TSTP Solution File: COM132+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM132+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 : Fri May 19 10:14:09 EDT 2023
% Result : Theorem 77.73s 19.82s
% Output : Refutation 77.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 90
% Syntax : Number of formulae : 159 ( 18 unt; 23 typ; 0 def)
% Number of atoms : 641 ( 461 equ; 0 cnn)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 1859 ( 95 ~; 34 |; 264 &;1259 @)
% ( 0 <=>; 207 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 6 con; 0-3 aty)
% Number of variables : 731 ( 0 ^; 595 !; 136 ?; 731 :)
% Comments :
%------------------------------------------------------------------------------
thf(visFreeVar_type,type,
visFreeVar: $i > $i > $o ).
thf(vtcheck_type,type,
vtcheck: $i > $i > $i > $o ).
thf(vbind_type,type,
vbind: $i > $i > $i > $i ).
thf(vabs_type,type,
vabs: $i > $i > $i > $i ).
thf(veabs_type,type,
veabs: $i ).
thf(vsubst_type,type,
vsubst: $i > $i > $i > $i ).
thf(vnoType_type,type,
vnoType: $i ).
thf(vsomeType_type,type,
vsomeType: $i > $i ).
thf(varrow_type,type,
varrow: $i > $i > $i ).
thf(valphaEquivalent_type,type,
valphaEquivalent: $i > $i > $o ).
thf(vgensym_type,type,
vgensym: $i > $i ).
thf(vapp_type,type,
vapp: $i > $i > $i ).
thf(vvar_type,type,
vvar: $i > $i ).
thf(vreduce_type,type,
vreduce: $i > $i ).
thf(vnoExp_type,type,
vnoExp: $i ).
thf(visSomeExp_type,type,
visSomeExp: $i > $o ).
thf(vsomeExp_type,type,
vsomeExp: $i > $i ).
thf(vempty_type,type,
vempty: $i ).
thf(visValue_type,type,
visValue: $i > $o ).
thf(visSomeType_type,type,
visSomeType: $i > $o ).
thf(vgetSomeExp_type,type,
vgetSomeExp: $i > $i ).
thf(vlookup_type,type,
vlookup: $i > $i > $i ).
thf(vgetSomeType_type,type,
vgetSomeType: $i > $i ).
thf(19,axiom,
( ( ( vnoType = vnoType )
=> $true )
& ( $true
=> ( vnoType = vnoType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-noType') ).
thf(156,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B
= ( vvar @ A ) )
=> ~ ( visValue @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( B
= ( vvar @ A ) )
=> ~ ( visValue @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i] :
( vnoType
!= ( vsomeType @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noType-someType') ).
thf(76,plain,
! [A: $i] :
( vnoType
!= ( vsomeType @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( A = E )
& ( B = F )
& ( C
= ( vabs @ H @ G @ J ) ) )
=> ( ( ( E != H )
& ( visFreeVar @ H @ F )
& ( I
= ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) ) )
=> ( ( D
= ( vsubst @ A @ B @ C ) )
=> ( D
= ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst4) ).
thf(414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( A = E )
& ( B = F )
& ( C
= ( vabs @ H @ G @ J ) ) )
=> ( ( ( E != H )
& ( visFreeVar @ H @ F )
& ( I
= ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) ) )
=> ( ( D
= ( vsubst @ A @ B @ C ) )
=> ( D
= ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vlookup @ B @ A )
= ( vsomeType @ C ) )
=> ( vtcheck @ A @ ( vvar @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-var') ).
thf(502,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vlookup @ B @ A )
= ( vsomeType @ C ) )
=> ( vtcheck @ A @ ( vvar @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( visFreeVar @ B @ A )
& ( valphaEquivalent @ A @ C ) )
=> ~ ( visFreeVar @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-FreeVar') ).
thf(450,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( visFreeVar @ B @ A )
& ( valphaEquivalent @ A @ C ) )
=> ~ ( visFreeVar @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = B )
& ( D = A )
& ( E
= ( vvar @ G ) ) )
=> ( ( B != G )
=> ( ( F
= ( vsubst @ C @ D @ E ) )
=> ( F
= ( vvar @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst1) ).
thf(418,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = B )
& ( D = A )
& ( E
= ( vvar @ G ) ) )
=> ( ( B != G )
=> ( ( F
= ( vsubst @ C @ D @ E ) )
=> ( F
= ( vvar @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B = E )
& ( C
= ( vabs @ D @ A @ F ) ) )
=> ( ( ( ( D != E )
& ( visFreeVar @ E @ F ) )
=> ( visFreeVar @ B @ C ) )
& ( ( visFreeVar @ B @ C )
=> ( ( D != E )
& ( visFreeVar @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
thf(283,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B = E )
& ( C
= ( vabs @ D @ A @ F ) ) )
=> ( ( ( ( D != E )
& ( visFreeVar @ E @ F ) )
=> ( visFreeVar @ B @ C ) )
& ( ( visFreeVar @ B @ C )
=> ( ( D != E )
& ( visFreeVar @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( visFreeVar @ A @ D )
& ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) )
=> ( vtcheck @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong') ).
thf(459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( visFreeVar @ A @ D )
& ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) )
=> ( vtcheck @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C != E )
& ( visFreeVar @ E @ D )
& ( vtcheck @ B @ D @ A )
& ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vabs @ E @ F @ veabs ) @ G ) )
=> ( vtcheck @ B @ ( vsubst @ C @ D @ ( vabs @ E @ F @ veabs ) ) @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-3') ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C != E )
& ( visFreeVar @ E @ D )
& ( vtcheck @ B @ D @ A )
& ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vabs @ E @ F @ veabs ) @ G ) )
=> ( vtcheck @ B @ ( vsubst @ C @ D @ ( vabs @ E @ F @ veabs ) ) @ G ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C != E )
& ( visFreeVar @ E @ D )
& ( vtcheck @ B @ D @ A )
& ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vabs @ E @ F @ veabs ) @ G ) )
=> ( vtcheck @ B @ ( vsubst @ C @ D @ ( vabs @ E @ F @ veabs ) ) @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( vtcheck @ B @ A @ D )
& ( valphaEquivalent @ A @ C ) )
=> ( vtcheck @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-typing') ).
thf(479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( vtcheck @ B @ A @ D )
& ( valphaEquivalent @ A @ C ) )
=> ( vtcheck @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( vtcheck @ C @ A @ B )
=> ( ? [D: $i] :
( ( A
= ( vvar @ D ) )
& ( ( vlookup @ D @ C )
= ( vsomeType @ B ) ) )
| ? [D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vabs @ D @ F @ E ) )
& ( B
= ( varrow @ F @ G ) )
& ( vtcheck @ ( vbind @ D @ F @ C ) @ E @ G ) )
| ? [D: $i,E: $i,F: $i] :
( ( A
= ( vapp @ D @ E ) )
& ( vtcheck @ C @ D @ ( varrow @ F @ B ) )
& ( vtcheck @ C @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-inv') ).
thf(518,plain,
! [A: $i,B: $i,C: $i] :
( ( vtcheck @ C @ A @ B )
=> ( ? [D: $i] :
( ( A
= ( vvar @ D ) )
& ( ( vlookup @ D @ C )
= ( vsomeType @ B ) ) )
| ? [D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vabs @ D @ F @ E ) )
& ( B
= ( varrow @ F @ G ) )
& ( vtcheck @ ( vbind @ D @ F @ C ) @ E @ G ) )
| ? [D: $i,E: $i,F: $i] :
( ( A
= ( vapp @ D @ E ) )
& ( vtcheck @ C @ D @ ( varrow @ F @ B ) )
& ( vtcheck @ C @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A = G )
& ( B = H )
& ( C
= ( vabs @ E @ F @ I ) ) )
=> ( ( ( G != E )
& ~ ( visFreeVar @ E @ H ) )
=> ( ( D
= ( vsubst @ A @ B @ C ) )
=> ( D
= ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst5) ).
thf(481,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A = G )
& ( B = H )
& ( C
= ( vabs @ E @ F @ I ) ) )
=> ( ( ( G != E )
& ~ ( visFreeVar @ E @ H ) )
=> ( ( D
= ( vsubst @ A @ B @ C ) )
=> ( D
= ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( A
= ( vsomeExp @ C ) )
=> ( ( B
= ( vgetSomeExp @ A ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeExp0) ).
thf(170,plain,
! [A: $i,B: $i,C: $i] :
( ( A
= ( vsomeExp @ C ) )
=> ( ( B
= ( vgetSomeExp @ A ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [A: $i] : ( valphaEquivalent @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-refl') ).
thf(115,plain,
! [A: $i] : ( valphaEquivalent @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( vlookup @ A @ C )
= vnoType )
& ( vtcheck @ C @ D @ E ) )
=> ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak') ).
thf(533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( vlookup @ A @ C )
= vnoType )
& ( vtcheck @ C @ D @ E ) )
=> ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = A )
& ( D = G )
& ( E
= ( vvar @ B ) ) )
=> ( ( A = B )
=> ( ( F
= ( vsubst @ C @ D @ E ) )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst0) ).
thf(550,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = A )
& ( D = G )
& ( E
= ( vvar @ B ) ) )
=> ( ( A = B )
=> ( ( F
= ( vsubst @ C @ D @ E ) )
=> ( F = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
& ( C = vempty ) )
=> ( ( D
= ( vlookup @ B @ C ) )
=> ( D = vnoType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup0) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
& ( C = vempty ) )
=> ( ( D
= ( vlookup @ B @ C ) )
=> ( D = vnoType ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( A
= ( vsomeType @ C ) )
=> ( ( B
= ( vgetSomeType @ A ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeType0) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( A
= ( vsomeType @ C ) )
=> ( ( B
= ( vgetSomeType @ A ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10,axiom,
( ( ( vempty = vempty )
=> $true )
& ( $true
=> ( vempty = vempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-empty') ).
thf(110,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i] :
( ( A = vnoType )
=> ~ ( visSomeType @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType0) ).
thf(157,plain,
! [A: $i] :
( ( A = vnoType )
=> ~ ( visSomeType @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C
= ( vapp @ ( vabs @ E @ A @ G ) @ F ) )
=> ( ( ( B
= ( vreduce @ F ) )
& ~ ( visSomeExp @ B )
& ( visValue @ F ) )
=> ( ( D
= ( vreduce @ C ) )
=> ( D
= ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce3) ).
thf(189,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C
= ( vapp @ ( vabs @ E @ A @ G ) @ F ) )
=> ( ( ( B
= ( vreduce @ F ) )
& ~ ( visSomeExp @ B )
& ( visValue @ F ) )
=> ( ( D
= ( vreduce @ C ) )
=> ( D
= ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( vgensym @ ( vapp @ ( vapp @ A @ B ) @ ( vvar @ C ) ) ) )
=> ( C != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-unequal-var-3') ).
thf(93,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( vgensym @ ( vapp @ ( vapp @ A @ B ) @ ( vvar @ C ) ) ) )
=> ( C != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B
= ( vsomeType @ A ) )
=> ( visSomeType @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType1) ).
thf(152,plain,
! [A: $i,B: $i] :
( ( B
= ( vsomeType @ A ) )
=> ( visSomeType @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( vsubst @ A @ B @ C )
= D )
=> ( ? [E: $i,F: $i,G: $i] :
( ( A = E )
& ( B = G )
& ( C
= ( vvar @ F ) )
& ( E = F )
& ( D = G ) )
| ? [E: $i,F: $i,G: $i] :
( ( A = F )
& ( B = E )
& ( C
= ( vvar @ G ) )
& ( F != G )
& ( D
= ( vvar @ G ) ) )
| ? [E: $i,F: $i,G: $i,H: $i] :
( ( A = F )
& ( B = G )
& ( C
= ( vapp @ E @ H ) )
& ( D
= ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) )
| ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( A = F )
& ( B = E )
& ( C
= ( vabs @ G @ H @ I ) )
& ( F = G )
& ( D
= ( vabs @ G @ H @ I ) ) )
| ? [E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A = E )
& ( B = F )
& ( C
= ( vabs @ H @ G @ J ) )
& ( E != H )
& ( visFreeVar @ H @ F )
& ( I
= ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) )
& ( D
= ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) )
| ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( A = G )
& ( B = H )
& ( C
= ( vabs @ E @ F @ I ) )
& ( G != E )
& ~ ( visFreeVar @ E @ H )
& ( D
= ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','subst-INV') ).
thf(316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( vsubst @ A @ B @ C )
= D )
=> ( ? [E: $i,F: $i,G: $i] :
( ( A = E )
& ( B = G )
& ( C
= ( vvar @ F ) )
& ( E = F )
& ( D = G ) )
| ? [E: $i,F: $i,G: $i] :
( ( A = F )
& ( B = E )
& ( C
= ( vvar @ G ) )
& ( F != G )
& ( D
= ( vvar @ G ) ) )
| ? [E: $i,F: $i,G: $i,H: $i] :
( ( A = F )
& ( B = G )
& ( C
= ( vapp @ E @ H ) )
& ( D
= ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) )
| ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( A = F )
& ( B = E )
& ( C
= ( vabs @ G @ H @ I ) )
& ( F = G )
& ( D
= ( vabs @ G @ H @ I ) ) )
| ? [E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A = E )
& ( B = F )
& ( C
= ( vabs @ H @ G @ J ) )
& ( E != H )
& ( visFreeVar @ H @ F )
& ( I
= ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) )
& ( D
= ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) )
| ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( A = G )
& ( B = H )
& ( C
= ( vabs @ E @ F @ I ) )
& ( G != E )
& ~ ( visFreeVar @ E @ H )
& ( D
= ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D = B )
& ( E
= ( vbind @ C @ G @ A ) ) )
=> ( ( B = C )
=> ( ( F
= ( vlookup @ D @ E ) )
=> ( F
= ( vsomeType @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup1) ).
thf(475,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D = B )
& ( E
= ( vbind @ C @ G @ A ) ) )
=> ( ( B = C )
=> ( ( F
= ( vlookup @ D @ E ) )
=> ( F
= ( vsomeType @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(25,axiom,
! [A: $i] :
( vnoExp
!= ( vsomeExp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
thf(179,plain,
! [A: $i] :
( vnoExp
!= ( vsomeExp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( vgensym @ ( vapp @ ( vapp @ A @ D ) @ ( vvar @ B ) ) ) )
=> ~ ( visFreeVar @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-free-2') ).
thf(443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( vgensym @ ( vapp @ ( vapp @ A @ D ) @ ( vvar @ B ) ) ) )
=> ~ ( visFreeVar @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = A )
& ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
=> ( vtcheck @ ( vbind @ C @ D @ E ) @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Duplicate') ).
thf(485,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = A )
& ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
=> ( vtcheck @ ( vbind @ C @ D @ E ) @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B
= ( vsomeExp @ A ) )
=> ( visSomeExp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp1) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( B
= ( vsomeExp @ A ) )
=> ( visSomeExp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( ( vvar @ A )
= ( vvar @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vvar @ A )
= ( vvar @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-var') ).
thf(121,plain,
! [A: $i,B: $i] :
( ( ( ( vvar @ A )
= ( vvar @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vvar @ A )
= ( vvar @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = F )
& ( D
= ( vbind @ B @ A @ G ) ) )
=> ( ( F != B )
=> ( ( E
= ( vlookup @ C @ D ) )
=> ( E
= ( vlookup @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup2) ).
thf(514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C = F )
& ( D
= ( vbind @ B @ A @ G ) ) )
=> ( ( F != B )
=> ( ( E
= ( vlookup @ C @ D ) )
=> ( E
= ( vlookup @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( vempty
!= ( vbind @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
thf(293,plain,
! [A: $i,B: $i,C: $i] :
( vempty
!= ( vbind @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( vapp @ A @ B )
= ( vapp @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( vapp @ A @ B )
= ( vapp @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-app') ).
thf(133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( vapp @ A @ B )
= ( vapp @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( vapp @ A @ B )
= ( vapp @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C != E )
& ~ ( visFreeVar @ E @ D )
& ( vtcheck @ B @ D @ A )
& ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vabs @ E @ F @ G ) @ H ) )
=> ( vtcheck @ B @ ( vsubst @ C @ D @ ( vabs @ E @ F @ G ) ) @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-2-gen') ).
thf(507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C != E )
& ~ ( visFreeVar @ E @ D )
& ( vtcheck @ B @ D @ A )
& ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vabs @ E @ F @ G ) @ H ) )
=> ( vtcheck @ B @ ( vsubst @ C @ D @ ( vabs @ E @ F @ G ) ) @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( vabs @ A @ B @ C ) )
=> ( visValue @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue0) ).
thf(312,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( vabs @ A @ B @ C ) )
=> ( visValue @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D
= ( vabs @ A @ B @ C ) )
=> ( ( E
= ( vreduce @ D ) )
=> ( E = vnoExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce1) ).
thf(307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D
= ( vabs @ A @ B @ C ) )
=> ( ( E
= ( vreduce @ D ) )
=> ( E = vnoExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( visFreeVar @ A @ D )
& ( vtcheck @ C @ D @ E ) )
=> ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar') ).
thf(452,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( visFreeVar @ A @ D )
& ( vtcheck @ C @ D @ E ) )
=> ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( vvar @ A )
!= ( vapp @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
thf(117,plain,
! [A: $i,B: $i,C: $i] :
( ( vvar @ A )
!= ( vapp @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i] :
( ( A = vnoExp )
=> ~ ( visSomeExp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp0) ).
thf(102,plain,
! [A: $i] :
( ( A = vnoExp )
=> ~ ( visSomeExp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = D )
& ( B
= ( vapp @ C @ E ) ) )
=> ( ( ( ( visFreeVar @ D @ C )
| ( visFreeVar @ D @ E ) )
=> ( visFreeVar @ A @ B ) )
& ( ( visFreeVar @ A @ B )
=> ( ( visFreeVar @ D @ C )
| ( visFreeVar @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar2) ).
thf(297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = D )
& ( B
= ( vapp @ C @ E ) ) )
=> ( ( ( ( visFreeVar @ D @ C )
| ( visFreeVar @ D @ E ) )
=> ( visFreeVar @ A @ B ) )
& ( ( visFreeVar @ A @ B )
=> ( ( visFreeVar @ D @ C )
| ( visFreeVar @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vbind @ A @ B @ C )
= ( vbind @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) )
& ( ( ( A = D )
& ( B = E )
& ( C = F ) )
=> ( ( vbind @ A @ B @ C )
= ( vbind @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-bind') ).
thf(424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vbind @ A @ B @ C )
= ( vbind @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) )
& ( ( ( A = D )
& ( B = E )
& ( C = F ) )
=> ( ( vbind @ A @ B @ C )
= ( vbind @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B
= ( vvar @ A ) )
=> ( ( C
= ( vreduce @ B ) )
=> ( C = vnoExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce0) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( B
= ( vvar @ A ) )
=> ( ( C
= ( vreduce @ B ) )
=> ( C = vnoExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vabs @ A @ B @ C )
= ( vabs @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) )
& ( ( ( A = D )
& ( B = E )
& ( C = F ) )
=> ( ( vabs @ A @ B @ C )
= ( vabs @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-abs') ).
thf(461,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( vabs @ A @ B @ C )
= ( vabs @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) )
& ( ( ( A = D )
& ( B = E )
& ( C = F ) )
=> ( ( vabs @ A @ B @ C )
= ( vabs @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vlookup @ A @ B )
= C )
=> ( ? [D: $i] :
( ( A = D )
& ( B = vempty )
& ( C = vnoType ) )
| ? [D: $i,E: $i,F: $i,G: $i] :
( ( A = E )
& ( B
= ( vbind @ F @ G @ D ) )
& ( E = F )
& ( C
= ( vsomeType @ G ) ) )
| ? [D: $i,E: $i,F: $i,G: $i] :
( ( A = F )
& ( B
= ( vbind @ E @ D @ G ) )
& ( F != E )
& ( C
= ( vlookup @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookup-INV') ).
thf(554,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vlookup @ A @ B )
= C )
=> ( ? [D: $i] :
( ( A = D )
& ( B = vempty )
& ( C = vnoType ) )
| ? [D: $i,E: $i,F: $i,G: $i] :
( ( A = E )
& ( B
= ( vbind @ F @ G @ D ) )
& ( E = F )
& ( C
= ( vsomeType @ G ) ) )
| ? [D: $i,E: $i,F: $i,G: $i] :
( ( A = F )
& ( B
= ( vbind @ E @ D @ G ) )
& ( F != E )
& ( C
= ( vlookup @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( vreduce @ A )
= B )
=> ( ? [C: $i] :
( ( A
= ( vvar @ C ) )
& ( B = vnoExp ) )
| ? [C: $i,D: $i,E: $i] :
( ( A
= ( vabs @ C @ D @ E ) )
& ( B = vnoExp ) )
| ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vapp @ ( vabs @ D @ E @ F ) @ C ) )
& ( G
= ( vreduce @ C ) )
& ( visSomeExp @ G )
& ( B
= ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) )
| ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vapp @ ( vabs @ E @ C @ G ) @ F ) )
& ( D
= ( vreduce @ F ) )
& ~ ( visSomeExp @ D )
& ( visValue @ F )
& ( B
= ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) )
| ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vapp @ ( vabs @ C @ D @ E ) @ G ) )
& ( F
= ( vreduce @ G ) )
& ~ ( visSomeExp @ F )
& ~ ( visValue @ G )
& ( B = vnoExp ) )
| ? [C: $i,D: $i,E: $i] :
( ( A
= ( vapp @ C @ E ) )
& ! [F: $i,G: $i,H: $i] :
( C
!= ( vabs @ F @ G @ H ) )
& ( D
= ( vreduce @ C ) )
& ( visSomeExp @ D )
& ( B
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) )
| ? [C: $i,D: $i,E: $i] :
( ( A
= ( vapp @ D @ C ) )
& ! [F: $i,G: $i,H: $i] :
( D
!= ( vabs @ F @ G @ H ) )
& ( E
= ( vreduce @ D ) )
& ~ ( visSomeExp @ E )
& ( B = vnoExp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-INV') ).
thf(193,plain,
! [A: $i,B: $i] :
( ( ( vreduce @ A )
= B )
=> ( ? [C: $i] :
( ( A
= ( vvar @ C ) )
& ( B = vnoExp ) )
| ? [C: $i,D: $i,E: $i] :
( ( A
= ( vabs @ C @ D @ E ) )
& ( B = vnoExp ) )
| ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vapp @ ( vabs @ D @ E @ F ) @ C ) )
& ( G
= ( vreduce @ C ) )
& ( visSomeExp @ G )
& ( B
= ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) )
| ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vapp @ ( vabs @ E @ C @ G ) @ F ) )
& ( D
= ( vreduce @ F ) )
& ~ ( visSomeExp @ D )
& ( visValue @ F )
& ( B
= ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) )
| ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A
= ( vapp @ ( vabs @ C @ D @ E ) @ G ) )
& ( F
= ( vreduce @ G ) )
& ~ ( visSomeExp @ F )
& ~ ( visValue @ G )
& ( B = vnoExp ) )
| ? [C: $i,D: $i,E: $i] :
( ( A
= ( vapp @ C @ E ) )
& ! [F: $i,G: $i,H: $i] :
( C
!= ( vabs @ F @ G @ H ) )
& ( D
= ( vreduce @ C ) )
& ( visSomeExp @ D )
& ( B
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) )
| ? [C: $i,D: $i,E: $i] :
( ( A
= ( vapp @ D @ C ) )
& ! [F: $i,G: $i,H: $i] :
( D
!= ( vabs @ F @ G @ H ) )
& ( E
= ( vreduce @ D ) )
& ~ ( visSomeExp @ E )
& ( B = vnoExp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F
= ( vapp @ ( vabs @ A @ B @ C ) @ E ) )
=> ( ( ( D
= ( vreduce @ E ) )
& ~ ( visSomeExp @ D )
& ~ ( visValue @ E ) )
=> ( ( G
= ( vreduce @ F ) )
=> ( G = vnoExp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce4) ).
thf(489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F
= ( vapp @ ( vabs @ A @ B @ C ) @ E ) )
=> ( ( ( D
= ( vreduce @ E ) )
& ~ ( visSomeExp @ D )
& ~ ( visValue @ E ) )
=> ( ( G
= ( vreduce @ F ) )
=> ( G = vnoExp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(21,axiom,
( ( ( vnoExp = vnoExp )
=> $true )
& ( $true
=> ( vnoExp = vnoExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-noExp') ).
thf(161,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( vabs @ A @ B @ C )
!= ( vapp @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-abs-app') ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( vabs @ A @ B @ C )
!= ( vapp @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( ( vsomeType @ A )
= ( vsomeType @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vsomeType @ A )
= ( vsomeType @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someType') ).
thf(144,plain,
! [A: $i,B: $i] :
( ( ( ( vsomeType @ A )
= ( vsomeType @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vsomeType @ A )
= ( vsomeType @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( C = B )
& ( D = A )
& ( E
= ( vabs @ G @ H @ I ) ) )
=> ( ( B = G )
=> ( ( F
= ( vsubst @ C @ D @ E ) )
=> ( F
= ( vabs @ G @ H @ I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst3) ).
thf(498,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( C = B )
& ( D = A )
& ( E
= ( vabs @ G @ H @ I ) ) )
=> ( ( B = G )
=> ( ( F
= ( vsubst @ C @ D @ E ) )
=> ( F
= ( vabs @ G @ H @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( vgensym @ B )
= A )
=> ~ ( visFreeVar @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
thf(494,plain,
! [A: $i,B: $i] :
( ( ( vgensym @ B )
= A )
=> ~ ( visFreeVar @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( valphaEquivalent @ B @ A )
=> ( valphaEquivalent @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-sym') ).
thf(91,plain,
! [A: $i,B: $i] :
( ( valphaEquivalent @ B @ A )
=> ( valphaEquivalent @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( varrow @ A @ B )
= ( varrow @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( varrow @ A @ B )
= ( varrow @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-arrow') ).
thf(80,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( varrow @ A @ B )
= ( varrow @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( varrow @ A @ B )
= ( varrow @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( visFreeVar @ C @ D )
=> ( valphaEquivalent @ ( vabs @ B @ A @ D ) @ ( vabs @ C @ A @ ( vsubst @ B @ ( vvar @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-subst-abs') ).
thf(505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( visFreeVar @ C @ D )
=> ( valphaEquivalent @ ( vabs @ B @ A @ D ) @ ( vabs @ C @ A @ ( vsubst @ B @ ( vvar @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B
= ( vapp @ A @ E ) )
& ! [F: $i,G: $i,H: $i] :
( A
!= ( vabs @ F @ G @ H ) ) )
=> ( ( ( D
= ( vreduce @ A ) )
& ( visSomeExp @ D ) )
=> ( ( C
= ( vreduce @ B ) )
=> ( C
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce5) ).
thf(438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B
= ( vapp @ A @ E ) )
& ! [F: $i,G: $i,H: $i] :
( A
!= ( vabs @ F @ G @ H ) ) )
=> ( ( ( D
= ( vreduce @ A ) )
& ( visSomeExp @ D ) )
=> ( ( C
= ( vreduce @ B ) )
=> ( C
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A = F )
& ( B = G )
& ( C
= ( vapp @ E @ H ) ) )
=> ( ( D
= ( vsubst @ A @ B @ C ) )
=> ( D
= ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst2) ).
thf(589,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A = F )
& ( B = G )
& ( C
= ( vapp @ E @ H ) ) )
=> ( ( D
= ( vsubst @ A @ B @ C ) )
=> ( D
= ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( ( vsomeExp @ A )
= ( vsomeExp @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vsomeExp @ A )
= ( vsomeExp @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someExp') ).
thf(162,plain,
! [A: $i,B: $i] :
( ( ( ( vsomeExp @ A )
= ( vsomeExp @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( vsomeExp @ A )
= ( vsomeExp @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( vtcheck @ B @ C @ ( varrow @ A @ E ) )
& ( vtcheck @ B @ D @ A ) )
=> ( vtcheck @ B @ ( vapp @ C @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-app') ).
thf(548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( vtcheck @ B @ C @ ( varrow @ A @ E ) )
& ( vtcheck @ B @ D @ A ) )
=> ( vtcheck @ B @ ( vapp @ C @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( vvar @ A )
!= ( vabs @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-abs') ).
thf(510,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( vvar @ A )
!= ( vabs @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = D )
& ( B
= ( vvar @ C ) ) )
=> ( ( ( C = D )
=> ( visFreeVar @ A @ B ) )
& ( ( visFreeVar @ A @ B )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar0) ).
thf(536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = D )
& ( B
= ( vvar @ C ) ) )
=> ( ( ( C = D )
=> ( visFreeVar @ A @ B ) )
& ( ( visFreeVar @ A @ B )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C != A )
& ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
=> ( vtcheck @ ( vbind @ A @ B @ ( vbind @ C @ D @ E ) ) @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C != A )
& ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
=> ( vtcheck @ ( vbind @ A @ B @ ( vbind @ C @ D @ E ) ) @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( valphaEquivalent @ B @ A )
& ( valphaEquivalent @ A @ C ) )
=> ( valphaEquivalent @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-trans') ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( ( valphaEquivalent @ B @ A )
& ( valphaEquivalent @ A @ C ) )
=> ( valphaEquivalent @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( vtcheck @ ( vbind @ B @ D @ A ) @ C @ E )
=> ( vtcheck @ A @ ( vabs @ B @ D @ C ) @ ( varrow @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-abs') ).
thf(422,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( vtcheck @ ( vbind @ B @ D @ A ) @ C @ E )
=> ( vtcheck @ A @ ( vabs @ B @ D @ C ) @ ( varrow @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( vapp @ A @ B ) )
=> ~ ( visValue @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
thf(111,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( vapp @ A @ B ) )
=> ~ ( visValue @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D
= ( vapp @ B @ A ) )
& ! [F: $i,G: $i,H: $i] :
( B
!= ( vabs @ F @ G @ H ) ) )
=> ( ( ( C
= ( vreduce @ B ) )
& ~ ( visSomeExp @ C ) )
=> ( ( E
= ( vreduce @ D ) )
=> ( E = vnoExp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce6) ).
thf(543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D
= ( vapp @ B @ A ) )
& ! [F: $i,G: $i,H: $i] :
( B
!= ( vabs @ F @ G @ H ) ) )
=> ( ( ( C
= ( vreduce @ B ) )
& ~ ( visSomeExp @ C ) )
=> ( ( E
= ( vreduce @ D ) )
=> ( E = vnoExp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B
= ( vapp @ ( vabs @ D @ E @ F ) @ A ) )
=> ( ( ( G
= ( vreduce @ A ) )
& ( visSomeExp @ G ) )
=> ( ( C
= ( vreduce @ B ) )
=> ( C
= ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce2) ).
thf(454,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B
= ( vapp @ ( vabs @ D @ E @ F ) @ A ) )
=> ( ( ( G
= ( vreduce @ A ) )
& ( visSomeExp @ G ) )
=> ( ( C
= ( vreduce @ B ) )
=> ( C
= ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(51407,plain,
$false,
inference(cvc4,[status(thm)],[156,129,76,414,502,450,418,283,459,69,479,518,481,170,115,533,550,174,185,110,157,189,93,152,316,475,179,443,485,106,121,514,293,133,507,312,307,452,117,102,297,424,97,461,554,193,489,161,279,144,498,494,91,80,505,438,589,162,548,510,536,447,183,422,111,543,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM132+1 : TPTP v8.1.2. Released v6.4.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 03:37:36 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.01 % [INFO] Parsing done (168ms).
% 1.58/1.02 % [INFO] Running in sequential loop mode.
% 1.86/1.21 % [INFO] eprover registered as external prover.
% 1.86/1.21 % [INFO] cvc4 registered as external prover.
% 1.86/1.22 % [INFO] Scanning for conjecture ...
% 1.98/1.30 % [INFO] Found a conjecture and 66 axioms. Running axiom selection ...
% 2.39/1.37 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.71/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.71/1.49 % [INFO] Type checking passed.
% 2.71/1.49 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 77.73/19.81 % External prover 'cvc4' found a proof!
% 77.73/19.81 % [INFO] Killing All external provers ...
% 77.73/19.81 % Time passed: 19295ms (effective reasoning time: 18792ms)
% 77.73/19.82 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 77.73/19.82 % Axioms used in derivation (66): EQ-bind, alpha-equiv-subst-abs, T-var, getSomeType0, lookup0, DIFF-noType-someType, reduce3, isSomeType1, isFreeVar0, DIFF-empty-bind, getSomeExp0, subst4, isValue2, isSomeExp0, reduce-INV, T-app, EQ-app, fresh-free-2, EQ-abs, reduce1, subst5, alpha-equiv-trans, DIFF-var-abs, reduce5, lookup1, EQ-someExp, T-abs, fresh-unequal-var-3, reduce4, reduce0, T-Weak, EQ-empty, T-subst-abs-2-gen, T-inv, alpha-equiv-sym, EQ-var, EQ-noExp, isFreeVar2, subst-INV, isValue0, subst1, subst2, isSomeType0, alpha-equiv-typing, T-Context-Duplicate, T-Weak-FreeVar, subst3, EQ-noType, isValue1, DIFF-abs-app, EQ-someType, EQ-arrow, isFreeVar1, gensym-is-fresh, reduce2, isSomeExp1, DIFF-var-app, reduce6, alpha-equiv-refl, alpha-equiv-FreeVar, subst0, lookup2, DIFF-noExp-someExp, lookup-INV, T-Strong, T-Context-Swap
% 77.73/19.82 % No. of inferences in proof: 136
% 77.73/19.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19295 ms resp. 18792 ms w/o parsing
% 77.80/19.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.80/19.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------