: $i] :
( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) )
<=> ! [X: $i] :
( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(756,axiom,
! [X: $i] :
( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
tff(757,plain,
! [X: $i] :
( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) ),
inference(modus_ponens,[status(thm)],[756,755]) ).
tff(758,plain,
! [X: $i] :
( cC168(X)
<=> ( ~ cC166(X)
& ~ cC162(X) ) ),
inference(skolemize,[status(sab)],[757]) ).
tff(759,plain,
! [X: $i] :
( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) ),
inference(modus_ponens,[status(thm)],[758,754]) ).
tff(760,plain,
! [X: $i] :
( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) ),
inference(modus_ponens,[status(thm)],[759,752]) ).
tff(761,plain,
( ~ ! [X: $i] :
( cC168(X)
<=> ~ ( cC162(X)
| cC166(X) ) )
| ( cC168(iV21026)
<=> ~ ( cC162(iV21026)
| cC166(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(762,plain,
( cC168(iV21026)
<=> ~ ( cC162(iV21026)
| cC166(iV21026) ) ),
inference(unit_resolution,[status(thm)],[761,760]) ).
tff(763,plain,
( ~ cC166(iV21026)
<=> ~ cC166(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(764,axiom,
~ cC166(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_101) ).
tff(765,plain,
~ cC166(iV21026),
inference(modus_ponens,[status(thm)],[764,763]) ).
tff(766,plain,
( ~ cC162(iV21026)
<=> ~ cC162(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(767,axiom,
~ cC162(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_100) ).
tff(768,plain,
~ cC162(iV21026),
inference(modus_ponens,[status(thm)],[767,766]) ).
tff(769,plain,
( ~ ( cC162(iV21026)
| cC166(iV21026) )
| cC162(iV21026)
| cC166(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(770,plain,
~ ( cC162(iV21026)
| cC166(iV21026) ),
inference(unit_resolution,[status(thm)],[769,768,765]) ).
tff(771,plain,
( ~ ( cC168(iV21026)
<=> ~ ( cC162(iV21026)
| cC166(iV21026) ) )
| cC168(iV21026)
| cC162(iV21026)
| cC166(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(772,plain,
( ~ ( cC168(iV21026)
<=> ~ ( cC162(iV21026)
| cC166(iV21026) ) )
| cC168(iV21026) ),
inference(unit_resolution,[status(thm)],[771,770]) ).
tff(773,plain,
cC168(iV21026),
inference(unit_resolution,[status(thm)],[772,762]) ).
tff(774,plain,
^ [X: $i] :
refl(
( ( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) )
<=> ( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(775,plain,
( ! [X: $i] :
( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) )
<=> ! [X: $i] :
( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) ) ),
inference(quant_intro,[status(thm)],[774]) ).
tff(776,plain,
^ [X: $i] :
rewrite(
( ( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) )
<=> ( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(777,plain,
( ! [X: $i] :
( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) )
<=> ! [X: $i] :
( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) ) ),
inference(quant_intro,[status(thm)],[776]) ).
tff(778,plain,
( ! [X: $i] :
( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) )
<=> ! [X: $i] :
( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(779,axiom,
! [X: $i] :
( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
tff(780,plain,
! [X: $i] :
( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) ),
inference(modus_ponens,[status(thm)],[779,778]) ).
tff(781,plain,
! [X: $i] :
( cC174(X)
<=> ( cC168(X)
& ~ cC172(X) ) ),
inference(skolemize,[status(sab)],[780]) ).
tff(782,plain,
! [X: $i] :
( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) ),
inference(modus_ponens,[status(thm)],[781,777]) ).
tff(783,plain,
! [X: $i] :
( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) ),
inference(modus_ponens,[status(thm)],[782,775]) ).
tff(784,plain,
( ~ ! [X: $i] :
( cC174(X)
<=> ~ ( cC172(X)
| ~ cC168(X) ) )
| ( cC174(iV21026)
<=> ~ ( cC172(iV21026)
| ~ cC168(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(785,plain,
( cC174(iV21026)
<=> ~ ( cC172(iV21026)
| ~ cC168(iV21026) ) ),
inference(unit_resolution,[status(thm)],[784,783]) ).
tff(786,plain,
( ~ cC172(iV21026)
<=> ~ cC172(iV21026) ),
inference(rewrite,[status(thm)],]) ).
tff(787,axiom,
~ cC172(iV21026),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_116) ).
tff(788,plain,
~ cC172(iV21026),
inference(modus_ponens,[status(thm)],[787,786]) ).
tff(789,plain,
( ~ ( cC172(iV21026)
| ~ cC168(iV21026) )
| cC172(iV21026)
| ~ cC168(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(790,plain,
( ~ ( cC172(iV21026)
| ~ cC168(iV21026) )
| ~ cC168(iV21026) ),
inference(unit_resolution,[status(thm)],[789,788]) ).
tff(791,plain,
~ ( cC172(iV21026)
| ~ cC168(iV21026) ),
inference(unit_resolution,[status(thm)],[790,773]) ).
tff(792,plain,
( ~ ( cC174(iV21026)
<=> ~ ( cC172(iV21026)
| ~ cC168(iV21026) ) )
| cC174(iV21026)
| cC172(iV21026)
| ~ cC168(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(793,plain,
cC174(iV21026),
inference(unit_resolution,[status(thm)],[792,791,785]) ).
tff(794,plain,
^ [X: $i] :
refl(
( ( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) )
<=> ( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(795,plain,
( ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) )
<=> ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) ) ),
inference(quant_intro,[status(thm)],[794]) ).
tff(796,plain,
^ [X: $i] :
rewrite(
( ( cC10(X)
<=> ( cC8(X)
& cC4(X) ) )
<=> ( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(797,plain,
( ! [X: $i] :
( cC10(X)
<=> ( cC8(X)
& cC4(X) ) )
<=> ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) ) ),
inference(quant_intro,[status(thm)],[796]) ).
tff(798,plain,
( ! [X: $i] :
( cC10(X)
<=> ( cC8(X)
& cC4(X) ) )
<=> ! [X: $i] :
( cC10(X)
<=> ( cC8(X)
& cC4(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(799,axiom,
! [X: $i] :
( cC10(X)
<=> ( cC8(X)
& cC4(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(800,plain,
! [X: $i] :
( cC10(X)
<=> ( cC8(X)
& cC4(X) ) ),
inference(modus_ponens,[status(thm)],[799,798]) ).
tff(801,plain,
! [X: $i] :
( cC10(X)
<=> ( cC8(X)
& cC4(X) ) ),
inference(skolemize,[status(sab)],[800]) ).
tff(802,plain,
! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) ),
inference(modus_ponens,[status(thm)],[801,797]) ).
tff(803,plain,
! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) ),
inference(modus_ponens,[status(thm)],[802,795]) ).
tff(804,plain,
( ~ ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC4(X)
| ~ cC8(X) ) )
| ( cC10(iV21026)
<=> ~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(805,plain,
( cC10(iV21026)
<=> ~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ) ),
inference(unit_resolution,[status(thm)],[804,803]) ).
tff(806,plain,
( ~ ( cC10(iV21026)
<=> ~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ) )
| ~ cC10(iV21026)
| ~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ) ),
inference(tautology,[status(thm)],]) ).
tff(807,plain,
( ~ ( cC10(iV21026)
<=> ~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ) )
| ~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ) ),
inference(unit_resolution,[status(thm)],[806,539]) ).
tff(808,plain,
~ ( ~ cC4(iV21026)
| ~ cC8(iV21026) ),
inference(unit_resolution,[status(thm)],[807,805]) ).
tff(809,plain,
( ~ cC4(iV21026)
| ~ cC8(iV21026)
| cC4(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(810,plain,
cC4(iV21026),
inference(unit_resolution,[status(thm)],[809,808]) ).
tff(811,plain,
( ~ cC4(iV21026)
| ~ cC8(iV21026)
| cC8(iV21026) ),
inference(tautology,[status(thm)],]) ).
tff(812,plain,
cC8(iV21026),
inference(unit_resolution,[status(thm)],[811,808]) ).
tff(813,plain,
( ~ ~ ( ~ cC84(iV21026)
| ~ cC16(iV21026)
| ~ cC36(iV21026)
| ~ cC42(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026)
| ~ cC174(iV21026)
| ~ cC20(iV21026)
| ~ cC156(iV21026)
| ~ cC60(iV21026)
| ~ cC38(iV21026)
| ~ cC158(iV21026)
| ~ cC10(iV21026)
| ~ cC134(iV21026)
| ~ cC22(iV21026)
| ~ cC168(iV21026)
| ~ cC56(iV21026)
| ~ cC78(iV21026)
| ~ cC58(iV21026)
| ~ cC152(iV21026)
| ~ cC40(iV21026)
| ~ cC132(iV21026)
| ~ cC130(iV21026)
| ~ cC62(iV21026)
| ~ cC154(iV21026)
| ~ cC80(iV21026)
| ~ cC8(iV21026)
| ~ cC136(iV21026)
| ~ cC112(iV21026)
| ~ cC180(iV21026)
| ~ cC114(iV21026)
| ~ cC64(iV21026)
| ~ cC110(iV21026)
| ~ cC116(iV21026)
| ~ cC82(iV21026)
| ~ cC138(iV21026)
| ~ cC4(iV21026)
| ~ cC108(iV21026)
| ~ cC14(iV21026)
| ~ cC90(iV21026)
| ~ cC30(iV21027)
| ~ cC24(iV21027)
| ~ cC50(iV21029)
| ~ cC44(iV21029)
| ~ cC66(iV21030)
| ~ cC72(iV21030) )
<=> ( ~ cC84(iV21026)
| ~ cC16(iV21026)
| ~ cC36(iV21026)
| ~ cC42(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026)
| ~ cC174(iV21026)
| ~ cC20(iV21026)
| ~ cC156(iV21026)
| ~ cC60(iV21026)
| ~ cC38(iV21026)
| ~ cC158(iV21026)
| ~ cC10(iV21026)
| ~ cC134(iV21026)
| ~ cC22(iV21026)
| ~ cC168(iV21026)
| ~ cC56(iV21026)
| ~ cC78(iV21026)
| ~ cC58(iV21026)
| ~ cC152(iV21026)
| ~ cC40(iV21026)
| ~ cC132(iV21026)
| ~ cC130(iV21026)
| ~ cC62(iV21026)
| ~ cC154(iV21026)
| ~ cC80(iV21026)
| ~ cC8(iV21026)
| ~ cC136(iV21026)
| ~ cC112(iV21026)
| ~ cC180(iV21026)
| ~ cC114(iV21026)
| ~ cC64(iV21026)
| ~ cC110(iV21026)
| ~ cC116(iV21026)
| ~ cC82(iV21026)
| ~ cC138(iV21026)
| ~ cC4(iV21026)
| ~ cC108(iV21026)
| ~ cC14(iV21026)
| ~ cC90(iV21026)
| ~ cC30(iV21027)
| ~ cC24(iV21027)
| ~ cC50(iV21029)
| ~ cC44(iV21029)
| ~ cC66(iV21030)
| ~ cC72(iV21030) ) ),
inference(rewrite,[status(thm)],]) ).
tff(814,plain,
( ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) )
<=> ~ ( ~ cC84(iV21026)
| ~ cC16(iV21026)
| ~ cC36(iV21026)
| ~ cC42(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026)
| ~ cC174(iV21026)
| ~ cC20(iV21026)
| ~ cC156(iV21026)
| ~ cC60(iV21026)
| ~ cC38(iV21026)
| ~ cC158(iV21026)
| ~ cC10(iV21026)
| ~ cC134(iV21026)
| ~ cC22(iV21026)
| ~ cC168(iV21026)
| ~ cC56(iV21026)
| ~ cC78(iV21026)
| ~ cC58(iV21026)
| ~ cC152(iV21026)
| ~ cC40(iV21026)
| ~ cC132(iV21026)
| ~ cC130(iV21026)
| ~ cC62(iV21026)
| ~ cC154(iV21026)
| ~ cC80(iV21026)
| ~ cC8(iV21026)
| ~ cC136(iV21026)
| ~ cC112(iV21026)
| ~ cC180(iV21026)
| ~ cC114(iV21026)
| ~ cC64(iV21026)
| ~ cC110(iV21026)
| ~ cC116(iV21026)
| ~ cC82(iV21026)
| ~ cC138(iV21026)
| ~ cC4(iV21026)
| ~ cC108(iV21026)
| ~ cC14(iV21026)
| ~ cC90(iV21026)
| ~ cC30(iV21027)
| ~ cC24(iV21027)
| ~ cC50(iV21029)
| ~ cC44(iV21029)
| ~ cC66(iV21030)
| ~ cC72(iV21030) ) ),
inference(rewrite,[status(thm)],]) ).
tff(815,plain,
( ~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) )
<=> ~ ~ ( ~ cC84(iV21026)
| ~ cC16(iV21026)
| ~ cC36(iV21026)
| ~ cC42(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026)
| ~ cC174(iV21026)
| ~ cC20(iV21026)
| ~ cC156(iV21026)
| ~ cC60(iV21026)
| ~ cC38(iV21026)
| ~ cC158(iV21026)
| ~ cC10(iV21026)
| ~ cC134(iV21026)
| ~ cC22(iV21026)
| ~ cC168(iV21026)
| ~ cC56(iV21026)
| ~ cC78(iV21026)
| ~ cC58(iV21026)
| ~ cC152(iV21026)
| ~ cC40(iV21026)
| ~ cC132(iV21026)
| ~ cC130(iV21026)
| ~ cC62(iV21026)
| ~ cC154(iV21026)
| ~ cC80(iV21026)
| ~ cC8(iV21026)
| ~ cC136(iV21026)
| ~ cC112(iV21026)
| ~ cC180(iV21026)
| ~ cC114(iV21026)
| ~ cC64(iV21026)
| ~ cC110(iV21026)
| ~ cC116(iV21026)
| ~ cC82(iV21026)
| ~ cC138(iV21026)
| ~ cC4(iV21026)
| ~ cC108(iV21026)
| ~ cC14(iV21026)
| ~ cC90(iV21026)
| ~ cC30(iV21027)
| ~ cC24(iV21027)
| ~ cC50(iV21029)
| ~ cC44(iV21029)
| ~ cC66(iV21030)
| ~ cC72(iV21030) ) ),
inference(monotonicity,[status(thm)],[814]) ).
tff(816,plain,
( ~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) )
<=> ( ~ cC84(iV21026)
| ~ cC16(iV21026)
| ~ cC36(iV21026)
| ~ cC42(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026)
| ~ cC174(iV21026)
| ~ cC20(iV21026)
| ~ cC156(iV21026)
| ~ cC60(iV21026)
| ~ cC38(iV21026)
| ~ cC158(iV21026)
| ~ cC10(iV21026)
| ~ cC134(iV21026)
| ~ cC22(iV21026)
| ~ cC168(iV21026)
| ~ cC56(iV21026)
| ~ cC78(iV21026)
| ~ cC58(iV21026)
| ~ cC152(iV21026)
| ~ cC40(iV21026)
| ~ cC132(iV21026)
| ~ cC130(iV21026)
| ~ cC62(iV21026)
| ~ cC154(iV21026)
| ~ cC80(iV21026)
| ~ cC8(iV21026)
| ~ cC136(iV21026)
| ~ cC112(iV21026)
| ~ cC180(iV21026)
| ~ cC114(iV21026)
| ~ cC64(iV21026)
| ~ cC110(iV21026)
| ~ cC116(iV21026)
| ~ cC82(iV21026)
| ~ cC138(iV21026)
| ~ cC4(iV21026)
| ~ cC108(iV21026)
| ~ cC14(iV21026)
| ~ cC90(iV21026)
| ~ cC30(iV21027)
| ~ cC24(iV21027)
| ~ cC50(iV21029)
| ~ cC44(iV21029)
| ~ cC66(iV21030)
| ~ cC72(iV21030) ) ),
inference(transitivity,[status(thm)],[815,813]) ).
tff(817,plain,
( ~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) )
<=> ~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) ) ),
inference(rewrite,[status(thm)],]) ).
tff(818,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) )
<=> ~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) ) ),
inference(rewrite,[status(thm)],]) ).
tff(819,plain,
( ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) )
<=> ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) ) ),
inference(rewrite,[status(thm)],]) ).
tff(820,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) ) ),
inference(monotonicity,[status(thm)],[819]) ).
tff(821,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) ) ),
inference(rewrite,[status(thm)],]) ).
tff(822,axiom,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
tff(823,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) ),
inference(modus_ponens,[status(thm)],[822,821]) ).
tff(824,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21026)
& cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cowlThing(iV21027)
& cC30(iV21027)
& cC24(iV21027)
& cowlThing(iV21029)
& cC50(iV21029)
& cC44(iV21029)
& cowlThing(iV21030)
& cC66(iV21030)
& cC72(iV21030) ),
inference(modus_ponens,[status(thm)],[823,820]) ).
tff(825,plain,
~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) ),
inference(modus_ponens,[status(thm)],[824,818]) ).
tff(826,plain,
~ ( cC84(iV21026)
& cC16(iV21026)
& cC36(iV21026)
& cC42(iV21026)
& cC88(iV21026)
& cC86(iV21026)
& cC174(iV21026)
& cC20(iV21026)
& cC156(iV21026)
& cC60(iV21026)
& cC38(iV21026)
& cC158(iV21026)
& cC10(iV21026)
& cC134(iV21026)
& cC22(iV21026)
& cC168(iV21026)
& cC56(iV21026)
& cC78(iV21026)
& cC58(iV21026)
& cC152(iV21026)
& cC40(iV21026)
& cC132(iV21026)
& cC130(iV21026)
& cC62(iV21026)
& cC154(iV21026)
& cC80(iV21026)
& cC8(iV21026)
& cC136(iV21026)
& cC112(iV21026)
& cC180(iV21026)
& cC114(iV21026)
& cC64(iV21026)
& cC110(iV21026)
& cC116(iV21026)
& cC82(iV21026)
& cC138(iV21026)
& cC4(iV21026)
& cC108(iV21026)
& cC14(iV21026)
& cC90(iV21026)
& cC30(iV21027)
& cC24(iV21027)
& cC50(iV21029)
& cC44(iV21029)
& cC66(iV21030)
& cC72(iV21030) ),
inference(modus_ponens,[status(thm)],[825,817]) ).
tff(827,plain,
( ~ cC84(iV21026)
| ~ cC16(iV21026)
| ~ cC36(iV21026)
| ~ cC42(iV21026)
| ~ cC88(iV21026)
| ~ cC86(iV21026)
| ~ cC174(iV21026)
| ~ cC20(iV21026)
| ~ cC156(iV21026)
| ~ cC60(iV21026)
| ~ cC38(iV21026)
| ~ cC158(iV21026)
| ~ cC10(iV21026)
| ~ cC134(iV21026)
| ~ cC22(iV21026)
| ~ cC168(iV21026)
| ~ cC56(iV21026)
| ~ cC78(iV21026)
| ~ cC58(iV21026)
| ~ cC152(iV21026)
| ~ cC40(iV21026)
| ~ cC132(iV21026)
| ~ cC130(iV21026)
| ~ cC62(iV21026)
| ~ cC154(iV21026)
| ~ cC80(iV21026)
| ~ cC8(iV21026)
| ~ cC136(iV21026)
| ~ cC112(iV21026)
| ~ cC180(iV21026)
| ~ cC114(iV21026)
| ~ cC64(iV21026)
| ~ cC110(iV21026)
| ~ cC116(iV21026)
| ~ cC82(iV21026)
| ~ cC138(iV21026)
| ~ cC4(iV21026)
| ~ cC108(iV21026)
| ~ cC14(iV21026)
| ~ cC90(iV21026)
| ~ cC30(iV21027)
| ~ cC24(iV21027)
| ~ cC50(iV21029)
| ~ cC44(iV21029)
| ~ cC66(iV21030)
| ~ cC72(iV21030) ),
inference(modus_ponens,[status(thm)],[826,816]) ).
tff(828,plain,
$false,
inference(unit_resolution,[status(thm)],[827,812,810,277,411,428,287,793,416,553,332,282,499,509,590,504,773,322,389,327,700,242,750,728,344,705,394,660,658,646,625,623,349,611,594,399,557,539,537,514,433,140,119,90,69,45,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS151+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 : n015.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 09:50:23 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.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------